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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/AVL-tree/00-META.yaml Normal file
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---
category:
- Data Structures
from: http://rosettacode.org/wiki/AVL_tree

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Task/AVL-tree/00-TASK.txt Normal file
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<br>
In computer science, an '''AVL tree''' is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log ''n'') time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with [[Red_black_trees|red-black trees]] because they support the same set of operations and because red-black trees also take O(log ''n'') time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
;Task:
Implement an AVL tree in the language of choice, and provide at least basic operations.
<br><br>
;Related task
[[Red_black_tree_sort]]
<br><br>

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Task/AVL-tree/AArch64-Assembly/avl-tree.aarch64 Normal file
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/* ARM assembly AARCH64 Raspberry PI 3B */
/* program avltree64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
.equ NBVAL, 12
/*******************************************/
/* Structures */
/********************************************/
/* structure tree */
.struct 0
tree_root: // root pointer (or node right)
.struct tree_root + 8
tree_size: // number of element of tree
.struct tree_size + 8
tree_suite:
.struct tree_suite + 24 // for alignement to node
tree_fin:
/* structure node tree */
.struct 0
node_right: // right pointer
.struct node_right + 8
node_left: // left pointer
.struct node_left + 8
node_value: // element value
.struct node_value + 8
node_height: // element value
.struct node_height + 8
node_parent: // element value
.struct node_parent + 8
node_fin:
/*******************************************/
/* Initialized data */
/*******************************************/
.data
szMessPreOrder: .asciz "PreOrder :\n"
szCarriageReturn: .asciz "\n"
/* datas error display */
szMessErreur: .asciz "Error detected.\n"
szMessKeyDbl: .asciz "Key exists in tree.\n"
szMessInsInv: .asciz "Insertion in inverse order.\n"
/* datas message display */
szMessResult: .asciz "Ele: @ G: @ D: @ val @ h @ \npere @\n"
/*******************************************/
/* UnInitialized data */
/*******************************************/
.bss
sZoneConv: .skip 24
stTree: .skip tree_fin // place to structure tree
stTree1: .skip tree_fin // place to structure tree
/*******************************************/
/* code section */
/*******************************************/
.text
.global main
main:
mov x20,#1 // node tree value
1: // loop insertion in order
ldr x0,qAdrstTree // structure tree address
mov x1,x20
bl insertElement // add element value x1
cmp x0,-1
beq 99f
add x20,x20,1 // increment value
cmp x20,NBVAL // end ?
ble 1b // no -> loop
ldr x0,qAdrstTree // structure tree address
mov x1,11 // verif key dobble
bl insertElement // add element value x1
cmp x0,-1
bne 2f
ldr x0,qAdrszMessErreur
bl affichageMess
2:
ldr x0,qAdrszMessPreOrder // load verification
bl affichageMess
ldr x3,qAdrstTree // tree root address (begin structure)
ldr x0,[x3,tree_root]
ldr x1,qAdrdisplayElement // function to execute
bl preOrder
ldr x0,qAdrszMessInsInv
bl affichageMess
mov x20,NBVAL // node tree value
3: // loop insertion inverse order
ldr x0,qAdrstTree1 // structure tree address
mov x1,x20
bl insertElement // add element value x1
cmp x0,-1
beq 99f
sub x20,x20,1 // increment value
cmp x20,0 // end ?
bgt 3b // no -> loop
ldr x0,qAdrszMessPreOrder // load verification
bl affichageMess
ldr x3,qAdrstTree1 // tree root address (begin structure)
ldr x0,[x3,tree_root]
ldr x1,qAdrdisplayElement // function to execute
bl preOrder
// search value
ldr x0,qAdrstTree1 // tree root address (begin structure)
mov x1,11 // value to search
bl searchTree
cmp x0,-1
beq 100f
mov x2,x0
ldr x0,qAdrszMessKeyDbl // key exists
bl affichageMess
// suppresssion previous value
mov x0,x2
ldr x1,qAdrstTree1
bl supprimer
ldr x0,qAdrszMessPreOrder // verification
bl affichageMess
ldr x3,qAdrstTree1 // tree root address (begin structure)
ldr x0,[x3,tree_root]
ldr x1,qAdrdisplayElement // function to execute
bl preOrder
b 100f
99: // display error
ldr x0,qAdrszMessErreur
bl affichageMess
100: // standard end of the program
mov x8, #EXIT // request to exit program
svc 0 // perform system call
qAdrszMessPreOrder: .quad szMessPreOrder
qAdrszMessErreur: .quad szMessErreur
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrstTree: .quad stTree
qAdrstTree1: .quad stTree1
qAdrdisplayElement: .quad displayElement
qAdrszMessInsInv: .quad szMessInsInv
/******************************************************************/
/* insert element in the tree */
/******************************************************************/
/* x0 contains the address of the tree structure */
/* x1 contains the value of element */
/* x0 returns address of element or - 1 if error */
insertElement: // INFO: insertElement
stp x1,lr,[sp,-16]! // save registers
mov x6,x0 // save head
mov x0,#node_fin // reservation place one element
bl allocHeap
cmp x0,#-1 // allocation error
beq 100f
mov x5,x0
str x1,[x5,#node_value] // store value in address heap
mov x3,#0
str x3,[x5,#node_left] // init left pointer with zero
str x3,[x5,#node_right] // init right pointer with zero
str x3,[x5,#node_height] // init balance with zero
ldr x2,[x6,#tree_size] // load tree size
cmp x2,#0 // 0 element ?
bne 1f
str x5,[x6,#tree_root] // yes -> store in root
b 4f
1: // else search free address in tree
ldr x3,[x6,#tree_root] // start with address root
2: // begin loop to insertion
ldr x4,[x3,#node_value] // load key
cmp x1,x4
beq 6f // key equal
blt 3f // key <
// key > insertion right
ldr x8,[x3,#node_right] // node empty ?
cmp x8,#0
csel x3,x8,x3,ne // current = right node if not
//movne x3,x8 // no -> next node
bne 2b // and loop
str x5,[x3,#node_right] // store node address in right pointer
b 4f
3: // left
ldr x8,[x3,#node_left] // left pointer empty ?
cmp x8,#0
csel x3,x8,x3,ne // current = left node if not
//movne x3,x8 //
bne 2b // no -> loop
str x5,[x3,#node_left] // store node address in left pointer
4:
str x3,[x5,#node_parent] // store parent
mov x4,#1
str x4,[x5,#node_height] // store height = 1
mov x0,x5 // begin node to requilbrate
mov x1,x6 // head address
bl equilibrer
5:
add x2,x2,#1 // increment tree size
str x2,[x6,#tree_size]
mov x0,#0
b 100f
6: // key equal ?
ldr x0,qAdrszMessKeyDbl
bl affichageMess
mov x0,#-1
b 100f
100:
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
qAdrszMessKeyDbl: .quad szMessKeyDbl
/******************************************************************/
/* equilibrer after insertion */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 contains the address of head */
equilibrer: // INFO: equilibrer
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
mov x3,#0 // balance factor
1: // begin loop
ldr x5,[x0,#node_parent] // load father
cmp x5,#0 // end ?
beq 8f
cmp x3,#2 // right tree too long
beq 8f
cmp x3,#-2 // left tree too long
beq 8f
mov x6,x0 // s = current
ldr x0,[x6,#node_parent] // current = father
ldr x7,[x0,#node_left]
mov x4,#0
cmp x7,#0
beq 2f
ldr x4,[x7,#node_height] // height left tree
2:
ldr x7,[x0,#node_right]
mov x2,#0
cmp x7,#0
beq 3f
ldr x2,[x7,#node_height] // height right tree
3:
cmp x4,x2
ble 4f
add x4,x4,#1
str x4,[x0,#node_height]
b 5f
4:
add x2,x2,#1
str x2,[x0,#node_height]
5:
ldr x7,[x0,#node_right]
mov x4,0
cmp x7,#0
beq 6f
ldr x4,[x7,#node_height]
6:
ldr x7,[x0,#node_left]
mov x2,0
cmp x7,#0
beq 7f
ldr x2,[x7,#node_height]
7:
sub x3,x4,x2 // compute balance factor
b 1b
8:
cmp x3,#2
beq 9f
cmp x3,#-2
beq 9f
b 100f
9:
mov x3,x1
mov x4,x0
mov x1,x6
bl equiUnSommet
// change head address ?
ldr x2,[x3,#tree_root]
cmp x2,x4
bne 100f
str x6,[x3,#tree_root]
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* equilibre 1 sommet */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 contains the address of the node */
equiUnSommet: // INFO: equiUnSommet
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
mov x5,x0 // save p
mov x6,x1 // s
ldr x2,[x5,#node_left]
cmp x2,x6
bne 6f
ldr x7,[x5,#node_right]
mov x4,#0
cmp x7,#0
beq 1f
ldr x4,[x7,#node_height]
1:
ldr x7,[x5,#node_left]
mov x2,0
cmp x7,#0
beq 2f
ldr x2,[x7,#node_height]
2:
sub x3,x4,x2
cmp x3,#-2
bne 100f
ldr x7,[x6,#node_right]
mov x4,0
cmp x7,#0
beq 3f
ldr x4,[x7,#node_height]
3:
ldr x7,[x6,#node_left]
mov x2,0
cmp x7,#0
beq 4f
ldr x2,[x7,#node_height]
4:
sub x3,x4,x2
cmp x3,#1
bge 5f
mov x0,x5
bl rotRight
b 100f
5:
mov x0,x6
bl rotLeft
mov x0,x5
bl rotRight
b 100f
6:
ldr x7,[x5,#node_right]
mov x4,0
cmp x7,#0
beq 7f
ldr x4,[x7,#node_height]
7:
ldr x7,[x5,#node_left]
mov x2,0
cmp x7,#0
beq 8f
ldr x2,[x7,#node_height]
8:
sub x3,x4,x2
cmp x3,2
bne 100f
ldr x7,[x6,#node_right]
mov x4,0
cmp x7,#0
beq 9f
ldr x4,[x7,#node_height]
9:
ldr x7,[x6,#node_left]
mov x2,0
cmp x7,#0
beq 10f
ldr x2,[x7,#node_height]
10:
sub x3,x4,x2
cmp x3,#-1
ble 11f
mov x0,x5
bl rotLeft
b 100f
11:
mov x0,x6
bl rotRight
mov x0,x5
bl rotLeft
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* right rotation */
/******************************************************************/
/* x0 contains the address of the node */
rotRight: // INFO: rotRight
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
// x2 x2
// x0 x1
// x1 x0
// x3 x3
ldr x1,[x0,#node_left] // load left children
ldr x2,[x0,#node_parent] // load father
cmp x2,#0 // no father ???
beq 2f
ldr x3,[x2,#node_left] // load left node father
cmp x3,x0 // equal current node ?
bne 1f
str x1,[x2,#node_left] // yes store left children
b 2f
1:
str x1,[x2,#node_right] // no store right
2:
str x2,[x1,#node_parent] // change parent
str x1,[x0,#node_parent]
ldr x3,[x1,#node_right]
str x3,[x0,#node_left]
cmp x3,#0
beq 3f
str x0,[x3,#node_parent] // change parent node left
3:
str x0,[x1,#node_right]
ldr x3,[x0,#node_left] // compute newbalance factor
mov x4,0
cmp x3,#0
beq 4f
ldr x4,[x3,#node_height]
4:
ldr x3,[x0,#node_right]
mov x5,0
cmp x3,#0
beq 5f
ldr x5,[x3,#node_height]
5:
cmp x4,x5
ble 6f
add x4,x4,#1
str x4,[x0,#node_height]
b 7f
6:
add x5,x5,#1
str x5,[x0,#node_height]
7:
//
ldr x3,[x1,#node_left] // compute new balance factor
mov x4,0
cmp x3,#0
beq 8f
ldr x4,[x3,#node_height]
8:
ldr x3,[x1,#node_right]
mov x5,0
cmp x3,#0
beq 9f
ldr x5,[x3,#node_height]
9:
cmp x4,x5
ble 10f
add x4,x4,#1
str x4,[x1,#node_height]
b 100f
10:
add x5,x5,#1
str x5,[x1,#node_height]
100:
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* left rotation */
/******************************************************************/
/* x0 contains the address of the node sommet */
rotLeft: // INFO: rotLeft
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
// x2 x2
// x0 x1
// x1 x0
// x3 x3
ldr x1,[x0,#node_right] // load right children
ldr x2,[x0,#node_parent] // load father (racine)
cmp x2,#0 // no father ???
beq 2f
ldr x3,[x2,#node_left] // load left node father
cmp x3,x0 // equal current node ?
bne 1f
str x1,[x2,#node_left] // yes store left children
b 2f
1:
str x1,[x2,#node_right] // no store to right
2:
str x2,[x1,#node_parent] // change parent of right children
str x1,[x0,#node_parent] // change parent of sommet
ldr x3,[x1,#node_left] // left children
str x3,[x0,#node_right] // left children pivot exists ?
cmp x3,#0
beq 3f
str x0,[x3,#node_parent] // yes store in
3:
str x0,[x1,#node_left]
//
ldr x3,[x0,#node_left] // compute new height for old summit
mov x4,0
cmp x3,#0
beq 4f
ldr x4,[x3,#node_height] // left height
4:
ldr x3,[x0,#node_right]
mov x5,0
cmp x3,#0
beq 5f
ldr x5,[x3,#node_height] // right height
5:
cmp x4,x5
ble 6f
add x4,x4,#1
str x4,[x0,#node_height] // if right > left
b 7f
6:
add x5,x5,#1
str x5,[x0,#node_height] // if left > right
7:
//
ldr x3,[x1,#node_left] // compute new height for new
mov x4,0
cmp x3,#0
beq 8f
ldr x4,[x3,#node_height]
8:
ldr x3,[x1,#node_right]
mov x5,0
cmp x3,#0
beq 9f
ldr x5,[x3,#node_height]
9:
cmp x4,x5
ble 10f
add x4,x4,#1
str x4,[x1,#node_height]
b 100f
10:
add x5,x5,#1
str x5,[x1,#node_height]
100:
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* search value in tree */
/******************************************************************/
/* x0 contains the address of structure of tree */
/* x1 contains the value to search */
searchTree: // INFO: searchTree
stp x2,lr,[sp,-16]! // save registers
stp x3,x4,[sp,-16]! // save registers
ldr x2,[x0,#tree_root]
1: // begin loop
ldr x4,[x2,#node_value] // load key
cmp x1,x4
beq 3f // key equal
blt 2f // key <
// key > insertion right
ldr x3,[x2,#node_right] // node empty ?
cmp x3,#0
csel x2,x3,x2,ne
//movne x2,x3 // no -> next node
bne 1b // and loop
mov x0,#-1 // not find
b 100f
2: // left
ldr x3,[x2,#node_left] // left pointer empty ?
cmp x3,#0
csel x2,x3,x2,ne
bne 1b // no -> loop
mov x0,#-1 // not find
b 100f
3:
mov x0,x2 // return node address
100:
ldp x3,x4,[sp],16 // restaur 2 registers
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* suppression node */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 contains structure tree address */
supprimer: // INFO: supprimer
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
ldr x1,[x0,#node_left]
cmp x1,#0
bne 5f
ldr x1,[x0,#node_right]
cmp x1,#0
bne 5f
// is a leaf
mov x4,#0
ldr x3,[x0,#node_parent] // father
cmp x3,#0
bne 11f
str x4,[x1,#tree_root]
b 100f
11:
ldr x1,[x3,#node_left]
cmp x1,x0
bne 2f
str x4,[x3,#node_left] // suppression left children
ldr x5,[x3,#node_right]
mov x6,#0
cmp x5,#0
beq 12f
ldr x6,[x5,#node_height]
12:
add x6,x6,#1
str x6,[x3,#node_height]
b 3f
2: // suppression right children
str x4,[x3,#node_right]
ldr x5,[x3,#node_left]
mov x6,#0
cmp x5,#0
beq 21f
ldr x6,[x5,#node_height]
21:
add x6,x6,#1
str x6,[x3,#node_height]
3: // new balance
mov x0,x3
bl equilibrerSupp
b 100f
5: // is not à leaf
ldr x7,[x0,#node_right]
cmp x7,#0
beq 7f
mov x2,x0
mov x0,x7
6:
ldr x6,[x0,#node_left] // search the litle element
cmp x6,#0
beq 9f
mov x0,x6
b 6b
7:
ldr x7,[x0,#node_left]
cmp x7,#0
beq 9f
mov x2,x0
mov x0,x7
8:
ldr x6,[x0,#node_right] // search the great element
cmp x6,#0
beq 9f
mov x0,x6
b 8b
9:
ldr x5,[x0,#node_value] // copy value
str x5,[x2,#node_value]
bl supprimer // suppression node x0
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* equilibrer after suppression */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 contains the address of head */
equilibrerSupp: // INFO: equilibrerSupp
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
stp x6,x7,[sp,-16]! // save registers
mov x3,#1 // balance factor
ldr x2,[x1,#tree_root]
1:
ldr x5,[x0,#node_parent] // load father
cmp x5,#0 // no father
beq 100f
cmp x3,#0 // balance equilibred
beq 100f
mov x6,x0 // save entry node
ldr x0,[x6,#node_parent] // current = father
ldr x7,[x0,#node_left]
mov x4,#0
cmp x7,#0
b 11f
ldr x4,[x7,#node_height] // height left tree
11:
ldr x7,[x0,#node_right]
mov x5,#0
cmp x7,#0
beq 12f
ldr x5,[x7,#node_height] // height right tree
12:
cmp x4,x5
ble 13f
add x4,x4,1
str x4,[x0,#node_height]
b 14f
13:
add x5,x5,1
str x5,[x0,#node_height]
14:
ldr x7,[x0,#node_right]
mov x4,#0
cmp x7,#0
beq 15f
ldr x4,[x7,#node_height]
15:
ldr x7,[x0,#node_left]
mov x5,0
cmp x7,#0
beq 16f
ldr x5,[x7,#node_height]
16:
sub x3,x4,x5 // compute balance factor
mov x2,x1
mov x7,x0 // save current
mov x1,x6
bl equiUnSommet
// change head address ?
cmp x2,x7
bne 17f
str x6,[x3,#tree_root]
17:
mov x0,x7 // restaur current
b 1b
100:
ldp x6,x7,[sp],16 // restaur 2 registers
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* preOrder */
/******************************************************************/
/* x0 contains the address of the node */
/* x1 function address */
preOrder: // INFO: preOrder
stp x2,lr,[sp,-16]! // save registers
cmp x0,#0
beq 100f
mov x2,x0
blr x1 // call function
ldr x0,[x2,#node_left]
bl preOrder
ldr x0,[x2,#node_right]
bl preOrder
100:
ldp x2,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/******************************************************************/
/* display node */
/******************************************************************/
/* x0 contains node address */
displayElement: // INFO: displayElement
stp x1,lr,[sp,-16]! // save registers
stp x2,x3,[sp,-16]! // save registers
stp x4,x5,[sp,-16]! // save registers
mov x2,x0
ldr x1,qAdrsZoneConv
bl conversion16
//strb wzr,[x1,x0]
ldr x0,qAdrszMessResult
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_left]
ldr x1,qAdrsZoneConv
bl conversion16
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_right]
ldr x1,qAdrsZoneConv
bl conversion16
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_value]
ldr x1,qAdrsZoneConv
bl conversion10
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_height]
ldr x1,qAdrsZoneConv
bl conversion10
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,#node_parent]
ldr x1,qAdrsZoneConv
bl conversion16
//strb wzr,[x1,x0]
mov x0,x3
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc
bl affichageMess
100:
ldp x4,x5,[sp],16 // restaur 2 registers
ldp x2,x3,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
qAdrszMessResult: .quad szMessResult
qAdrsZoneConv: .quad sZoneConv
/******************************************************************/
/* memory allocation on the heap */
/******************************************************************/
/* x0 contains the size to allocate */
/* x0 returns address of memory heap or - 1 if error */
/* CAUTION : The size of the allowance must be a multiple of 4 */
allocHeap:
stp x1,lr,[sp,-16]! // save registers
stp x2,x8,[sp,-16]! // save registers
// allocation
mov x1,x0 // save size
mov x0,0 // read address start heap
mov x8,BRK // call system 'brk'
svc 0
mov x2,x0 // save address heap for return
add x0,x0,x1 // reservation place for size
mov x8,BRK // call system 'brk'
svc 0
cmp x0,-1 // allocation error
beq 100f
mov x0,x2 // return address memory heap
100:
ldp x2,x8,[sp],16 // restaur 2 registers
ldp x1,lr,[sp],16 // restaur 2 registers
ret // return to address lr x30
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"

764
Task/AVL-tree/ARM-Assembly/avl-tree.arm Normal file
View file

@ -0,0 +1,764 @@
/* ARM assembly Raspberry PI */
/* program avltree2.s */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/*******************************************/
/* Constantes */
/*******************************************/
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
.equ BRK, 0x2d @ Linux syscall
.equ CHARPOS, '@'
.equ NBVAL, 12
/*******************************************/
/* Structures */
/********************************************/
/* structure tree */
.struct 0
tree_root: @ root pointer (or node right)
.struct tree_root + 4
tree_size: @ number of element of tree
.struct tree_size + 4
tree_suite:
.struct tree_suite + 12 @ for alignement to node
tree_fin:
/* structure node tree */
.struct 0
node_right: @ right pointer
.struct node_right + 4
node_left: @ left pointer
.struct node_left + 4
node_value: @ element value
.struct node_value + 4
node_height: @ element value
.struct node_height + 4
node_parent: @ element value
.struct node_parent + 4
node_fin:
/* structure queue*/
.struct 0
queue_begin: @ next pointer
.struct queue_begin + 4
queue_end: @ element value
.struct queue_end + 4
queue_fin:
/* structure node queue */
.struct 0
queue_node_next: @ next pointer
.struct queue_node_next + 4
queue_node_value: @ element value
.struct queue_node_value + 4
queue_node_fin:
/*******************************************/
/* Initialized data */
/*******************************************/
.data
szMessPreOrder: .asciz "PreOrder :\n"
szCarriageReturn: .asciz "\n"
/* datas error display */
szMessErreur: .asciz "Error detected.\n"
szMessKeyDbl: .asciz "Key exists in tree.\n"
szMessInsInv: .asciz "Insertion in inverse order.\n"
/* datas message display */
szMessResult: .asciz "Ele: @ G: @ D: @ val @ h @ pere @\n"
sValue: .space 12,' '
.asciz "\n"
/*******************************************/
/* UnInitialized data */
/*******************************************/
.bss
sZoneConv: .skip 24
stTree: .skip tree_fin @ place to structure tree
stTree1: .skip tree_fin @ place to structure tree
stQueue: .skip queue_fin @ place to structure queue
/*******************************************/
/* code section */
/*******************************************/
.text
.global main
main:
mov r8,#1 @ node tree value
1: @ loop insertion in order
ldr r0,iAdrstTree @ structure tree address
mov r1,r8
bl insertElement @ add element value r1
cmp r0,#-1
beq 99f
//ldr r3,iAdrstTree @ tree root address (begin structure)
//ldr r0,[r3,#tree_root]
//ldr r1,iAdrdisplayElement @ function to execute
//bl preOrder
add r8,#1 @ increment value
cmp r8,#NBVAL @ end ?
ble 1b @ no -> loop
ldr r0,iAdrstTree @ structure tree address
mov r1,#11 @ verif key dobble
bl insertElement @ add element value r1
cmp r0,#-1
bne 2f
ldr r0,iAdrszMessErreur
bl affichageMess
2:
ldr r0,iAdrszMessPreOrder @ load verification
bl affichageMess
ldr r3,iAdrstTree @ tree root address (begin structure)
ldr r0,[r3,#tree_root]
ldr r1,iAdrdisplayElement @ function to execute
bl preOrder
ldr r0,iAdrszMessInsInv
bl affichageMess
mov r8,#NBVAL @ node tree value
3: @ loop insertion inverse order
ldr r0,iAdrstTree1 @ structure tree address
mov r1,r8
bl insertElement @ add element value r1
cmp r0,#-1
beq 99f
sub r8,#1 @ increment value
cmp r8,#0 @ end ?
bgt 3b @ no -> loop
ldr r0,iAdrszMessPreOrder @ load verification
bl affichageMess
ldr r3,iAdrstTree1 @ tree root address (begin structure)
ldr r0,[r3,#tree_root]
ldr r1,iAdrdisplayElement @ function to execute
bl preOrder
@ search value
ldr r0,iAdrstTree1 @ tree root address (begin structure)
mov r1,#11 @ value to search
bl searchTree
cmp r0,#-1
beq 100f
mov r2,r0
ldr r0,iAdrszMessKeyDbl @ key exists
bl affichageMess
@ suppresssion previous value
mov r0,r2
ldr r1,iAdrstTree1
bl supprimer
ldr r0,iAdrszMessPreOrder @ verification
bl affichageMess
ldr r3,iAdrstTree1 @ tree root address (begin structure)
ldr r0,[r3,#tree_root]
ldr r1,iAdrdisplayElement @ function to execute
bl preOrder
b 100f
99: @ display error
ldr r0,iAdrszMessErreur
bl affichageMess
100: @ standard end of the program
mov r7, #EXIT @ request to exit program
svc 0 @ perform system call
iAdrszMessPreOrder: .int szMessPreOrder
iAdrszMessErreur: .int szMessErreur
iAdrszCarriageReturn: .int szCarriageReturn
iAdrstTree: .int stTree
iAdrstTree1: .int stTree1
iAdrstQueue: .int stQueue
iAdrdisplayElement: .int displayElement
iAdrszMessInsInv: .int szMessInsInv
/******************************************************************/
/* insert element in the tree */
/******************************************************************/
/* r0 contains the address of the tree structure */
/* r1 contains the value of element */
/* r0 returns address of element or - 1 if error */
insertElement: @ INFO: insertElement
push {r1-r8,lr} @ save registers
mov r7,r0 @ save head
mov r0,#node_fin @ reservation place one element
bl allocHeap
cmp r0,#-1 @ allocation error
beq 100f
mov r5,r0
str r1,[r5,#node_value] @ store value in address heap
mov r3,#0
str r3,[r5,#node_left] @ init left pointer with zero
str r3,[r5,#node_right] @ init right pointer with zero
str r3,[r5,#node_height] @ init balance with zero
ldr r2,[r7,#tree_size] @ load tree size
cmp r2,#0 @ 0 element ?
bne 1f
str r5,[r7,#tree_root] @ yes -> store in root
b 4f
1: @ else search free address in tree
ldr r3,[r7,#tree_root] @ start with address root
2: @ begin loop to insertion
ldr r4,[r3,#node_value] @ load key
cmp r1,r4
beq 6f @ key equal
blt 3f @ key <
@ key > insertion right
ldr r8,[r3,#node_right] @ node empty ?
cmp r8,#0
movne r3,r8 @ no -> next node
bne 2b @ and loop
str r5,[r3,#node_right] @ store node address in right pointer
b 4f
3: @ left
ldr r8,[r3,#node_left] @ left pointer empty ?
cmp r8,#0
movne r3,r8 @
bne 2b @ no -> loop
str r5,[r3,#node_left] @ store node address in left pointer
4:
str r3,[r5,#node_parent] @ store parent
mov r4,#1
str r4,[r5,#node_height] @ store height = 1
mov r0,r5 @ begin node to requilbrate
mov r1,r7 @ head address
bl equilibrer
5:
add r2,#1 @ increment tree size
str r2,[r7,#tree_size]
mov r0,#0
b 100f
6: @ key equal ?
ldr r0,iAdrszMessKeyDbl
bl affichageMess
mov r0,#-1
b 100f
100:
pop {r1-r8,lr} @ restaur registers
bx lr @ return
iAdrszMessKeyDbl: .int szMessKeyDbl
/******************************************************************/
/* equilibrer after insertion */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 contains the address of head */
equilibrer: @ INFO: equilibrer
push {r1-r8,lr} @ save registers
mov r3,#0 @ balance factor
1: @ begin loop
ldr r5,[r0,#node_parent] @ load father
cmp r5,#0 @ end ?
beq 5f
cmp r3,#2 @ right tree too long
beq 5f
cmp r3,#-2 @ left tree too long
beq 5f
mov r6,r0 @ s = current
ldr r0,[r6,#node_parent] @ current = father
ldr r7,[r0,#node_left]
cmp r7,#0
ldrne r8,[r7,#node_height] @ height left tree
moveq r8,#0
ldr r7,[r0,#node_right]
cmp r7,#0
ldrne r9,[r7,#node_height] @ height right tree
moveq r9,#0
cmp r8,r9
addgt r8,#1
strgt r8,[r0,#node_height]
addle r9,#1
strle r9,[r0,#node_height]
//
ldr r7,[r0,#node_right]
cmp r7,#0
ldrne r8,[r7,#node_height]
moveq r8,#0
ldr r7,[r0,#node_left]
cmp r7,#0
ldrne r9,[r7,#node_height]
moveq r9,#0
sub r3,r8,r9 @ compute balance factor
b 1b
5:
cmp r3,#2
beq 6f
cmp r3,#-2
beq 6f
b 100f
6:
mov r3,r1
mov r4,r0
mov r1,r6
bl equiUnSommet
@ change head address ?
ldr r2,[r3,#tree_root]
cmp r2,r4
streq r6,[r3,#tree_root]
100:
pop {r1-r8,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* equilibre 1 sommet */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 contains the address of the node */
equiUnSommet: @ INFO: equiUnSommet
push {r1-r9,lr} @ save registers
mov r5,r0 @ save p
mov r6,r1 // s
ldr r2,[r5,#node_left]
cmp r2,r6
bne 5f
ldr r7,[r5,#node_right]
cmp r7,#0
moveq r8,#0
ldrne r8,[r7,#node_height]
ldr r7,[r5,#node_left]
cmp r7,#0
moveq r9,#0
ldrne r9,[r7,#node_height]
sub r3,r8,r9
cmp r3,#-2
bne 100f
ldr r7,[r6,#node_right]
cmp r7,#0
moveq r8,#0
ldrne r8,[r7,#node_height]
ldr r7,[r6,#node_left]
cmp r7,#0
moveq r9,#0
ldrne r9,[r7,#node_height]
sub r3,r8,r9
cmp r3,#1
bge 2f
mov r0,r5
bl rotRight
b 100f
2:
mov r0,r6
bl rotLeft
mov r0,r5
bl rotRight
b 100f
5:
ldr r7,[r5,#node_right]
cmp r7,#0
moveq r8,#0
ldrne r8,[r7,#node_height]
ldr r7,[r5,#node_left]
cmp r7,#0
moveq r9,#0
ldrne r9,[r7,#node_height]
sub r3,r8,r9
cmp r3,#2
bne 100f
ldr r7,[r6,#node_right]
cmp r7,#0
moveq r8,#0
ldrne r8,[r7,#node_height]
ldr r7,[r6,#node_left]
cmp r7,#0
moveq r9,#0
ldrne r9,[r7,#node_height]
sub r3,r8,r9
cmp r3,#-1
ble 2f
mov r0,r5
bl rotLeft
b 100f
2:
mov r0,r6
bl rotRight
mov r0,r5
bl rotLeft
b 100f
100:
pop {r1-r9,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* right rotation */
/******************************************************************/
/* r0 contains the address of the node */
rotRight: @ INFO: rotRight
push {r1-r5,lr} @ save registers
// r2 r2
// r0 r1
// r1 r0
// r3 r3
ldr r1,[r0,#node_left] @ load left children
ldr r2,[r0,#node_parent] @ load father
cmp r2,#0 @ no father ???
beq 2f
ldr r3,[r2,#node_left] @ load left node father
cmp r3,r0 @ equal current node ?
streq r1,[r2,#node_left] @ yes store left children
strne r1,[r2,#node_right] @ no store right
2:
str r2,[r1,#node_parent] @ change parent
str r1,[r0,#node_parent]
ldr r3,[r1,#node_right]
str r3,[r0,#node_left]
cmp r3,#0
strne r0,[r3,#node_parent] @ change parent node left
str r0,[r1,#node_right]
ldr r3,[r0,#node_left] @ compute newbalance factor
cmp r3,#0
moveq r4,#0
ldrne r4,[r3,#node_height]
ldr r3,[r0,#node_right]
cmp r3,#0
moveq r5,#0
ldrne r5,[r3,#node_height]
cmp r4,r5
addgt r4,#1
strgt r4,[r0,#node_height]
addle r5,#1
strle r5,[r0,#node_height]
//
ldr r3,[r1,#node_left] @ compute new balance factor
cmp r3,#0
moveq r4,#0
ldrne r4,[r3,#node_height]
ldr r3,[r1,#node_right]
cmp r3,#0
moveq r5,#0
ldrne r5,[r3,#node_height]
cmp r4,r5
addgt r4,#1
strgt r4,[r1,#node_height]
addle r5,#1
strle r5,[r1,#node_height]
100:
pop {r1-r5,lr} @ restaur registers
bx lr
/******************************************************************/
/* left rotation */
/******************************************************************/
/* r0 contains the address of the node sommet */
rotLeft: @ INFO: rotLeft
push {r1-r5,lr} @ save registers
// r2 r2
// r0 r1
// r1 r0
// r3 r3
ldr r1,[r0,#node_right] @ load right children
ldr r2,[r0,#node_parent] @ load father (racine)
cmp r2,#0 @ no father ???
beq 2f
ldr r3,[r2,#node_left] @ load left node father
cmp r3,r0 @ equal current node ?
streq r1,[r2,#node_left] @ yes store left children
strne r1,[r2,#node_right] @ no store to right
2:
str r2,[r1,#node_parent] @ change parent of right children
str r1,[r0,#node_parent] @ change parent of sommet
ldr r3,[r1,#node_left] @ left children
str r3,[r0,#node_right] @ left children pivot exists ?
cmp r3,#0
strne r0,[r3,#node_parent] @ yes store in
str r0,[r1,#node_left]
//
ldr r3,[r0,#node_left] @ compute new height for old summit
cmp r3,#0
moveq r4,#0
ldrne r4,[r3,#node_height] @ left height
ldr r3,[r0,#node_right]
cmp r3,#0
moveq r5,#0
ldrne r5,[r3,#node_height] @ right height
cmp r4,r5
addgt r4,#1
strgt r4,[r0,#node_height] @ if right > left
addle r5,#1
strle r5,[r0,#node_height] @ if left > right
//
ldr r3,[r1,#node_left] @ compute new height for new
cmp r3,#0
moveq r4,#0
ldrne r4,[r3,#node_height]
ldr r3,[r1,#node_right]
cmp r3,#0
moveq r5,#0
ldrne r5,[r3,#node_height]
cmp r4,r5
addgt r4,#1
strgt r4,[r1,#node_height]
addle r5,#1
strle r5,[r1,#node_height]
100:
pop {r1-r5,lr} @ restaur registers
bx lr
/******************************************************************/
/* search value in tree */
/******************************************************************/
/* r0 contains the address of structure of tree */
/* r1 contains the value to search */
searchTree: @ INFO: searchTree
push {r1-r4,lr} @ save registers
ldr r2,[r0,#tree_root]
1: @ begin loop
ldr r4,[r2,#node_value] @ load key
cmp r1,r4
beq 3f @ key equal
blt 2f @ key <
@ key > insertion right
ldr r3,[r2,#node_right] @ node empty ?
cmp r3,#0
movne r2,r3 @ no -> next node
bne 1b @ and loop
mov r0,#-1 @ not find
b 100f
2: @ left
ldr r3,[r2,#node_left] @ left pointer empty ?
cmp r3,#0
movne r2,r3 @
bne 1b @ no -> loop
mov r0,#-1 @ not find
b 100f
3:
mov r0,r2 @ return node address
100:
pop {r1-r4,lr} @ restaur registers
bx lr
/******************************************************************/
/* suppression node */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 contains structure tree address */
supprimer: @ INFO: supprimer
push {r1-r8,lr} @ save registers
ldr r1,[r0,#node_left]
cmp r1,#0
bne 5f
ldr r1,[r0,#node_right]
cmp r1,#0
bne 5f
@ is a leaf
mov r4,#0
ldr r3,[r0,#node_parent] @ father
cmp r3,#0
streq r4,[r1,#tree_root]
beq 100f
ldr r1,[r3,#node_left]
cmp r1,r0
bne 2f
str r4,[r3,#node_left] @ suppression left children
ldr r5,[r3,#node_right]
cmp r5,#0
moveq r6,#0
ldrne r6,[r5,#node_height]
add r6,#1
str r6,[r3,#node_height]
b 3f
2: @ suppression right children
str r4,[r3,#node_right]
ldr r5,[r3,#node_left]
cmp r5,#0
moveq r6,#0
ldrne r6,[r5,#node_height]
add r6,#1
str r6,[r3,#node_height]
3: @ new balance
mov r0,r3
bl equilibrerSupp
b 100f
5: @ is not à leaf
ldr r7,[r0,#node_right]
cmp r7,#0
beq 7f
mov r8,r0
mov r0,r7
6:
ldr r6,[r0,#node_left]
cmp r6,#0
movne r0,r6
bne 6b
b 9f
7:
ldr r7,[r0,#node_left] @ search the litle element
cmp r7,#0
beq 9f
mov r8,r0
mov r0,r7
8:
ldr r6,[r0,#node_right] @ search the great element
cmp r6,#0
movne r0,r6
bne 8b
9:
ldr r5,[r0,#node_value] @ copy value
str r5,[r8,#node_value]
bl supprimer @ suppression node r0
100:
pop {r1-r8,lr} @ restaur registers
bx lr
/******************************************************************/
/* equilibrer after suppression */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 contains the address of head */
equilibrerSupp: @ INFO: equilibrerSupp
push {r1-r8,lr} @ save registers
mov r3,#1 @ balance factor
ldr r2,[r1,#tree_root]
1:
ldr r5,[r0,#node_parent] @ load father
cmp r5,#0 @ no father
beq 100f
cmp r3,#0 @ balance equilibred
beq 100f
mov r6,r0 @ save entry node
ldr r0,[r6,#node_parent] @ current = father
ldr r7,[r0,#node_left]
cmp r7,#0
ldrne r8,[r7,#node_height] @ height left tree
moveq r8,#0
ldr r7,[r0,#node_right]
cmp r7,#0
ldrne r9,[r7,#node_height] @ height right tree
moveq r9,#0
cmp r8,r9
addgt r8,#1
strgt r8,[r0,#node_height]
addle r9,#1
strle r9,[r0,#node_height]
//
ldr r7,[r0,#node_right]
cmp r7,#0
ldrne r8,[r7,#node_height]
moveq r8,#0
ldr r7,[r0,#node_left]
cmp r7,#0
ldrne r9,[r7,#node_height]
moveq r9,#0
sub r3,r8,r9 @ compute balance factor
mov r2,r1
mov r4,r0 @ save current
mov r1,r6
bl equiUnSommet
@ change head address ?
cmp r2,r4
streq r6,[r3,#tree_root]
mov r0,r4 @ restaur current
b 1b
100:
pop {r1-r8,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* preOrder */
/******************************************************************/
/* r0 contains the address of the node */
/* r1 function address */
preOrder: @ INFO: preOrder
push {r1-r2,lr} @ save registers
cmp r0,#0
beq 100f
mov r2,r0
blx r1 @ call function
ldr r0,[r2,#node_left]
bl preOrder
ldr r0,[r2,#node_right]
bl preOrder
100:
pop {r1-r2,lr} @ restaur registers
bx lr
/******************************************************************/
/* display node */
/******************************************************************/
/* r0 contains node address */
displayElement: @ INFO: displayElement
push {r1,r2,r3,lr} @ save registers
mov r2,r0
ldr r1,iAdrsZoneConv
bl conversion16
mov r4,#0
strb r4,[r1,r0]
ldr r0,iAdrszMessResult
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_left]
ldr r1,iAdrsZoneConv
bl conversion16
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_right]
ldr r1,iAdrsZoneConv
bl conversion16
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_value]
ldr r1,iAdrsZoneConv
bl conversion10
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_height]
ldr r1,iAdrsZoneConv
bl conversion10
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#node_parent]
ldr r1,iAdrsZoneConv
bl conversion16
mov r4,#0
strb r4,[r1,r0]
mov r0,r3
ldr r1,iAdrsZoneConv
bl strInsertAtCharInc
bl affichageMess
100:
pop {r1,r2,r3,lr} @ restaur registers
bx lr @ return
iAdrszMessResult: .int szMessResult
iAdrsZoneConv: .int sZoneConv
iAdrsValue: .int sValue
/******************************************************************/
/* memory allocation on the heap */
/******************************************************************/
/* r0 contains the size to allocate */
/* r0 returns address of memory heap or - 1 if error */
/* CAUTION : The size of the allowance must be a multiple of 4 */
allocHeap:
push {r5-r7,lr} @ save registers
@ allocation
mov r6,r0 @ save size
mov r0,#0 @ read address start heap
mov r7,#0x2D @ call system 'brk'
svc #0
mov r5,r0 @ save address heap for return
add r0,r6 @ reservation place for size
mov r7,#0x2D @ call system 'brk'
svc #0
cmp r0,#-1 @ allocation error
movne r0,r5 @ return address memory heap
pop {r5-r7,lr} @ restaur registers
bx lr @ return
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
.include "../affichage.inc"

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with Ada.Text_IO, Ada.Finalization, Ada.Unchecked_Deallocation;
procedure Main is
generic
type Key_Type is private;
with function "<"(a, b : Key_Type) return Boolean is <>;
with function "="(a, b : Key_Type) return Boolean is <>;
with function "<="(a, b : Key_Type) return Boolean is <>;
package AVL_Tree is
type Tree is tagged limited private;
function insert(self : in out Tree; key : Key_Type) return Boolean;
procedure delete(self : in out Tree; key : Key_Type);
procedure print_balance(self : in out Tree);
private
type Height_Amt is range -1 .. Integer'Last;
-- Since only one key is inserted before each rebalance, the balance of
-- all trees/subtrees will stay in range -2 .. 2
type Balance_Amt is range -2 .. 2;
type Node;
type Node_Ptr is access Node;
type Node is new Ada.Finalization.Limited_Controlled with record
left, right, parent : Node_Ptr := null;
key : Key_Type;
balance : Balance_Amt := 0;
end record;
overriding procedure Finalize(self : in out Node);
subtype Node_Parent is Ada.Finalization.Limited_Controlled;
type Tree is new Ada.Finalization.Limited_Controlled with record
root : Node_Ptr := null;
end record;
overriding procedure Finalize(self : in out Tree);
end AVL_Tree;
package body AVL_Tree is
procedure Free_Node is new Ada.Unchecked_Deallocation(Node, Node_Ptr);
overriding procedure Finalize(self : in out Node) is
begin
Free_Node(self.left);
Free_Node(self.right);
end Finalize;
overriding procedure Finalize(self : in out Tree) is
begin
Free_Node(self.root);
end Finalize;
function height(n : Node_Ptr) return Height_Amt is
begin
if n = null then
return -1;
else
return 1 + Height_Amt'Max(height(n.left), height(n.right));
end if;
end height;
procedure set_balance(n : not null Node_Ptr) is
begin
n.balance := Balance_Amt(height(n.right) - height(n.left));
end set_balance;
procedure update_parent(parent : Node_Ptr; new_child : Node_Ptr; old_child : Node_Ptr) is
begin
if parent /= null then
if parent.right = old_child then
parent.right := new_child;
else
parent.left := new_child;
end if;
end if;
end update_parent;
function rotate_left(a : not null Node_Ptr) return Node_Ptr is
b : Node_Ptr := a.right;
begin
b.parent := a.parent;
a.right := b.left;
if a.right /= null then
a.right.parent := a;
end if;
b.left := a;
a.parent := b;
update_parent(parent => b.parent, new_child => b, old_child => a);
set_balance(a);
set_balance(b);
return b;
end rotate_left;
function rotate_right(a : not null Node_Ptr) return Node_Ptr is
b : Node_Ptr := a.left;
begin
b.parent := a.parent;
a.left := b.right;
if a.left /= null then
a.left.parent := a;
end if;
b.right := a;
a.parent := b;
update_parent(parent => b.parent, new_child => b, old_child => a);
set_balance(a);
set_balance(b);
return b;
end rotate_right;
function rotate_left_right(n : not null Node_Ptr) return Node_Ptr is
begin
n.left := rotate_left(n.left);
return rotate_right(n);
end rotate_left_right;
function rotate_right_left(n : not null Node_Ptr) return Node_Ptr is
begin
n.right := rotate_right(n.right);
return rotate_left(n);
end rotate_right_left;
procedure rebalance(self : in out Tree; n : not null Node_Ptr) is
new_n : Node_Ptr := n;
begin
set_balance(new_n);
if new_n.balance = -2 then
if height(new_n.left.left) >= height(new_n.left.right) then
new_n := rotate_right(new_n);
else
new_n := rotate_left_right(new_n);
end if;
elsif new_n.balance = 2 then
if height(new_n.right.right) >= height(new_n.right.left) then
new_n := rotate_left(new_n);
else
new_n := rotate_right_left(new_n);
end if;
end if;
if new_n.parent /= null then
rebalance(self, new_n.parent);
else
self.root := new_n;
end if;
end rebalance;
function new_node(key : Key_Type) return Node_Ptr is
(new Node'(Node_Parent with key => key, others => <>));
function insert(self : in out Tree; key : Key_Type) return Boolean is
curr, parent : Node_Ptr;
go_left : Boolean;
begin
if self.root = null then
self.root := new_node(key);
return True;
end if;
curr := self.root;
while curr.key /= key loop
parent := curr;
go_left := key < curr.key;
curr := (if go_left then curr.left else curr.right);
if curr = null then
if go_left then
parent.left := new_node(key);
parent.left.parent := parent;
else
parent.right := new_node(key);
parent.right.parent := parent;
end if;
rebalance(self, parent);
return True;
end if;
end loop;
return False;
end insert;
procedure delete(self : in out Tree; key : Key_Type) is
successor, parent, child : Node_Ptr := self.root;
to_delete : Node_Ptr := null;
begin
if self.root = null then
return;
end if;
while child /= null loop
parent := successor;
successor := child;
child := (if successor.key <= key then successor.right else successor.left);
if successor.key = key then
to_delete := successor;
end if;
end loop;
if to_delete = null then
return;
end if;
to_delete.key := successor.key;
child := (if successor.left = null then successor.right else successor.left);
if self.root.key = key then
self.root := child;
else
update_parent(parent => parent, new_child => child, old_child => successor);
rebalance(self, parent);
end if;
Free_Node(successor);
end delete;
procedure print_balance(n : Node_Ptr) is
begin
if n /= null then
print_balance(n.left);
Ada.Text_IO.Put(n.balance'Image);
print_balance(n.right);
end if;
end print_balance;
procedure print_balance(self : in out Tree) is
begin
print_balance(self.root);
end print_balance;
end AVL_Tree;
package Int_AVL_Tree is new AVL_Tree(Integer);
tree : Int_AVL_Tree.Tree;
success : Boolean;
begin
for i in 1 .. 10 loop
success := tree.insert(i);
end loop;
Ada.Text_IO.Put("Printing balance: ");
tree.print_balance;
Ada.Text_IO.New_Line;
end Main;

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module Avl where
-- The Peano naturals
data Nat : Set where
z : Nat
s : Nat -> Nat
-- An AVL tree's type is indexed by a natural.
-- Avl N is the type of AVL trees of depth N. There arj 3 different
-- node constructors:
-- Left: The left subtree is one level deeper than the right
-- Balanced: The subtrees have the same depth
-- Right: The right Subtree is one level deeper than the left
-- Since the AVL invariant is that the depths of a node's subtrees
-- always differ by at most 1, this perfectly encodes the AVL depth invariant.
data Avl : Nat -> Set where
Empty : Avl z
Left : {X : Nat} -> Nat -> Avl (s X) -> Avl X -> Avl (s (s X))
Balanced : {X : Nat} -> Nat -> Avl X -> Avl X -> Avl (s X)
Right : {X : Nat} -> Nat -> Avl X -> Avl (s X) -> Avl (s (s X))
-- A wrapper type that hides the AVL tree invariant. This is the interface
-- exposed to the user.
data Tree : Set where
avl : {N : Nat} -> Avl N -> Tree
-- Comparison result
data Ord : Set where
Less : Ord
Equal : Ord
Greater : Ord
-- Comparison function
cmp : Nat -> Nat -> Ord
cmp z (s X) = Less
cmp z z = Equal
cmp (s X) z = Greater
cmp (s X) (s Y) = cmp X Y
-- Insertions can either leave the depth the same or
-- increase it by one. Encode this in the type.
data InsertResult : Nat -> Set where
Same : {X : Nat} -> Avl X -> InsertResult X
Bigger : {X : Nat} -> Avl (s X) -> InsertResult X
-- If the left subtree is 2 levels deeper than the right, rotate to the right.
-- balance-left X L R means X is the root, L is the left subtree and R is the right.
balance-left : {N : Nat} -> Nat -> Avl (s (s N)) -> Avl N -> InsertResult (s (s N))
balance-left X (Right Y A (Balanced Z B C)) D = Same (Balanced Z (Balanced X A B) (Balanced Y C D))
balance-left X (Right Y A (Left Z B C)) D = Same (Balanced Z (Balanced X A B) (Right Y C D))
balance-left X (Right Y A (Right Z B C)) D = Same (Balanced Z (Left X A B) (Balanced Y C D))
balance-left X (Left Y (Balanced Z A B) C) D = Same (Balanced Z (Balanced X A B) (Balanced Y C D))
balance-left X (Left Y (Left Z A B) C) D = Same (Balanced Z (Left X A B) (Balanced Y C D))
balance-left X (Left Y (Right Z A B) C) D = Same (Balanced Z (Right X A B) (Balanced Y C D))
balance-left X (Balanced Y (Balanced Z A B) C) D = Bigger (Right Z (Balanced X A B) (Left Y C D))
balance-left X (Balanced Y (Left Z A B) C) D = Bigger (Right Z (Left X A B) (Left Y C D))
balance-left X (Balanced Y (Right Z A B) C) D = Bigger (Right Z (Right X A B) (Left Y C D))
-- Symmetric with balance-left
balance-right : {N : Nat} -> Nat -> Avl N -> Avl (s (s N)) -> InsertResult (s (s N))
balance-right X A (Left Y (Left Z B C) D) = Same (Balanced Z (Balanced X A B) (Right Y C D))
balance-right X A (Left Y (Balanced Z B C) D) = Same(Balanced Z (Balanced X A B) (Balanced Y C D))
balance-right X A (Left Y (Right Z B C) D) = Same(Balanced Z (Left X A B) (Balanced Y C D))
balance-right X A (Balanced Z B (Left Y C D)) = Bigger(Left Z (Right X A B) (Left Y C D))
balance-right X A (Balanced Z B (Balanced Y C D)) = Bigger (Left Z (Right X A B) (Balanced Y C D))
balance-right X A (Balanced Z B (Right Y C D)) = Bigger (Left Z (Right X A B) (Right Y C D))
balance-right X A (Right Z B (Left Y C D)) = Same (Balanced Z (Balanced X A B) (Left Y C D))
balance-right X A (Right Z B (Balanced Y C D)) = Same (Balanced Z (Balanced X A B) (Balanced Y C D))
balance-right X A (Right Z B (Right Y C D)) = Same (Balanced Z (Balanced X A B) (Right Y C D))
-- insert' T N does all the work of inserting the element N into the tree T.
insert' : {N : Nat} -> Avl N -> Nat -> InsertResult N
insert' Empty N = Bigger (Balanced N Empty Empty)
insert' (Left Y L R) X with cmp X Y
insert' (Left Y L R) X | Less with insert' L X
insert' (Left Y L R) X | Less | Same L' = Same (Left Y L' R)
insert' (Left Y L R) X | Less | Bigger L' = balance-left Y L' R
insert' (Left Y L R) X | Equal = Same (Left Y L R)
insert' (Left Y L R) X | Greater with insert' R X
insert' (Left Y L R) X | Greater | Same R' = Same (Left Y L R')
insert' (Left Y L R) X | Greater | Bigger R' = Same (Balanced Y L R')
insert' (Balanced Y L R) X with cmp X Y
insert' (Balanced Y L R) X | Less with insert' L X
insert' (Balanced Y L R) X | Less | Same L' = Same (Balanced Y L' R)
insert' (Balanced Y L R) X | Less | Bigger L' = Bigger (Left Y L' R)
insert' (Balanced Y L R) X | Equal = Same (Balanced Y L R)
insert' (Balanced Y L R) X | Greater with insert' R X
insert' (Balanced Y L R) X | Greater | Same R' = Same (Balanced Y L R')
insert' (Balanced Y L R) X | Greater | Bigger R' = Bigger (Right Y L R')
insert' (Right Y L R) X with cmp X Y
insert' (Right Y L R) X | Less with insert' L X
insert' (Right Y L R) X | Less | Same L' = Same (Right Y L' R)
insert' (Right Y L R) X | Less | Bigger L' = Same (Balanced Y L' R)
insert' (Right Y L R) X | Equal = Same (Right Y L R)
insert' (Right Y L R) X | Greater with insert' R X
insert' (Right Y L R) X | Greater | Same R' = Same (Right Y L R')
insert' (Right Y L R) X | Greater | Bigger R' = balance-right Y L R'
-- Wrapper around insert' to use the depth-agnostic type Tree.
insert : Tree -> Nat -> Tree
insert (avl T) X with insert' T X
... | Same T' = avl T'
... | Bigger T' = avl T'

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#include <algorithm>
#include <iostream>
/* AVL node */
template <class T>
class AVLnode {
public:
T key;
int balance;
AVLnode *left, *right, *parent;
AVLnode(T k, AVLnode *p) : key(k), balance(0), parent(p),
left(NULL), right(NULL) {}
~AVLnode() {
delete left;
delete right;
}
};
/* AVL tree */
template <class T>
class AVLtree {
public:
AVLtree(void);
~AVLtree(void);
bool insert(T key);
void deleteKey(const T key);
void printBalance();
private:
AVLnode<T> *root;
AVLnode<T>* rotateLeft ( AVLnode<T> *a );
AVLnode<T>* rotateRight ( AVLnode<T> *a );
AVLnode<T>* rotateLeftThenRight ( AVLnode<T> *n );
AVLnode<T>* rotateRightThenLeft ( AVLnode<T> *n );
void rebalance ( AVLnode<T> *n );
int height ( AVLnode<T> *n );
void setBalance ( AVLnode<T> *n );
void printBalance ( AVLnode<T> *n );
};
/* AVL class definition */
template <class T>
void AVLtree<T>::rebalance(AVLnode<T> *n) {
setBalance(n);
if (n->balance == -2) {
if (height(n->left->left) >= height(n->left->right))
n = rotateRight(n);
else
n = rotateLeftThenRight(n);
}
else if (n->balance == 2) {
if (height(n->right->right) >= height(n->right->left))
n = rotateLeft(n);
else
n = rotateRightThenLeft(n);
}
if (n->parent != NULL) {
rebalance(n->parent);
}
else {
root = n;
}
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateLeft(AVLnode<T> *a) {
AVLnode<T> *b = a->right;
b->parent = a->parent;
a->right = b->left;
if (a->right != NULL)
a->right->parent = a;
b->left = a;
a->parent = b;
if (b->parent != NULL) {
if (b->parent->right == a) {
b->parent->right = b;
}
else {
b->parent->left = b;
}
}
setBalance(a);
setBalance(b);
return b;
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateRight(AVLnode<T> *a) {
AVLnode<T> *b = a->left;
b->parent = a->parent;
a->left = b->right;
if (a->left != NULL)
a->left->parent = a;
b->right = a;
a->parent = b;
if (b->parent != NULL) {
if (b->parent->right == a) {
b->parent->right = b;
}
else {
b->parent->left = b;
}
}
setBalance(a);
setBalance(b);
return b;
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateLeftThenRight(AVLnode<T> *n) {
n->left = rotateLeft(n->left);
return rotateRight(n);
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateRightThenLeft(AVLnode<T> *n) {
n->right = rotateRight(n->right);
return rotateLeft(n);
}
template <class T>
int AVLtree<T>::height(AVLnode<T> *n) {
if (n == NULL)
return -1;
return 1 + std::max(height(n->left), height(n->right));
}
template <class T>
void AVLtree<T>::setBalance(AVLnode<T> *n) {
n->balance = height(n->right) - height(n->left);
}
template <class T>
void AVLtree<T>::printBalance(AVLnode<T> *n) {
if (n != NULL) {
printBalance(n->left);
std::cout << n->balance << " ";
printBalance(n->right);
}
}
template <class T>
AVLtree<T>::AVLtree(void) : root(NULL) {}
template <class T>
AVLtree<T>::~AVLtree(void) {
delete root;
}
template <class T>
bool AVLtree<T>::insert(T key) {
if (root == NULL) {
root = new AVLnode<T>(key, NULL);
}
else {
AVLnode<T>
*n = root,
*parent;
while (true) {
if (n->key == key)
return false;
parent = n;
bool goLeft = n->key > key;
n = goLeft ? n->left : n->right;
if (n == NULL) {
if (goLeft) {
parent->left = new AVLnode<T>(key, parent);
}
else {
parent->right = new AVLnode<T>(key, parent);
}
rebalance(parent);
break;
}
}
}
return true;
}
template <class T>
void AVLtree<T>::deleteKey(const T delKey) {
if (root == NULL)
return;
AVLnode<T>
*n = root,
*parent = root,
*delNode = NULL,
*child = root;
while (child != NULL) {
parent = n;
n = child;
child = delKey >= n->key ? n->right : n->left;
if (delKey == n->key)
delNode = n;
}
if (delNode != NULL) {
delNode->key = n->key;
child = n->left != NULL ? n->left : n->right;
if (root->key == delKey) {
root = child;
}
else {
if (parent->left == n) {
parent->left = child;
}
else {
parent->right = child;
}
rebalance(parent);
}
}
}
template <class T>
void AVLtree<T>::printBalance() {
printBalance(root);
std::cout << std::endl;
}
int main(void)
{
AVLtree<int> t;
std::cout << "Inserting integer values 1 to 10" << std::endl;
for (int i = 1; i <= 10; ++i)
t.insert(i);
std::cout << "Printing balance: ";
t.printBalance();
}

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(defpackage :avl-tree
(:use :cl)
(:export
:avl-tree
:make-avl-tree
:avl-tree-count
:avl-tree-p
:avl-tree-key<=
:gettree
:remtree
:clrtree
:dfs-maptree
:bfs-maptree))
(in-package :avl-tree)
(defstruct %tree
key
value
(height 0 :type fixnum)
left
right)
(defstruct (avl-tree (:constructor %make-avl-tree))
key<=
tree
(count 0 :type fixnum))
(defun make-avl-tree (key<=)
"Create a new AVL tree using the given comparison function KEY<=
for emplacing keys into the tree."
(%make-avl-tree :key<= key<=))
(declaim (inline
recalc-height
height balance
swap-kv
right-right-rotate
right-left-rotate
left-right-rotate
left-left-rotate
rotate))
(defun recalc-height (tree)
"Calculate the new height of the tree from the heights of the children."
(when tree
(setf (%tree-height tree)
(1+ (the fixnum (max (height (%tree-right tree))
(height (%tree-left tree))))))))
(declaim (ftype (function (t) fixnum) height balance))
(defun height (tree)
(if tree (%tree-height tree) 0))
(defun balance (tree)
(if tree
(- (height (%tree-right tree))
(height (%tree-left tree)))
0))
(defmacro swap (place-a place-b)
"Swap the values of two places."
(let ((tmp (gensym)))
`(let ((,tmp ,place-a))
(setf ,place-a ,place-b)
(setf ,place-b ,tmp))))
(defun swap-kv (tree-a tree-b)
"Swap the keys and values of two trees."
(swap (%tree-value tree-a) (%tree-value tree-b))
(swap (%tree-key tree-a) (%tree-key tree-b)))
;; We should really use gensyms for the variables in here.
(defmacro slash-rotate (tree right left)
"Rotate nodes in a slash `/` imbalance."
`(let* ((a ,tree)
(b (,right a))
(c (,right b))
(a-left (,left a))
(b-left (,left b)))
(setf (,right a) c)
(setf (,left a) b)
(setf (,left b) a-left)
(setf (,right b) b-left)
(swap-kv a b)
(recalc-height b)
(recalc-height a)))
(defmacro angle-rotate (tree right left)
"Rotate nodes in an angle bracket `<` imbalance."
`(let* ((a ,tree)
(b (,right a))
(c (,left b))
(a-left (,left a))
(c-left (,left c))
(c-right (,right c)))
(setf (,left a) c)
(setf (,left c) a-left)
(setf (,right c) c-left)
(setf (,left b) c-right)
(swap-kv a c)
(recalc-height c)
(recalc-height b)
(recalc-height a)))
(defun right-right-rotate (tree)
(slash-rotate tree %tree-right %tree-left))
(defun left-left-rotate (tree)
(slash-rotate tree %tree-left %tree-right))
(defun right-left-rotate (tree)
(angle-rotate tree %tree-right %tree-left))
(defun left-right-rotate (tree)
(angle-rotate tree %tree-left %tree-right))
(defun rotate (tree)
(declare (type %tree tree))
"Perform a rotation on the given TREE if it is imbalanced."
(recalc-height tree)
(with-slots (left right) tree
(let ((balance (balance tree)))
(cond ((< 1 balance) ;; Right imbalanced tree
(if (<= 0 (balance right))
(right-right-rotate tree)
(right-left-rotate tree)))
((> -1 balance) ;; Left imbalanced tree
(if (<= 0 (balance left))
(left-right-rotate tree)
(left-left-rotate tree)))))))
(defun gettree (key avl-tree &optional default)
"Finds an entry in AVL-TREE whos key is KEY and returns the
associated value and T as multiple values, or returns DEFAULT and NIL
if there was no such entry. Entries can be added using SETF."
(with-slots (key<= tree) avl-tree
(labels
((rec (tree)
(if tree
(with-slots ((t-key key) left right value) tree
(if (funcall key<= t-key key)
(if (funcall key<= key t-key)
(values value t)
(rec right))
(rec left)))
(values default nil))))
(rec tree))))
(defun puttree (value key avl-tree)
;;(declare (optimize speed))
(declare (type avl-tree avl-tree))
"Emplace the the VALUE with the given KEY into the AVL-TREE, or
overwrite the value if the given key already exists."
(let ((node (make-%tree :key key :value value)))
(with-slots (key<= tree count) avl-tree
(cond (tree
(labels
((rec (tree)
(with-slots ((t-key key) left right) tree
(if (funcall key<= t-key key)
(if (funcall key<= key t-key)
(setf (%tree-value tree) value)
(cond (right (rec right))
(t (setf right node)
(incf count))))
(cond (left (rec left))
(t (setf left node)
(incf count))))
(rotate tree))))
(rec tree)))
(t (setf tree node)
(incf count))))
value))
(defun (setf gettree) (value key avl-tree &optional default)
(declare (ignore default))
(puttree value key avl-tree))
(defun remtree (key avl-tree)
(declare (type avl-tree avl-tree))
"Remove the entry in AVL-TREE associated with KEY. Return T if
there was such an entry, or NIL if not."
(with-slots (key<= tree count) avl-tree
(labels
((find-left (tree)
(with-slots ((t-key key) left right) tree
(if left
(find-left left)
tree)))
(rec (tree &optional parent type)
(when tree
(prog1
(with-slots ((t-key key) left right) tree
(if (funcall key<= t-key key)
(cond
((funcall key<= key t-key)
(cond
((and left right)
(let ((sub-left (find-left right)))
(swap-kv sub-left tree)
(rec right tree :right)))
(t
(let ((sub (or left right)))
(case type
(:right (setf (%tree-right parent) sub))
(:left (setf (%tree-left parent) sub))
(nil (setf (avl-tree-tree avl-tree) sub))))
(decf count)))
t)
(t (rec right tree :right)))
(rec left tree :left)))
(when parent (rotate parent))))))
(rec tree))))
(defun clrtree (avl-tree)
"This removes all the entries from AVL-TREE and returns the tree itself."
(setf (avl-tree-tree avl-tree) nil)
(setf (avl-tree-count avl-tree) 0)
avl-tree)
(defun dfs-maptree (function avl-tree)
"For each entry in AVL-TREE call the two-argument FUNCTION on
the key and value of each entry in depth-first order from left to right.
Consequences are undefined if AVL-TREE is modified during this call."
(with-slots (key<= tree) avl-tree
(labels
((rec (tree)
(when tree
(with-slots ((t-key key) left right key value) tree
(rec left)
(funcall function key value)
(rec right)))))
(rec tree))))
(defun bfs-maptree (function avl-tree)
"For each entry in AVL-TREE call the two-argument FUNCTION on
the key and value of each entry in breadth-first order from left to right.
Consequences are undefined if AVL-TREE is modified during this call."
(with-slots (key<= tree) avl-tree
(let* ((queue (cons nil nil))
(end queue))
(labels ((pushend (value)
(when value
(setf (cdr end) (cons value nil))
(setf end (cdr end))))
(empty-p () (eq nil (cdr queue)))
(popfront ()
(prog1 (pop (cdr queue))
(when (empty-p) (setf end queue)))))
(when tree
(pushend tree)
(loop until (empty-p)
do (let ((current (popfront)))
(with-slots (key value left right) current
(funcall function key value)
(pushend left)
(pushend right)))))))))
(defun test ()
(let ((tree (make-avl-tree #'<=))
(printer (lambda (k v) (print (list k v)))))
(loop for key in '(0 8 6 4 2 3 7 9 1 5 5)
for value in '(a b c d e f g h i j k)
do (setf (gettree key tree) value))
(loop for key in '(0 1 2 3 4 10)
do (print (multiple-value-list (gettree key tree))))
(terpri)
(print tree)
(terpri)
(dfs-maptree printer tree)
(terpri)
(bfs-maptree printer tree)
(terpri)
(loop for key in '(0 1 2 3 10 7)
do (print (remtree key tree)))
(terpri)
(print tree)
(terpri)
(clrtree tree)
(print tree))
(values))
(defun profile-test ()
(let ((tree (make-avl-tree #'<=))
(randoms (loop repeat 1000000 collect (random 100.0))))
(loop for key in randoms do (setf (gettree key tree) key))))

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MODULE RosettaAVLTrees;
(* An implementation of persistent AVL Trees *)
TYPE
Order = ABSTRACT RECORD END;
Tree* = POINTER TO Node;
Node* = ABSTRACT RECORD (Order)
left, right: Tree;
height: INTEGER
END; (* Contains the left and right child nodes and the height of the node *)
Out* = ABSTRACT RECORD END; (* Used for output by the `Draw` procedure *)
Void = RECORD (Order) END; (* Used by the `Ordered` procedure *)
(* The following abstract procedures must be implemented by a user of `Node` *)
(* They must be implemented correctly for the AVL tree to work *)
(* Compares one node with another and returns a boolean value based on which is less *)
PROCEDURE (IN n: Order) Less- (IN m: Node): BOOLEAN, NEW, ABSTRACT;
(* Compares one node with another and returns a boolean value based on which is more *)
PROCEDURE (IN n: Order) More- (IN m: Node): BOOLEAN, NEW, ABSTRACT;
(* Creates a new root node *)
PROCEDURE (IN n: Node) Alloc- (): Tree, NEW, ABSTRACT;
(* Returns TRUE if n is in the tree t, FALSE otherwise *)
PROCEDURE (IN n: Node) Lookup* (t: Tree): BOOLEAN, NEW;
BEGIN
IF t = NIL THEN RETURN FALSE END;
IF n.Less(t) THEN RETURN n.Lookup(t.left) END;
IF n.More(t) THEN RETURN n.Lookup(t.right) END;
RETURN TRUE
END Lookup;
(* Returns the height of the AVL tree t *)
PROCEDURE Height (t: Tree): INTEGER;
BEGIN
IF t = NIL THEN RETURN 0 END;
RETURN t.height
END Height;
(* Creates and returns a new Node with the given children *)
PROCEDURE (IN n: Node) New (left, right: Tree): Tree, NEW;
VAR t: Tree;
BEGIN
t := n.Alloc(); (* Create a new root node *)
t.left := left; t.right := right; (* set the children *)
(* set the height of the node based on its children *)
t.height := MAX(Height(left), Height(right)) + 1;
RETURN t
END New;
(* Returns the difference in height between the left and right children of a node *)
PROCEDURE Slope (l, r: Tree): INTEGER;
BEGIN RETURN Height(l) - Height(r) END Slope;
(* Returns an AVL tree if it is right-heavy *)
PROCEDURE (IN n: Node) BalL (l, r: Tree): Tree, NEW;
BEGIN
IF Slope(l, r) = - 2 THEN
IF Slope(r.left, r.right) = 1 THEN
RETURN r.left.New(n.New(l, r.left.left),
r.New(r.left.right, r.right))
END;
RETURN r.New(n.New(l, r.left), r.right)
END;
RETURN n.New(l, r)
END BalL;
(* Returns an AVL tree if it is left-heavy *)
PROCEDURE (IN n: Node) BalR (l, r: Tree): Tree, NEW;
BEGIN
IF Slope(l, r) = 2 THEN
IF Slope(l.left, l.right) = - 1 THEN
RETURN l.right.New(l.New(l.left, l.right.left),
n.New(l.right.right, r))
END;
RETURN l.New(l.left, n.New(l.right, r))
END;
RETURN n.New(l, r)
END BalR;
(* Returns the AVL tree t with the node n *)
PROCEDURE (IN n: Node) Insert* (t: Tree): Tree, NEW;
BEGIN
IF t = NIL THEN RETURN n.New(NIL, NIL) END;
IF n.Less(t) THEN RETURN t.BalR(n.Insert(t.left), t.right) END;
IF n.More(t) THEN RETURN t.BalL(t.left, n.Insert(t.right)) END;
RETURN t
END Insert;
(* Returns the leftmost node of the non-empty tree t *)
PROCEDURE (t: Tree) Head (): Tree, NEW;
BEGIN
IF t.left = NIL THEN RETURN t END;
RETURN t.left.Head()
END Head;
(* Returns the rightmost node of the non-empty tree t *)
PROCEDURE (t: Tree) Last (): Tree, NEW;
BEGIN
IF t.right = NIL THEN RETURN t END;
RETURN t.right.Last()
END Last;
(* Returns the AVL tree t without the leftmost node *)
PROCEDURE (IN t: Node) Tail* (): Tree, NEW;
BEGIN
IF t.left = NIL THEN RETURN t.right END;
RETURN t.BalL(t.left.Tail(), t.right)
END Tail;
(* Returns the AVL tree t without the rightmost node *)
PROCEDURE (IN t: Node) Init* (): Tree, NEW;
BEGIN
IF t.right = NIL THEN RETURN t.left END;
RETURN t.BalR(t.left, t.right.Init())
END Init;
(* Returns the AVL tree t without node n *)
PROCEDURE (IN n: Node) Delete* (t: Tree): Tree, NEW;
BEGIN
IF t = NIL THEN RETURN NIL END;
IF n.Less(t) THEN RETURN t.BalL(n.Delete(t.left), t.right) END;
IF n.More(t) THEN RETURN t.BalR(t.left, n.Delete(t.right)) END;
IF Slope(t.left, t.right) = 1 THEN
RETURN t.left.Last().BalL(t.left.Init(), t.right)
END;
IF t.right = NIL THEN RETURN t.left END;
RETURN t.right.Head().BalR(t.left, t.right.Tail())
END Delete;
(* The following procedures are used for debugging *)
PROCEDURE (IN n: Void) Less- (IN m: Node): BOOLEAN;
BEGIN RETURN TRUE END Less;
PROCEDURE (IN n: Void) More- (IN m: Node): BOOLEAN;
BEGIN RETURN TRUE END More;
(* Returns TRUE if the AVL tree t is ordered, FALSE otherwise *)
PROCEDURE Ordered* (t: Tree): BOOLEAN;
VAR void: Void;
PROCEDURE Bounded (IN lo, hi: Order; t: Tree): BOOLEAN;
BEGIN
IF t = NIL THEN RETURN TRUE END;
RETURN lo.Less(t) & hi.More(t) &
Bounded(lo, t, t.left) & Bounded(t, hi, t.right)
END Bounded;
BEGIN RETURN Bounded(void, void, t) END Ordered;
(* The following abstract procedures must be implemented by a user of `Out` *)
(* Writes a string *)
PROCEDURE (IN o: Out) Str- (s: ARRAY OF CHAR), NEW, ABSTRACT;
(* Writes an integer *)
PROCEDURE (IN o: Out) Int- (i: INTEGER), NEW, ABSTRACT;
(* Writes a new-line *)
PROCEDURE (IN o: Out) Ln-, NEW, ABSTRACT;
(* Writes a node *)
PROCEDURE (IN o: Out) Node- (IN n: Node), NEW, ABSTRACT;
(* Writes a tree (rotated) *)
PROCEDURE (IN o: Out) Draw* (t: Tree), NEW;
PROCEDURE Bars (bars, bar: ARRAY OF CHAR);
BEGIN
IF LEN(bars + bar) # 0 THEN o.Str(bars + "+--") END
END Bars;
PROCEDURE Do (lBar, rBar, bars: ARRAY OF CHAR; t: Tree);
BEGIN
IF t = NIL THEN Bars(bars, lBar); o.Str("|"); o.Ln
ELSIF (t.left = NIL) & (t.right = NIL) THEN
Bars(bars, lBar); o.Node(t); o.Ln
ELSE
Do("| ", " ", bars + rBar, t.right);
o.Str(bars + rBar + "|"); o.Ln;
Bars(bars, lBar); o.Node(t);
IF Slope(t.left, t.right) # 0 THEN
o.Str(" ["); o.Int(Slope(t.left, t.right)); o.Str("]")
END;
o.Ln;
o.Str(bars + lBar + "|"); o.Ln;
Do(" ", "| ", bars + lBar, t.left)
END
END Do;
BEGIN
Do("", "", "", t)
END Draw;
END RosettaAVLTrees.

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DEFINITION RosettaAVLTrees;
TYPE
Tree = POINTER TO Node;
Node = ABSTRACT RECORD (Order)
(IN n: Node) Alloc- (): Tree, NEW, ABSTRACT;
(IN n: Node) Delete (t: Tree): Tree, NEW;
(IN t: Node) Init (): Tree, NEW;
(IN n: Node) Insert (t: Tree): Tree, NEW;
(IN n: Node) Lookup (t: Tree): BOOLEAN, NEW;
(IN t: Node) Tail (): Tree, NEW
END;
Out = ABSTRACT RECORD
(IN o: Out) Draw (t: Tree), NEW;
(IN o: Out) Int- (i: INTEGER), NEW, ABSTRACT;
(IN o: Out) Ln-, NEW, ABSTRACT;
(IN o: Out) Node- (IN n: Node), NEW, ABSTRACT;
(IN o: Out) Str- (s: ARRAY OF CHAR), NEW, ABSTRACT
END;
PROCEDURE Ordered (t: Tree): BOOLEAN;
END RosettaAVLTrees.

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MODULE RosettaAVLTreesUse;
IMPORT Set := RosettaAVLTrees, Log := StdLog;
TYPE
Height = RECORD (Set.Node) height: INTEGER END;
(* Note that Set.Node already contains an integer field `height`. *)
(* It does not cause a duplicate field error as it is hidden from this module *)
Out = RECORD (Set.Out) END; (* Used for output by the `Draw` procedure *)
(* The following three procedures are implemented here for use by Set.Node *)
(* Compares one node with another and returns a boolean value based on which is less *)
PROCEDURE (IN h: Height) Less- (IN n: Set.Node): BOOLEAN;
BEGIN RETURN h.height < n(Height).height END Less;
(* Compares one node with another and returns a boolean value based on which is more *)
PROCEDURE (IN h: Height) More- (IN n: Set.Node): BOOLEAN;
BEGIN RETURN h.height > n(Height).height END More;
(* Creates a new root node *)
PROCEDURE (IN h: Height) Alloc- (): Set.Tree;
VAR r: POINTER TO Height;
BEGIN NEW(r); r.height := h.height; RETURN r END Alloc;
(* The following four procedures are implemented here for use by Set.Out *)
(* Writes a string *)
PROCEDURE (IN o: Out) Str- (s: ARRAY OF CHAR);
BEGIN Log.String(s) END Str;
(* Writes an integer *)
PROCEDURE (IN o: Out) Int- (i: INTEGER);
BEGIN Log.IntForm(i, Log.decimal, 0, ' ', Log.hideBase) END Int;
(* Writes a new-line *)
PROCEDURE (IN o: Out) Ln-; BEGIN Log.Ln END Ln;
(* Writes a node *)
PROCEDURE (IN o: Out) Node- (IN n: Set.Node);
BEGIN
Log.IntForm(n(Height).height, Log.decimal, 0, ' ', Log.hideBase)
END Node;
PROCEDURE Use*;
TYPE BAD = POINTER TO Height;
VAR h: Height; hs, save: Set.Tree; i: INTEGER; o: Out;
BEGIN
h.height := 10; hs := h.Insert(hs);
FOR i := 0 TO 9 DO h.height := i; hs := h.Insert(hs) END;
o.Draw(hs); Log.Ln; Log.Ln;
save := hs;
FOR i := 0 TO 9 DO h.height := i; hs := h.Delete(hs) END;
o.Draw(hs); Log.Ln; Log.Ln;
o.Draw(save); Log.Ln; Log.Ln; (* Tree demonstrates persistence *)
ASSERT(Set.Ordered(save)); (* This ASSERT succeeds *)
save(BAD).height := 11; (* UNSAFE STATEMENT *)
o.Draw(save);
ASSERT(Set.Ordered(save)) (* This ASSERT fails *)
END Use;
END RosettaAVLTreesUse.

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import std.stdio, std.algorithm;
class AVLtree {
private Node* root;
private static struct Node {
private int key, balance;
private Node* left, right, parent;
this(in int k, Node* p) pure nothrow @safe @nogc {
key = k;
parent = p;
}
}
public bool insert(in int key) pure nothrow @safe {
if (root is null)
root = new Node(key, null);
else {
Node* n = root;
Node* parent;
while (true) {
if (n.key == key)
return false;
parent = n;
bool goLeft = n.key > key;
n = goLeft ? n.left : n.right;
if (n is null) {
if (goLeft) {
parent.left = new Node(key, parent);
} else {
parent.right = new Node(key, parent);
}
rebalance(parent);
break;
}
}
}
return true;
}
public void deleteKey(in int delKey) pure nothrow @safe @nogc {
if (root is null)
return;
Node* n = root;
Node* parent = root;
Node* delNode = null;
Node* child = root;
while (child !is null) {
parent = n;
n = child;
child = delKey >= n.key ? n.right : n.left;
if (delKey == n.key)
delNode = n;
}
if (delNode !is null) {
delNode.key = n.key;
child = n.left !is null ? n.left : n.right;
if (root.key == delKey) {
root = child;
} else {
if (parent.left is n) {
parent.left = child;
} else {
parent.right = child;
}
rebalance(parent);
}
}
}
private void rebalance(Node* n) pure nothrow @safe @nogc {
setBalance(n);
if (n.balance == -2) {
if (height(n.left.left) >= height(n.left.right))
n = rotateRight(n);
else
n = rotateLeftThenRight(n);
} else if (n.balance == 2) {
if (height(n.right.right) >= height(n.right.left))
n = rotateLeft(n);
else
n = rotateRightThenLeft(n);
}
if (n.parent !is null) {
rebalance(n.parent);
} else {
root = n;
}
}
private Node* rotateLeft(Node* a) pure nothrow @safe @nogc {
Node* b = a.right;
b.parent = a.parent;
a.right = b.left;
if (a.right !is null)
a.right.parent = a;
b.left = a;
a.parent = b;
if (b.parent !is null) {
if (b.parent.right is a) {
b.parent.right = b;
} else {
b.parent.left = b;
}
}
setBalance(a, b);
return b;
}
private Node* rotateRight(Node* a) pure nothrow @safe @nogc {
Node* b = a.left;
b.parent = a.parent;
a.left = b.right;
if (a.left !is null)
a.left.parent = a;
b.right = a;
a.parent = b;
if (b.parent !is null) {
if (b.parent.right is a) {
b.parent.right = b;
} else {
b.parent.left = b;
}
}
setBalance(a, b);
return b;
}
private Node* rotateLeftThenRight(Node* n) pure nothrow @safe @nogc {
n.left = rotateLeft(n.left);
return rotateRight(n);
}
private Node* rotateRightThenLeft(Node* n) pure nothrow @safe @nogc {
n.right = rotateRight(n.right);
return rotateLeft(n);
}
private int height(in Node* n) const pure nothrow @safe @nogc {
if (n is null)
return -1;
return 1 + max(height(n.left), height(n.right));
}
private void setBalance(Node*[] nodes...) pure nothrow @safe @nogc {
foreach (n; nodes)
n.balance = height(n.right) - height(n.left);
}
public void printBalance() const @safe {
printBalance(root);
}
private void printBalance(in Node* n) const @safe {
if (n !is null) {
printBalance(n.left);
write(n.balance, ' ');
printBalance(n.right);
}
}
}
void main() @safe {
auto tree = new AVLtree();
writeln("Inserting values 1 to 10");
foreach (immutable i; 1 .. 11)
tree.insert(i);
write("Printing balance: ");
tree.printBalance;
}

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module avl_trees
!
! References:
!
! * Niklaus Wirth, 1976. Algorithms + Data Structures =
! Programs. Prentice-Hall, Englewood Cliffs, New Jersey.
!
! * Niklaus Wirth, 2004. Algorithms and Data Structures. Updated
! by Fyodor Tkachov, 2014.
!
implicit none
private
! The type for an AVL tree.
public :: avl_tree_t
! The type for a pair of pointers to key and data within the tree.
! (Be careful with these!)
public :: avl_pointer_pair_t
! Insertion, replacement, modification, etc.
public :: avl_insert_or_modify
! Insert or replace.
public :: avl_insert
! Is the key in the tree?
public :: avl_contains
! Retrieve data from a tree.
public :: avl_retrieve
! Delete data from a tree. This is a generic function.
public :: avl_delete
! Implementations of avl_delete.
public :: avl_delete_with_found
public :: avl_delete_without_found
! How many nodes are there in the tree?
public :: avl_size
! Return a list of avl_pointer_pair_t for the elements in the
! tree. The list will be in order.
public :: avl_pointer_pairs
! Print a representation of the tree to an output unit.
public :: avl_write
! Check the AVL condition (that the heights of the two branches from
! a node should differ by zero or one). ERROR STOP if the condition
! is not met.
public :: avl_check
! Procedure types.
public :: avl_less_than_t
public :: avl_insertion_t
public :: avl_key_data_writer_t
type :: avl_node_t
class(*), allocatable :: key, data
type(avl_node_t), pointer :: left
type(avl_node_t), pointer :: right
integer :: bal ! bal == -1, 0, 1
end type avl_node_t
type :: avl_tree_t
type(avl_node_t), pointer :: p => null ()
contains
final :: avl_tree_t_final
end type avl_tree_t
type :: avl_pointer_pair_t
class(*), pointer :: p_key, p_data
class(avl_pointer_pair_t), pointer :: next => null ()
contains
final :: avl_pointer_pair_t_final
end type avl_pointer_pair_t
interface avl_delete
module procedure avl_delete_with_found
module procedure avl_delete_without_found
end interface avl_delete
interface
function avl_less_than_t (key1, key2) result (key1_lt_key2)
!
! The ordering predicate (‘<’).
!
! Two keys a,b are considered equivalent if neither a<b nor
! b<a.
!
class(*), intent(in) :: key1, key2
logical key1_lt_key2
end function avl_less_than_t
subroutine avl_insertion_t (key, data, p_is_new, p)
!
! Insertion or modification of a found node.
!
import avl_node_t
class(*), intent(in) :: key, data
logical, intent(in) :: p_is_new
type(avl_node_t), pointer, intent(inout) :: p
end subroutine avl_insertion_t
subroutine avl_key_data_writer_t (unit, key, data)
!
! Printing the key and data of a node.
!
integer, intent(in) :: unit
class(*), intent(in) :: key, data
end subroutine avl_key_data_writer_t
end interface
contains
subroutine avl_tree_t_final (tree)
type(avl_tree_t), intent(inout) :: tree
type(avl_node_t), pointer :: p
p => tree%p
call free_the_nodes (p)
contains
recursive subroutine free_the_nodes (p)
type(avl_node_t), pointer, intent(inout) :: p
if (associated (p)) then
call free_the_nodes (p%left)
call free_the_nodes (p%right)
deallocate (p)
end if
end subroutine free_the_nodes
end subroutine avl_tree_t_final
recursive subroutine avl_pointer_pair_t_final (node)
type(avl_pointer_pair_t), intent(inout) :: node
if (associated (node%next)) deallocate (node%next)
end subroutine avl_pointer_pair_t_final
function avl_contains (less_than, key, tree) result (found)
procedure(avl_less_than_t) :: less_than
class(*), intent(in) :: key
class(avl_tree_t), intent(in) :: tree
logical :: found
found = avl_contains_recursion (less_than, key, tree%p)
end function avl_contains
recursive function avl_contains_recursion (less_than, key, p) result (found)
procedure(avl_less_than_t) :: less_than
class(*), intent(in) :: key
type(avl_node_t), pointer, intent(in) :: p
logical :: found
if (.not. associated (p)) then
found = .false.
else if (less_than (key, p%key)) then
found = avl_contains_recursion (less_than, key, p%left)
else if (less_than (p%key, key)) then
found = avl_contains_recursion (less_than, key, p%right)
else
found = .true.
end if
end function avl_contains_recursion
subroutine avl_retrieve (less_than, key, tree, found, data)
procedure(avl_less_than_t) :: less_than
class(*), intent(in) :: key
class(avl_tree_t), intent(in) :: tree
logical, intent(out) :: found
class(*), allocatable, intent(inout) :: data
call avl_retrieve_recursion (less_than, key, tree%p, found, data)
end subroutine avl_retrieve
recursive subroutine avl_retrieve_recursion (less_than, key, p, found, data)
procedure(avl_less_than_t) :: less_than
class(*), intent(in) :: key
type(avl_node_t), pointer, intent(in) :: p
logical, intent(out) :: found
class(*), allocatable, intent(inout) :: data
if (.not. associated (p)) then
found = .false.
else if (less_than (key, p%key)) then
call avl_retrieve_recursion (less_than, key, p%left, found, data)
else if (less_than (p%key, key)) then
call avl_retrieve_recursion (less_than, key, p%right, found, data)
else
found = .true.
data = p%data
end if
end subroutine avl_retrieve_recursion
subroutine avl_insert (less_than, key, data, tree)
procedure(avl_less_than_t) :: less_than
class(*), intent(in) :: key, data
class(avl_tree_t), intent(inout) :: tree
call avl_insert_or_modify (less_than, insert_or_replace, key, data, tree)
end subroutine avl_insert
subroutine insert_or_replace (key, data, p_is_new, p)
class(*), intent(in) :: key, data
logical, intent(in) :: p_is_new
type(avl_node_t), pointer, intent(inout) :: p
p%data = data
end subroutine insert_or_replace
subroutine avl_insert_or_modify (less_than, insertion, key, data, tree)
procedure(avl_less_than_t) :: less_than
procedure(avl_insertion_t) :: insertion ! Or modification in place.
class(*), intent(in) :: key, data
class(avl_tree_t), intent(inout) :: tree
logical :: fix_balance
fix_balance = .false.
call insertion_search (less_than, insertion, key, data, tree%p, fix_balance)
end subroutine avl_insert_or_modify
recursive subroutine insertion_search (less_than, insertion, key, data, p, fix_balance)
procedure(avl_less_than_t) :: less_than
procedure(avl_insertion_t) :: insertion
class(*), intent(in) :: key, data
type(avl_node_t), pointer, intent(inout) :: p
logical, intent(inout) :: fix_balance
type(avl_node_t), pointer :: p1, p2
if (.not. associated (p)) then
! The key was not found. Make a new node.
allocate (p)
p%key = key
p%left => null ()
p%right => null ()
p%bal = 0
call insertion (key, data, .true., p)
fix_balance = .true.
else if (less_than (key, p%key)) then
! Continue searching.
call insertion_search (less_than, insertion, key, data, p%left, fix_balance)
if (fix_balance) then
! A new node has been inserted on the left side.
select case (p%bal)
case (1)
p%bal = 0
fix_balance = .false.
case (0)
p%bal = -1
case (-1)
! Rebalance.
p1 => p%left
select case (p1%bal)
case (-1)
! A single LL rotation.
p%left => p1%right
p1%right => p
p%bal = 0
p => p1
p%bal = 0
fix_balance = .false.
case (0, 1)
! A double LR rotation.
p2 => p1%right
p1%right => p2%left
p2%left => p1
p%left => p2%right
p2%right => p
p%bal = -(min (p2%bal, 0))
p1%bal = -(max (p2%bal, 0))
p => p2
p%bal = 0
fix_balance = .false.
case default
error stop
end select
case default
error stop
end select
end if
else if (less_than (p%key, key)) then
call insertion_search (less_than, insertion, key, data, p%right, fix_balance)
if (fix_balance) then
! A new node has been inserted on the right side.
select case (p%bal)
case (-1)
p%bal = 0
fix_balance = .false.
case (0)
p%bal = 1
case (1)
! Rebalance.
p1 => p%right
select case (p1%bal)
case (1)
! A single RR rotation.
p%right => p1%left
p1%left => p
p%bal = 0
p => p1
p%bal = 0
fix_balance = .false.
case (-1, 0)
! A double RL rotation.
p2 => p1%left
p1%left => p2%right
p2%right => p1
p%right => p2%left
p2%left => p
p%bal = -(max (p2%bal, 0))
p1%bal = -(min (p2%bal, 0))
p => p2
p%bal = 0
fix_balance = .false.
case default
error stop
end select
case default
error stop
end select
end if
else
! The key was found. The pointer p points to an existing node.
call insertion (key, data, .false., p)
end if
end subroutine insertion_search
subroutine avl_delete_with_found (less_than, key, tree, found)
procedure(avl_less_than_t) :: less_than
class(*), intent(in) :: key
class(avl_tree_t), intent(inout) :: tree
logical, intent(out) :: found
logical :: fix_balance
fix_balance = .false.
call deletion_search (less_than, key, tree%p, fix_balance, found)
end subroutine avl_delete_with_found
subroutine avl_delete_without_found (less_than, key, tree)
procedure(avl_less_than_t) :: less_than
class(*), intent(in) :: key
class(avl_tree_t), intent(inout) :: tree
logical :: found
call avl_delete_with_found (less_than, key, tree, found)
end subroutine avl_delete_without_found
recursive subroutine deletion_search (less_than, key, p, fix_balance, found)
procedure(avl_less_than_t) :: less_than
class(*), intent(in) :: key
type(avl_node_t), pointer, intent(inout) :: p
logical, intent(inout) :: fix_balance
logical, intent(out) :: found
type(avl_node_t), pointer :: q
if (.not. associated (p)) then
! The key is not in the tree.
found = .false.
else if (less_than (key, p%key)) then
call deletion_search (less_than, key, p%left, fix_balance, found)
if (fix_balance) call balance_for_shrunken_left (p, fix_balance)
else if (less_than (p%key, key)) then
call deletion_search (less_than, key, p%right, fix_balance, found)
if (fix_balance) call balance_for_shrunken_right (p, fix_balance)
else
q => p
if (.not. associated (q%right)) then
p => q%left
fix_balance = .true.
else if (.not. associated (q%left)) then
p => q%right
fix_balance = .true.
else
call del (q%left, q, fix_balance)
if (fix_balance) call balance_for_shrunken_left (p, fix_balance)
end if
deallocate (q)
found = .true.
end if
end subroutine deletion_search
recursive subroutine del (r, q, fix_balance)
type(avl_node_t), pointer, intent(inout) :: r, q
logical, intent(inout) :: fix_balance
if (associated (r%right)) then
call del (r%right, q, fix_balance)
if (fix_balance) call balance_for_shrunken_right (r, fix_balance)
else
q%key = r%key
q%data = r%data
q => r
r => r%left
fix_balance = .true.
end if
end subroutine del
subroutine balance_for_shrunken_left (p, fix_balance)
type(avl_node_t), pointer, intent(inout) :: p
logical, intent(inout) :: fix_balance
! The left side has lost a node.
type(avl_node_t), pointer :: p1, p2
if (.not. fix_balance) error stop
select case (p%bal)
case (-1)
p%bal = 0
case (0)
p%bal = 1
fix_balance = .false.
case (1)
! Rebalance.
p1 => p%right
select case (p1%bal)
case (0)
! A single RR rotation.
p%right => p1%left
p1%left => p
p%bal = 1
p1%bal = -1
p => p1
fix_balance = .false.
case (1)
! A single RR rotation.
p%right => p1%left
p1%left => p
p%bal = 0
p1%bal = 0
p => p1
fix_balance = .true.
case (-1)
! A double RL rotation.
p2 => p1%left
p1%left => p2%right
p2%right => p1
p%right => p2%left
p2%left => p
p%bal = -(max (p2%bal, 0))
p1%bal = -(min (p2%bal, 0))
p => p2
p2%bal = 0
case default
error stop
end select
case default
error stop
end select
end subroutine balance_for_shrunken_left
subroutine balance_for_shrunken_right (p, fix_balance)
type(avl_node_t), pointer, intent(inout) :: p
logical, intent(inout) :: fix_balance
! The right side has lost a node.
type(avl_node_t), pointer :: p1, p2
if (.not. fix_balance) error stop
select case (p%bal)
case (1)
p%bal = 0
case (0)
p%bal = -1
fix_balance = .false.
case (-1)
! Rebalance.
p1 => p%left
select case (p1%bal)
case (0)
! A single LL rotation.
p%left => p1%right
p1%right => p
p1%bal = 1
p%bal = -1
p => p1
fix_balance = .false.
case (-1)
! A single LL rotation.
p%left => p1%right
p1%right => p
p1%bal = 0
p%bal = 0
p => p1
fix_balance = .true.
case (1)
! A double LR rotation.
p2 => p1%right
p1%right => p2%left
p2%left => p1
p%left => p2%right
p2%right => p
p%bal = -(min (p2%bal, 0))
p1%bal = -(max (p2%bal, 0))
p => p2
p2%bal = 0
case default
error stop
end select
case default
error stop
end select
end subroutine balance_for_shrunken_right
function avl_size (tree) result (size)
class(avl_tree_t), intent(in) :: tree
integer :: size
size = traverse (tree%p)
contains
recursive function traverse (p) result (size)
type(avl_node_t), pointer, intent(in) :: p
integer :: size
if (associated (p)) then
! The order of traversal is arbitrary.
size = 1 + traverse (p%left) + traverse (p%right)
else
size = 0
end if
end function traverse
end function avl_size
function avl_pointer_pairs (tree) result (lst)
class(avl_tree_t), intent(in) :: tree
type(avl_pointer_pair_t), pointer :: lst
! Reverse in-order traversal of the tree, to produce a CONS-list
! of pointers to the contents.
lst => null ()
if (associated (tree%p)) lst => traverse (tree%p, lst)
contains
recursive function traverse (p, lst1) result (lst2)
type(avl_node_t), pointer, intent(in) :: p
type(avl_pointer_pair_t), pointer, intent(in) :: lst1
type(avl_pointer_pair_t), pointer :: lst2
type(avl_pointer_pair_t), pointer :: new_entry
lst2 => lst1
if (associated (p%right)) lst2 => traverse (p%right, lst2)
allocate (new_entry)
new_entry%p_key => p%key
new_entry%p_data => p%data
new_entry%next => lst2
lst2 => new_entry
if (associated (p%left)) lst2 => traverse (p%left, lst2)
end function traverse
end function avl_pointer_pairs
subroutine avl_write (write_key_data, unit, tree)
procedure(avl_key_data_writer_t) :: write_key_data
integer, intent(in) :: unit
class(avl_tree_t), intent(in) :: tree
character(len = *), parameter :: tab = achar (9)
type(avl_node_t), pointer :: p
p => tree%p
if (.not. associated (p)) then
continue
else
call traverse (p%left, 1, .true.)
call write_key_data (unit, p%key, p%data)
write (unit, '(2A, "depth = ", I0, " bal = ", I0)') tab, tab, 0, p%bal
call traverse (p%right, 1, .false.)
end if
contains
recursive subroutine traverse (p, depth, left)
type(avl_node_t), pointer, intent(in) :: p
integer, value :: depth
logical, value :: left
if (.not. associated (p)) then
continue
else
call traverse (p%left, depth + 1, .true.)
call pad (depth, left)
call write_key_data (unit, p%key, p%data)
write (unit, '(2A, "depth = ", I0, " bal = ", I0)') tab, tab, depth, p%bal
call traverse (p%right, depth + 1, .false.)
end if
end subroutine traverse
subroutine pad (depth, left)
integer, value :: depth
logical, value :: left
integer :: i
do i = 1, depth
write (unit, '(2X)', advance = 'no')
end do
end subroutine pad
end subroutine avl_write
subroutine avl_check (tree)
use, intrinsic :: iso_fortran_env, only: error_unit
class(avl_tree_t), intent(in) :: tree
type(avl_node_t), pointer :: p
integer :: height_L, height_R
p => tree%p
call get_heights (p, height_L, height_R)
call check_heights (height_L, height_R)
contains
recursive subroutine get_heights (p, height_L, height_R)
type(avl_node_t), pointer, intent(in) :: p
integer, intent(out) :: height_L, height_R
integer :: height_LL, height_LR
integer :: height_RL, height_RR
height_L = 0
height_R = 0
if (associated (p)) then
call get_heights (p%left, height_LL, height_LR)
call check_heights (height_LL, height_LR)
height_L = height_LL + height_LR
call get_heights (p%right, height_RL, height_RR)
call check_heights (height_RL, height_RR)
height_R = height_RL + height_RR
end if
end subroutine get_heights
subroutine check_heights (height_L, height_R)
integer, value :: height_L, height_R
if (2 <= abs (height_L - height_R)) then
write (error_unit, '("*** AVL condition violated ***")')
error stop
end if
end subroutine check_heights
end subroutine avl_check
end module avl_trees
program avl_trees_demo
use, intrinsic :: iso_fortran_env, only: output_unit
use, non_intrinsic :: avl_trees
implicit none
integer, parameter :: keys_count = 20
type(avl_tree_t) :: tree
logical :: found
class(*), allocatable :: retval
integer :: the_keys(1:keys_count)
integer :: i, j
do i = 1, keys_count
the_keys(i) = i
end do
call fisher_yates_shuffle (the_keys, keys_count)
call avl_check (tree)
do i = 1, keys_count
call avl_insert (lt, the_keys(i), real (the_keys(i)), tree)
call avl_check (tree)
if (avl_size (tree) /= i) error stop
do j = 1, keys_count
if (avl_contains (lt, the_keys(j), tree) .neqv. (j <= i)) error stop
end do
do j = 1, keys_count
call avl_retrieve (lt, the_keys(j), tree, found, retval)
if (found .neqv. (j <= i)) error stop
if (found) then
! This crazy way to write ‘/=’ is to quell those tiresome
! warnings about using ‘==’ or ‘/=’ with floating point
! numbers. Floating point numbers can represent integers
! *exactly*.
if (0 < abs (real_cast (retval) - real (the_keys(j)))) error stop
end if
if (found) then
block
character(len = 1), parameter :: ch = '*'
!
! Try replacing the data with a character and then
! restoring the number.
!
call avl_insert (lt, the_keys(j), ch, tree)
call avl_retrieve (lt, the_keys(j), tree, found, retval)
if (.not. found) error stop
if (char_cast (retval) /= ch) error stop
call avl_insert (lt, the_keys(j), real (the_keys(j)), tree)
call avl_retrieve (lt, the_keys(j), tree, found, retval)
if (.not. found) error stop
if (0 < abs (real_cast (retval) - real (the_keys(j)))) error stop
end block
end if
end do
end do
write (output_unit, '(70("-"))')
call avl_write (int_real_writer, output_unit, tree)
write (output_unit, '(70("-"))')
call print_contents (output_unit, tree)
write (output_unit, '(70("-"))')
call fisher_yates_shuffle (the_keys, keys_count)
do i = 1, keys_count
call avl_delete (lt, the_keys(i), tree)
call avl_check (tree)
if (avl_size (tree) /= keys_count - i) error stop
! Try deleting a second time.
call avl_delete (lt, the_keys(i), tree)
call avl_check (tree)
if (avl_size (tree) /= keys_count - i) error stop
do j = 1, keys_count
if (avl_contains (lt, the_keys(j), tree) .neqv. (i < j)) error stop
end do
do j = 1, keys_count
call avl_retrieve (lt, the_keys(j), tree, found, retval)
if (found .neqv. (i < j)) error stop
if (found) then
if (0 < abs (real_cast (retval) - real (the_keys(j)))) error stop
end if
end do
end do
contains
subroutine fisher_yates_shuffle (keys, n)
integer, intent(inout) :: keys(*)
integer, intent(in) :: n
integer :: i, j
real :: randnum
integer :: tmp
do i = 1, n - 1
call random_number (randnum)
j = i + floor (randnum * (n - i + 1))
tmp = keys(i)
keys(i) = keys(j)
keys(j) = tmp
end do
end subroutine fisher_yates_shuffle
function int_cast (u) result (v)
class(*), intent(in) :: u
integer :: v
select type (u)
type is (integer)
v = u
class default
! This case is not handled.
error stop
end select
end function int_cast
function real_cast (u) result (v)
class(*), intent(in) :: u
real :: v
select type (u)
type is (real)
v = u
class default
! This case is not handled.
error stop
end select
end function real_cast
function char_cast (u) result (v)
class(*), intent(in) :: u
character(len = 1) :: v
select type (u)
type is (character(*))
v = u
class default
! This case is not handled.
error stop
end select
end function char_cast
function lt (u, v) result (u_lt_v)
class(*), intent(in) :: u, v
logical :: u_lt_v
select type (u)
type is (integer)
select type (v)
type is (integer)
u_lt_v = (u < v)
class default
! This case is not handled.
error stop
end select
class default
! This case is not handled.
error stop
end select
end function lt
subroutine int_real_writer (unit, key, data)
integer, intent(in) :: unit
class(*), intent(in) :: key, data
write (unit, '("(", I0, ", ", F0.1, ")")', advance = 'no') &
& int_cast(key), real_cast(data)
end subroutine int_real_writer
subroutine print_contents (unit, tree)
integer, intent(in) :: unit
class(avl_tree_t), intent(in) :: tree
type(avl_pointer_pair_t), pointer :: ppairs, pp
write (unit, '("tree size = ", I0)') avl_size (tree)
ppairs => avl_pointer_pairs (tree)
pp => ppairs
do while (associated (pp))
write (unit, '("(", I0, ", ", F0.1, ")")') &
& int_cast (pp%p_key), real_cast (pp%p_data)
pp => pp%next
end do
if (associated (ppairs)) deallocate (ppairs)
end subroutine print_contents
end program avl_trees_demo

166
Task/AVL-tree/Go/avl-tree-1.go Normal file
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package avl
// AVL tree adapted from Julienne Walker's presentation at
// http://eternallyconfuzzled.com/tuts/datastructures/jsw_tut_avl.aspx.
// This port uses similar indentifier names.
// The Key interface must be supported by data stored in the AVL tree.
type Key interface {
Less(Key) bool
Eq(Key) bool
}
// Node is a node in an AVL tree.
type Node struct {
Data Key // anything comparable with Less and Eq.
Balance int // balance factor
Link [2]*Node // children, indexed by "direction", 0 or 1.
}
// A little readability function for returning the opposite of a direction,
// where a direction is 0 or 1. Go inlines this.
// Where JW writes !dir, this code has opp(dir).
func opp(dir int) int {
return 1 - dir
}
// single rotation
func single(root *Node, dir int) *Node {
save := root.Link[opp(dir)]
root.Link[opp(dir)] = save.Link[dir]
save.Link[dir] = root
return save
}
// double rotation
func double(root *Node, dir int) *Node {
save := root.Link[opp(dir)].Link[dir]
root.Link[opp(dir)].Link[dir] = save.Link[opp(dir)]
save.Link[opp(dir)] = root.Link[opp(dir)]
root.Link[opp(dir)] = save
save = root.Link[opp(dir)]
root.Link[opp(dir)] = save.Link[dir]
save.Link[dir] = root
return save
}
// adjust valance factors after double rotation
func adjustBalance(root *Node, dir, bal int) {
n := root.Link[dir]
nn := n.Link[opp(dir)]
switch nn.Balance {
case 0:
root.Balance = 0
n.Balance = 0
case bal:
root.Balance = -bal
n.Balance = 0
default:
root.Balance = 0
n.Balance = bal
}
nn.Balance = 0
}
func insertBalance(root *Node, dir int) *Node {
n := root.Link[dir]
bal := 2*dir - 1
if n.Balance == bal {
root.Balance = 0
n.Balance = 0
return single(root, opp(dir))
}
adjustBalance(root, dir, bal)
return double(root, opp(dir))
}
func insertR(root *Node, data Key) (*Node, bool) {
if root == nil {
return &Node{Data: data}, false
}
dir := 0
if root.Data.Less(data) {
dir = 1
}
var done bool
root.Link[dir], done = insertR(root.Link[dir], data)
if done {
return root, true
}
root.Balance += 2*dir - 1
switch root.Balance {
case 0:
return root, true
case 1, -1:
return root, false
}
return insertBalance(root, dir), true
}
// Insert a node into the AVL tree.
// Data is inserted even if other data with the same key already exists.
func Insert(tree **Node, data Key) {
*tree, _ = insertR(*tree, data)
}
func removeBalance(root *Node, dir int) (*Node, bool) {
n := root.Link[opp(dir)]
bal := 2*dir - 1
switch n.Balance {
case -bal:
root.Balance = 0
n.Balance = 0
return single(root, dir), false
case bal:
adjustBalance(root, opp(dir), -bal)
return double(root, dir), false
}
root.Balance = -bal
n.Balance = bal
return single(root, dir), true
}
func removeR(root *Node, data Key) (*Node, bool) {
if root == nil {
return nil, false
}
if root.Data.Eq(data) {
switch {
case root.Link[0] == nil:
return root.Link[1], false
case root.Link[1] == nil:
return root.Link[0], false
}
heir := root.Link[0]
for heir.Link[1] != nil {
heir = heir.Link[1]
}
root.Data = heir.Data
data = heir.Data
}
dir := 0
if root.Data.Less(data) {
dir = 1
}
var done bool
root.Link[dir], done = removeR(root.Link[dir], data)
if done {
return root, true
}
root.Balance += 1 - 2*dir
switch root.Balance {
case 1, -1:
return root, true
case 0:
return root, false
}
return removeBalance(root, dir)
}
// Remove a single item from an AVL tree.
// If key does not exist, function has no effect.
func Remove(tree **Node, data Key) {
*tree, _ = removeR(*tree, data)
}

43
Task/AVL-tree/Go/avl-tree-2.go Normal file
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package main
import (
"encoding/json"
"fmt"
"log"
"avl"
)
type intKey int
// satisfy avl.Key
func (k intKey) Less(k2 avl.Key) bool { return k < k2.(intKey) }
func (k intKey) Eq(k2 avl.Key) bool { return k == k2.(intKey) }
// use json for cheap tree visualization
func dump(tree *avl.Node) {
b, err := json.MarshalIndent(tree, "", " ")
if err != nil {
log.Fatal(err)
}
fmt.Println(string(b))
}
func main() {
var tree *avl.Node
fmt.Println("Empty tree:")
dump(tree)
fmt.Println("\nInsert test:")
avl.Insert(&tree, intKey(3))
avl.Insert(&tree, intKey(1))
avl.Insert(&tree, intKey(4))
avl.Insert(&tree, intKey(1))
avl.Insert(&tree, intKey(5))
dump(tree)
fmt.Println("\nRemove test:")
avl.Remove(&tree, intKey(3))
avl.Remove(&tree, intKey(1))
dump(tree)
}

75
Task/AVL-tree/Haskell/avl-tree.hs Normal file
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data Tree a
= Leaf
| Node
Int
(Tree a)
a
(Tree a)
deriving (Show, Eq)
foldTree :: Ord a => [a] -> Tree a
foldTree = foldr insert Leaf
height :: Tree a -> Int
height Leaf = -1
height (Node h _ _ _) = h
depth :: Tree a -> Tree a -> Int
depth a b = succ (max (height a) (height b))
insert :: Ord a => a -> Tree a -> Tree a
insert v Leaf = Node 1 Leaf v Leaf
insert v t@(Node n left v_ right)
| v_ < v = rotate $ Node n left v_ (insert v right)
| v_ > v = rotate $ Node n (insert v left) v_ right
| otherwise = t
max_ :: Ord a => Tree a -> Maybe a
max_ Leaf = Nothing
max_ (Node _ _ v right) =
case right of
Leaf -> Just v
_ -> max_ right
delete :: Ord a => a -> Tree a -> Tree a
delete _ Leaf = Leaf
delete x (Node h left v right)
| x == v =
maybe left (rotate . (Node h left <*> (`delete` right))) (max_ right)
| x > v = rotate $ Node h left v (delete x right)
| x < v = rotate $ Node h (delete x left) v right
rotate :: Tree a -> Tree a
rotate Leaf = Leaf
rotate (Node h (Node lh ll lv lr) v r)
-- Left Left.
| lh - height r > 1 && height ll - height lr > 0 =
Node lh ll lv (Node (depth r lr) lr v r)
rotate (Node h l v (Node rh rl rv rr))
-- Right Right.
| rh - height l > 1 && height rr - height rl > 0 =
Node rh (Node (depth l rl) l v rl) rv rr
rotate (Node h (Node lh ll lv (Node rh rl rv rr)) v r)
-- Left Right.
| lh - height r > 1 =
Node h (Node (rh + 1) (Node (lh - 1) ll lv rl) rv rr) v r
rotate (Node h l v (Node rh (Node lh ll lv lr) rv rr))
-- Right Left.
| rh - height l > 1 =
Node h l v (Node (lh + 1) ll lv (Node (rh - 1) lr rv rr))
rotate (Node h l v r) =
-- Re-weighting.
let (l_, r_) = (rotate l, rotate r)
in Node (depth l_ r_) l_ v r_
draw :: Show a => Tree a -> String
draw t = '\n' : draw_ t 0 <> "\n"
where
draw_ Leaf _ = []
draw_ (Node h l v r) d = draw_ r (d + 1) <> node <> draw_ l (d + 1)
where
node = padding d <> show (v, h) <> "\n"
padding n = replicate (n * 4) ' '
main :: IO ()
main = putStr $ draw $ foldTree [1 .. 31]

90
Task/AVL-tree/J/avl-tree.j Normal file
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insert=: {{
X=.1 {::2{.x,x NB. middle element of x (don't fail on empty x)
Y=.1 {::2{.y,y NB. middle element of y (don't fail on empty y)
select.#y
case.0 do.x NB. y is an empty node
case.1 do. NB. y is a leaf node
select.*Y-X
case._1 do.a:,y;<x
case. 0 do.y
case. 1 do.x;y;a:
end.
case.3 do. NB. y is a parent node
select.*Y-X
case._1 do.balance (}:y),<x insert 2{::y
case. 0 do.y
case. 1 do.balance (x insert 0{::y);}.y
end.
end.
}}
delete=: {{
select.#y
case.0 do.y
case.1 do.y-.x
case.3 do.
select.*(1{::y)-x
case._1 do.balance (}:y),<x delete 2{::y
case. 0 do.balance (0{::y) insert 2{::y
case. 1 do.balance (x delete 0{::y);}.y
end.
end.
}}
lookup=: {{
select.#y
case.0 do.y
case.1 do.if.x=y do.y else.'' end.
case.3 do.
select.*(1{::y)-x
case._1 do.x lookup 2{::y
case. 0 do.y
case. 1 do.x lookup 0{::y
end.
end.
}}
clean=: {{
's0 x s2'=. #every y
if.*/0=s0,s2 do. 1{:: y NB. degenerate to leaf
else. y end.
}}
balance=: {{
if. 2>#y do. y return.end. NB. leaf or empty
's0 x s2'=. ,#every y
if. */0=s0,s2 do. 1{:: y return.end. NB. degenerate to leaf
'l0 x l2'=. L.every y
if. 2>|l2-l0 do. y return.end. NB. adequately balanced
if. l2>l0 do.
'l20 x l22'=. L.every 2{::y
if. l22 >: l20 do. rotLeft y
else. rotRightLeft y end.
else.
'l00 x l02'=. L.every 0{::y
if. l00 >: l02 do. rotRight y
else. rotLeftRight y end.
end.
}}
rotLeft=: {{
't0 t1 t2'=. y
't20 t21 t22'=. t2
(clean t0;t1;<t20);t21;<t22
}}
rotRight=: {{
't0 t1 t2'=. y
't00 t01 t02'=. t0
t00;t01;<clean t02;t1;<t2
}}
rotRightLeft=: {{
't0 t1 t2'=. y
rotLeft t0;t1;<rotRight t2
}}
rotLeftRight=: {{
't0 t1 t2'=. y
rotRight (rotLeft t0);t1;<t2
}}

218
Task/AVL-tree/Java/avl-tree.java Normal file
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public class AVLtree {
private Node root;
private static class Node {
private int key;
private int balance;
private int height;
private Node left;
private Node right;
private Node parent;
Node(int key, Node parent) {
this.key = key;
this.parent = parent;
}
}
public boolean insert(int key) {
if (root == null) {
root = new Node(key, null);
return true;
}
Node n = root;
while (true) {
if (n.key == key)
return false;
Node parent = n;
boolean goLeft = n.key > key;
n = goLeft ? n.left : n.right;
if (n == null) {
if (goLeft) {
parent.left = new Node(key, parent);
} else {
parent.right = new Node(key, parent);
}
rebalance(parent);
break;
}
}
return true;
}
private void delete(Node node) {
if (node.left == null && node.right == null) {
if (node.parent == null) {
root = null;
} else {
Node parent = node.parent;
if (parent.left == node) {
parent.left = null;
} else {
parent.right = null;
}
rebalance(parent);
}
return;
}
if (node.left != null) {
Node child = node.left;
while (child.right != null) child = child.right;
node.key = child.key;
delete(child);
} else {
Node child = node.right;
while (child.left != null) child = child.left;
node.key = child.key;
delete(child);
}
}
public void delete(int delKey) {
if (root == null)
return;
Node child = root;
while (child != null) {
Node node = child;
child = delKey >= node.key ? node.right : node.left;
if (delKey == node.key) {
delete(node);
return;
}
}
}
private void rebalance(Node n) {
setBalance(n);
if (n.balance == -2) {
if (height(n.left.left) >= height(n.left.right))
n = rotateRight(n);
else
n = rotateLeftThenRight(n);
} else if (n.balance == 2) {
if (height(n.right.right) >= height(n.right.left))
n = rotateLeft(n);
else
n = rotateRightThenLeft(n);
}
if (n.parent != null) {
rebalance(n.parent);
} else {
root = n;
}
}
private Node rotateLeft(Node a) {
Node b = a.right;
b.parent = a.parent;
a.right = b.left;
if (a.right != null)
a.right.parent = a;
b.left = a;
a.parent = b;
if (b.parent != null) {
if (b.parent.right == a) {
b.parent.right = b;
} else {
b.parent.left = b;
}
}
setBalance(a, b);
return b;
}
private Node rotateRight(Node a) {
Node b = a.left;
b.parent = a.parent;
a.left = b.right;
if (a.left != null)
a.left.parent = a;
b.right = a;
a.parent = b;
if (b.parent != null) {
if (b.parent.right == a) {
b.parent.right = b;
} else {
b.parent.left = b;
}
}
setBalance(a, b);
return b;
}
private Node rotateLeftThenRight(Node n) {
n.left = rotateLeft(n.left);
return rotateRight(n);
}
private Node rotateRightThenLeft(Node n) {
n.right = rotateRight(n.right);
return rotateLeft(n);
}
private int height(Node n) {
if (n == null)
return -1;
return n.height;
}
private void setBalance(Node... nodes) {
for (Node n : nodes) {
reheight(n);
n.balance = height(n.right) - height(n.left);
}
}
public void printBalance() {
printBalance(root);
}
private void printBalance(Node n) {
if (n != null) {
printBalance(n.left);
System.out.printf("%s ", n.balance);
printBalance(n.right);
}
}
private void reheight(Node node) {
if (node != null) {
node.height = 1 + Math.max(height(node.left), height(node.right));
}
}
public static void main(String[] args) {
AVLtree tree = new AVLtree();
System.out.println("Inserting values 1 to 10");
for (int i = 1; i < 10; i++)
tree.insert(i);
System.out.print("Printing balance: ");
tree.printBalance();
}
}

91
Task/AVL-tree/JavaScript/avl-tree-1.js Normal file
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function tree(less, val, more) {
return {
depth: 1+Math.max(less.depth, more.depth),
less: less,
val: val,
more: more,
};
}
function node(val) {
return tree({depth: 0}, val, {depth: 0});
}
function insert(x,y) {
if (0 == y.depth) return x;
if (0 == x.depth) return y;
if (1 == x.depth && 1 == y.depth) {
switch (Math.sign(y.val)-x.val) {
case -1: return tree(y, x.val, {depth: 0});
case 0: return y;
case 1: return tree(x, y.val, {depth: 0});
}
}
switch (Math.sign(y.val-x.val)) {
case -1: return balance(insert(x.less, y), x.val, x.more);
case 0: return balance(insert(x.less, y.less), x.val, insert(x.more, y.more));
case 1: return balance(x.less. x.val, insert(x.more, y));
}
}
function balance(less,val,more) {
if (2 > Math.abs(less.depth-more.depth))
return tree(less,val,more);
if (more.depth > less.depth) {
if (more.more.depth >= more.less.depth) {
// 'more' was heavy
return moreHeavy(less, val, more);
} else {
return moreHeavy(less,val,lessHeavy(more.less, more.val, more.more));
}
} else {
if(less.less.depth >= less.more.depth) {
return lessHeavy(less, val, more);
} else {
return lessHeavy(moreHeavy(less.less, less.val, less.more), val, more);
}
}
}
function moreHeavy(less,val,more) {
return tree(tree(less,val,more.less), more.val, more.more)
}
function lessHeavy(less,val,more) {
return tree(less.less, less.val, tree(less.more, val, more));
}
function remove(val, y) {
switch (y.depth) {
case 0: return y;
case 1:
if (val == y.val) {
return y.less;
} else {
return y;
}
default:
switch (Math.sign(y.val - val)) {
case -1: return balance(y.less, y.val, remove(val, y.more));
case 0: return insert(y.less, y.more);
case 1: return balance(remove(val, y.less), y.val, y.more)
}
}
}
function lookup(val, y) {
switch (y.depth) {
case 0: return y;
case 1: if (val == y.val) {
return y;
} else {
return {depth: 0};
}
default:
switch (Math.sign(y.val-val)) {
case -1: return lookup(val, y.more);
case 0: return y;
case 1: return lookup(val, y.less);
}
}
}

20
Task/AVL-tree/JavaScript/avl-tree-2.js Normal file
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function dumptree(t) {
switch (t.depth) {
case 0: return '';
case 1: return t.val;
default: return '('+dumptree(t.less)+','+t.val+','+dumptree(t.more)+')';
}
}
function example() {
let t= node(0);
for (let j= 1; j<20; j++) {
t= insert(node(j), t);
}
console.log(dumptree(t));
t= remove(2, t);
console.log(dumptree(t));
console.log(dumptree(lookup(5, t)));
console.log(dumptree(remove(5, t)));
}
example();

180
Task/AVL-tree/Julia/avl-tree.julia Normal file
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module AVLTrees
import Base.print
export AVLNode, AVLTree, insert, deletekey, deletevalue, findnodebykey, findnodebyvalue, allnodes
@enum Direction LEFT RIGHT
avlhash(x) = Int32(hash(x) & 0xfffffff)
const MIDHASH = Int32(div(0xfffffff, 2))
mutable struct AVLNode{T}
value::T
key::Int32
balance::Int32
left::Union{AVLNode, Nothing}
right::Union{AVLNode, Nothing}
parent::Union{AVLNode, Nothing}
end
AVLNode(v::T, b, l, r, p) where T <: Real = AVLNode(v, avlhash(v), Int32(b), l, r, p)
AVLNode(v::T, h, b::Int64, l, r, p) where T <: Real = AVLNode(v, h, Int32(b), l, r, p)
AVLNode(v::T) where T <: Real = AVLNode(v, avlhash(v), Int32(0), nothing, nothing, nothing)
AVLTree(typ::Type) = AVLNode(typ(0), MIDHASH, Int32(0), nothing, nothing, nothing)
const MaybeAVL = Union{AVLNode, Nothing}
height(node::MaybeAVL) = (node == nothing) ? 0 : 1 + max(height(node.right), height(node.left))
function insert(node, value)
if node == nothing
node = AVLNode(value)
return true
end
key, n, parent::MaybeAVL = avlhash(value), node, nothing
while true
if n.key == key
return false
end
parent = n
ngreater = n.key > key
n = ngreater ? n.left : n.right
if n == nothing
if ngreater
parent.left = AVLNode(value, key, 0, nothing, nothing, parent)
else
parent.right = AVLNode(value, key, 0, nothing, nothing, parent)
end
rebalance(parent)
break
end
end
return true
end
function deletekey(node, delkey)
node == nothing && return nothing
n, parent = MaybeAVL(node), MaybeAVL(node)
delnode, child = MaybeAVL(nothing), MaybeAVL(node)
while child != nothing
parent, n = n, child
child = delkey >= n.key ? n.right : n.left
if delkey == n.key
delnode = n
end
end
if delnode != nothing
delnode.key = n.key
delnode.value = n.value
child = (n.left != nothing) ? n.left : n.right
if node.key == delkey
root = child
else
if parent.left == n
parent.left = child
else
parent.right = child
end
rebalance(parent)
end
end
end
deletevalue(node, val) = deletekey(node, avlhash(val))
function rebalance(node::MaybeAVL)
node == nothing && return nothing
setbalance(node)
if node.balance < -1
if height(node.left.left) >= height(node.left.right)
node = rotate(node, RIGHT)
else
node = rotatetwice(node, LEFT, RIGHT)
end
elseif node.balance > 1
if node.right != nothing && height(node.right.right) >= height(node.right.left)
node = rotate(node, LEFT)
else
node = rotatetwice(node, RIGHT, LEFT)
end
end
if node != nothing && node.parent != nothing
rebalance(node.parent)
end
end
function rotate(a, direction)
(a == nothing || a.parent == nothing) && return nothing
b = direction == LEFT ? a.right : a.left
b == nothing && return
b.parent = a.parent
if direction == LEFT
a.right = b.left
else
a.left = b.right
end
if a.right != nothing
a.right.parent = a
end
if direction == LEFT
b.left = a
else
b.right = a
end
a.parent = b
if b.parent != nothing
if b.parent.right == a
b.parent.right = b
else
b.parent.left = b
end
end
setbalance([a, b])
return b
end
function rotatetwice(n, dir1, dir2)
n.left = rotate(n.left, dir1)
rotate(n, dir2)
end
setbalance(n::AVLNode) = begin n.balance = height(n.right) - height(n.left) end
setbalance(n::Nothing) = 0
setbalance(nodes::Vector) = for n in nodes setbalance(n) end
function findnodebykey(node, key)
result::MaybeAVL = node == nothing ? nothing : node.key == key ? node :
node.left != nothing && (n = findbykey(n, key) != nothing) ? n :
node.right != nothing ? findbykey(node.right, key) : nothing
return result
end
findnodebyvalue(node, val) = findnodebykey(node, avlhash(v))
function allnodes(node)
result = AVLNode[]
if node != nothing
append!(result, allnodes(node.left))
if node.key != MIDHASH
push!(result, node)
end
append!(result, node.right)
end
return result
end
function Base.print(io::IO, n::MaybeAVL)
if n != nothing
n.left != nothing && print(io, n.left)
print(io, n.key == MIDHASH ? "<ROOT> " : "<$(n.key):$(n.value):$(n.balance)> ")
n.right != nothing && print(io, n.right)
end
end
end # module
using .AVLTrees
const tree = AVLTree(Int)
println("Inserting 10 values.")
foreach(x -> insert(tree, x), rand(collect(1:80), 10))
println("Printing tree after insertion: ")
println(tree)

175
Task/AVL-tree/Kotlin/avl-tree.kotlin Normal file
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class AvlTree {
private var root: Node? = null
private class Node(var key: Int, var parent: Node?) {
var balance: Int = 0
var left : Node? = null
var right: Node? = null
}
fun insert(key: Int): Boolean {
if (root == null)
root = Node(key, null)
else {
var n: Node? = root
var parent: Node
while (true) {
if (n!!.key == key) return false
parent = n
val goLeft = n.key > key
n = if (goLeft) n.left else n.right
if (n == null) {
if (goLeft)
parent.left = Node(key, parent)
else
parent.right = Node(key, parent)
rebalance(parent)
break
}
}
}
return true
}
fun delete(delKey: Int) {
if (root == null) return
var n: Node? = root
var parent: Node? = root
var delNode: Node? = null
var child: Node? = root
while (child != null) {
parent = n
n = child
child = if (delKey >= n.key) n.right else n.left
if (delKey == n.key) delNode = n
}
if (delNode != null) {
delNode.key = n!!.key
child = if (n.left != null) n.left else n.right
if (0 == root!!.key.compareTo(delKey)) {
root = child
if (null != root) {
root!!.parent = null
}
} else {
if (parent!!.left == n)
parent.left = child
else
parent.right = child
if (null != child) {
child.parent = parent
}
rebalance(parent)
}
}
private fun rebalance(n: Node) {
setBalance(n)
var nn = n
if (nn.balance == -2)
if (height(nn.left!!.left) >= height(nn.left!!.right))
nn = rotateRight(nn)
else
nn = rotateLeftThenRight(nn)
else if (nn.balance == 2)
if (height(nn.right!!.right) >= height(nn.right!!.left))
nn = rotateLeft(nn)
else
nn = rotateRightThenLeft(nn)
if (nn.parent != null) rebalance(nn.parent!!)
else root = nn
}
private fun rotateLeft(a: Node): Node {
val b: Node? = a.right
b!!.parent = a.parent
a.right = b.left
if (a.right != null) a.right!!.parent = a
b.left = a
a.parent = b
if (b.parent != null) {
if (b.parent!!.right == a)
b.parent!!.right = b
else
b.parent!!.left = b
}
setBalance(a, b)
return b
}
private fun rotateRight(a: Node): Node {
val b: Node? = a.left
b!!.parent = a.parent
a.left = b.right
if (a.left != null) a.left!!.parent = a
b.right = a
a.parent = b
if (b.parent != null) {
if (b.parent!!.right == a)
b.parent!!.right = b
else
b.parent!!.left = b
}
setBalance(a, b)
return b
}
private fun rotateLeftThenRight(n: Node): Node {
n.left = rotateLeft(n.left!!)
return rotateRight(n)
}
private fun rotateRightThenLeft(n: Node): Node {
n.right = rotateRight(n.right!!)
return rotateLeft(n)
}
private fun height(n: Node?): Int {
if (n == null) return -1
return 1 + Math.max(height(n.left), height(n.right))
}
private fun setBalance(vararg nodes: Node) {
for (n in nodes) n.balance = height(n.right) - height(n.left)
}
fun printKey() {
printKey(root)
println()
}
private fun printKey(n: Node?) {
if (n != null) {
printKey(n.left)
print("${n.key} ")
printKey(n.right)
}
}
fun printBalance() {
printBalance(root)
println()
}
private fun printBalance(n: Node?) {
if (n != null) {
printBalance(n.left)
print("${n.balance} ")
printBalance(n.right)
}
}
}
fun main(args: Array<String>) {
val tree = AvlTree()
println("Inserting values 1 to 10")
for (i in 1..10) tree.insert(i)
print("Printing key : ")
tree.printKey()
print("Printing balance : ")
tree.printBalance()
}

7
Task/AVL-tree/Logtalk/avl-tree.logtalk Normal file
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:- object(avltree,
implements(dictionaryp),
extends(term)).
% ... lots of elision ...
:- end_object.

132
Task/AVL-tree/Lua/avl-tree.lua Normal file
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AVL={balance=0}
AVL.__mt={__index = AVL}
function AVL:new(list)
local o={}
setmetatable(o, AVL.__mt)
for _,v in ipairs(list or {}) do
o=o:insert(v)
end
return o
end
function AVL:rebalance()
local rotated=false
if self.balance>1 then
if self.right.balance<0 then
self.right, self.right.left.right, self.right.left = self.right.left, self.right, self.right.left.right
self.right.right.balance=self.right.balance>-1 and 0 or 1
self.right.balance=self.right.balance>0 and 2 or 1
end
self, self.right.left, self.right = self.right, self, self.right.left
self.left.balance=1-self.balance
self.balance=self.balance==0 and -1 or 0
rotated=true
elseif self.balance<-1 then
if self.left.balance>0 then
self.left, self.left.right.left, self.left.right = self.left.right, self.left, self.left.right.left
self.left.left.balance=self.left.balance<1 and 0 or -1
self.left.balance=self.left.balance<0 and -2 or -1
end
self, self.left.right, self.left = self.left, self, self.left.right
self.right.balance=-1-self.balance
self.balance=self.balance==0 and 1 or 0
rotated=true
end
return self,rotated
end
function AVL:insert(v)
if not self.value then
self.value=v
self.balance=0
return self,1
end
local grow
if v==self.value then
return self,0
elseif v<self.value then
if not self.left then self.left=self:new() end
self.left,grow=self.left:insert(v)
self.balance=self.balance-grow
else
if not self.right then self.right=self:new() end
self.right,grow=self.right:insert(v)
self.balance=self.balance+grow
end
self,rotated=self:rebalance()
return self, (rotated or self.balance==0) and 0 or grow
end
function AVL:delete_move(dir,other,mul)
if self[dir] then
local sb2,v
self[dir], sb2, v=self[dir]:delete_move(dir,other,mul)
self.balance=self.balance+sb2*mul
self,sb2=self:rebalance()
return self,(sb2 or self.balance==0) and -1 or 0,v
else
return self[other],-1,self.value
end
end
function AVL:delete(v,isSubtree)
local grow=0
if v==self.value then
local v
if self.balance>0 then
self.right,grow,v=self.right:delete_move("left","right",-1)
elseif self.left then
self.left,grow,v=self.left:delete_move("right","left",1)
grow=-grow
else
return not isSubtree and AVL:new(),-1
end
self.value=v
self.balance=self.balance+grow
elseif v<self.value and self.left then
self.left,grow=self.left:delete(v,true)
self.balance=self.balance-grow
elseif v>self.value and self.right then
self.right,grow=self.right:delete(v,true)
self.balance=self.balance+grow
else
return self,0
end
self,rotated=self:rebalance()
return self, grow~=0 and (rotated or self.balance==0) and -1 or 0
end
-- output functions
function AVL:toList(list)
if not self.value then return {} end
list=list or {}
if self.left then self.left:toList(list) end
list[#list+1]=self.value
if self.right then self.right:toList(list) end
return list
end
function AVL:dump(depth)
if not self.value then return end
depth=depth or 0
if self.right then self.right:dump(depth+1) end
print(string.rep(" ",depth)..self.value.." ("..self.balance..")")
if self.left then self.left:dump(depth+1) end
end
-- test
local test=AVL:new{1,10,5,15,20,3,5,14,7,13,2,8,3,4,5,10,9,8,7}
test:dump()
print("\ninsert 17:")
test=test:insert(17)
test:dump()
print("\ndelete 10:")
test=test:delete(10)
test:dump()
print("\nlist:")
print(unpack(test:toList()))

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#[ AVL tree adapted from Julienne Walker's presentation at
http://eternallyconfuzzled.com/tuts/datastructures/jsw_tut_avl.aspx.
Uses bounded recursive versions for insertion and deletion.
]#
type
# Objects strored in the tree must be comparable.
Comparable = concept x, y
(x == y) is bool
(x < y) is bool
# Direction used to select a child.
Direction = enum Left, Right
# Description of the tree node.
Node[T: Comparable] = ref object
data: T # Payload.
balance: range[-2..2] # Balance factor (bounded).
links: array[Direction, Node[T]] # Children.
# Description of a tree.
AvlTree[T: Comparable] = object
root: Node[T]
#---------------------------------------------------------------------------------------------------
func opp(dir: Direction): Direction {.inline.} =
## Return the opposite of a direction.
Direction(1 - ord(dir))
#---------------------------------------------------------------------------------------------------
func single(root: Node; dir: Direction): Node =
## Single rotation.
result = root.links[opp(dir)]
root.links[opp(dir)] = result.links[dir]
result.links[dir] = root
#---------------------------------------------------------------------------------------------------
func double(root: Node; dir: Direction): Node =
## Double rotation.
let save = root.links[opp(dir)].links[dir]
root.links[opp(dir)].links[dir] = save.links[opp(dir)]
save.links[opp(dir)] = root.links[opp(dir)]
root.links[opp(dir)] = save
result = root.links[opp(dir)]
root.links[opp(dir)] = result.links[dir]
result.links[dir] = root
#---------------------------------------------------------------------------------------------------
func adjustBalance(root: Node; dir: Direction; balance: int) =
## Adjust balance factors after double rotation.
let node1 = root.links[dir]
let node2 = node1.links[opp(dir)]
if node2.balance == 0:
root.balance = 0
node1.balance = 0
elif node2.balance == balance:
root.balance = -balance
node1.balance = 0
else:
root.balance = 0
node1.balance = balance
node2.balance = 0
#---------------------------------------------------------------------------------------------------
func insertBalance(root: Node; dir: Direction): Node =
## Rebalancing after an insertion.
let node = root.links[dir]
let balance = 2 * ord(dir) - 1
if node.balance == balance:
root.balance = 0
node.balance = 0
result = root.single(opp(dir))
else:
root.adjustBalance(dir, balance)
result = root.double(opp(dir))
#---------------------------------------------------------------------------------------------------
func insertR(root: Node; data: root.T): tuple[node: Node, done: bool] =
## Insert data (recursive way).
if root.isNil:
return (Node(data: data), false)
let dir = if root.data < data: Right else: Left
var done: bool
(root.links[dir], done) = root.links[dir].insertR(data)
if done:
return (root, true)
inc root.balance, 2 * ord(dir) - 1
result = case root.balance
of 0: (root, true)
of -1, 1: (root, false)
else: (root.insertBalance(dir), true)
#---------------------------------------------------------------------------------------------------
func removeBalance(root: Node; dir: Direction): tuple[node: Node, done: bool] =
## Rebalancing after a deletion.
let node = root.links[opp(dir)]
let balance = 2 * ord(dir) - 1
if node.balance == -balance:
root.balance = 0
node.balance = 0
result = (root.single(dir), false)
elif node.balance == balance:
root.adjustBalance(opp(dir), -balance)
result = (root.double(dir), false)
else:
root.balance = -balance
node.balance = balance
result = (root.single(dir), true)
#---------------------------------------------------------------------------------------------------
func removeR(root: Node; data: root.T): tuple[node: Node, done: bool] =
## Remove data (recursive way).
if root.isNil:
return (nil, false)
var data = data
if root.data == data:
if root.links[Left].isNil:
return (root.links[Right], false)
if root.links[Right].isNil:
return (root.links[Left], false)
var heir = root.links[Left]
while not heir.links[Right].isNil:
heir = heir.links[Right]
root.data = heir.data
data = heir.data
let dir = if root.data < data: Right else: Left
var done: bool
(root.links[dir], done) = root.links[dir].removeR(data)
if done:
return (root, true)
dec root.balance, 2 * ord(dir) - 1
result = case root.balance
of -1, 1: (root, true)
of 0: (root, false)
else: root.removeBalance(dir)
#---------------------------------------------------------------------------------------------------
func insert(tree: var AvlTree; data: tree.T) =
## Insert data in an AVL tree.
tree.root = tree.root.insertR(data).node
#---------------------------------------------------------------------------------------------------
func remove(tree: var AvlTree; data: tree.T) =
## Remove data from an AVL tree.
tree.root = tree.root.removeR(data).node
#———————————————————————————————————————————————————————————————————————————————————————————————————
import json
var tree: AvlTree[int]
echo pretty(%tree)
echo "Insert test:"
tree.insert(3)
tree.insert(1)
tree.insert(4)
tree.insert(1)
tree.insert(5)
echo pretty(%tree)
echo ""
echo "Remove test:"
tree.remove(3)
tree.remove(1)
echo pretty(%tree)

283
Task/AVL-tree/Objeck/avl-tree.objeck Normal file
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class AVLNode {
@key : Int;
@balance : Int;
@height : Int;
@left : AVLNode;
@right : AVLNode;
@above : AVLNode;
New(key : Int, above : AVLNode) {
@key := key;
@above := above;
}
method : public : GetKey() ~ Int {
return @key;
}
method : public : GetLeft() ~ AVLNode {
return @left;
}
method : public : GetRight() ~ AVLNode {
return @right;
}
method : public : GetAbove() ~ AVLNode {
return @above;
}
method : public : GetBalance() ~ Int {
return @balance;
}
method : public : GetHeight() ~ Int {
return @height;
}
method : public : SetBalance(balance : Int) ~ Nil {
@balance := balance;
}
method : public : SetHeight(height : Int) ~ Nil {
@height := height;
}
method : public : SetAbove(above : AVLNode) ~ Nil {
@above := above;
}
method : public : SetLeft(left : AVLNode) ~ Nil {
@left := left;
}
method : public : SetRight(right : AVLNode) ~ Nil {
@right := right;
}
method : public : SetKey(key : Int) ~ Nil {
@key := key;
}
}
class AVLTree {
@root : AVLNode;
New() {}
method : public : Insert(key : Int) ~ Bool {
if(@root = Nil) {
@root := AVLNode->New( key, Nil);
return true;
};
n := @root;
while(true) {
if(n->GetKey() = key) {
return false;
};
parent := n;
goLeft := n->GetKey() > key;
n := goLeft ? n->GetLeft() : n->GetRight();
if(n = Nil) {
if(goLeft) {
parent->SetLeft(AVLNode->New( key, parent));
} else {
parent->SetRight(AVLNode->New( key, parent));
};
Rebalance(parent);
break;
};
};
return true;
}
method : Delete(node : AVLNode) ~ Nil {
if (node->GetLeft() = Nil & node->GetRight() = Nil) {
if (node ->GetAbove() = Nil) {
@root := Nil;
} else {
parent := node ->GetAbove();
if (parent->GetLeft() = node) {
parent->SetLeft(Nil);
} else {
parent->SetRight(Nil);
};
Rebalance(parent);
};
return;
};
if (node->GetLeft() <> Nil) {
child := node->GetLeft();
while (child->GetRight() <> Nil) {
child := child->GetRight();
};
node->SetKey(child->GetKey());
Delete(child);
} else {
child := node->GetRight();
while (child->GetLeft() <> Nil) {
child := child->GetLeft();
};
node->SetKey(child->GetKey());
Delete(child);
};
}
method : public : Delete(delKey : Int) ~ Nil {
if (@root = Nil) {
return;
};
child := @root;
while (child <> Nil) {
node := child;
child := delKey >= node->GetKey() ? node->GetRight() : node->GetLeft();
if (delKey = node->GetKey()) {
Delete(node);
return;
};
};
}
method : Rebalance(n : AVLNode) ~ Nil {
SetBalance(n);
if (n->GetBalance() = -2) {
if (Height(n->GetLeft()->GetLeft()) >= Height(n->GetLeft()->GetRight())) {
n := RotateRight(n);
}
else {
n := RotateLeftThenRight(n);
};
} else if (n->GetBalance() = 2) {
if(Height(n->GetRight()->GetRight()) >= Height(n->GetRight()->GetLeft())) {
n := RotateLeft(n);
}
else {
n := RotateRightThenLeft(n);
};
};
if(n->GetAbove() <> Nil) {
Rebalance(n->GetAbove());
} else {
@root := n;
};
}
method : RotateLeft(a : AVLNode) ~ AVLNode {
b := a->GetRight();
b->SetAbove(a->GetAbove());
a->SetRight(b->GetLeft());
if(a->GetRight() <> Nil) {
a->GetRight()->SetAbove(a);
};
b->SetLeft(a);
a->SetAbove(b);
if (b->GetAbove() <> Nil) {
if (b->GetAbove()->GetRight() = a) {
b->GetAbove()->SetRight(b);
} else {
b->GetAbove()->SetLeft(b);
};
};
SetBalance(a);
SetBalance(b);
return b;
}
method : RotateRight(a : AVLNode) ~ AVLNode {
b := a->GetLeft();
b->SetAbove(a->GetAbove());
a->SetLeft(b->GetRight());
if (a->GetLeft() <> Nil) {
a->GetLeft()->SetAbove(a);
};
b->SetRight(a);
a->SetAbove(b);
if (b->GetAbove() <> Nil) {
if (b->GetAbove()->GetRight() = a) {
b->GetAbove()->SetRight(b);
} else {
b->GetAbove()->SetLeft(b);
};
};
SetBalance(a);
SetBalance(b);
return b;
}
method : RotateLeftThenRight(n : AVLNode) ~ AVLNode {
n->SetLeft(RotateLeft(n->GetLeft()));
return RotateRight(n);
}
method : RotateRightThenLeft(n : AVLNode) ~ AVLNode {
n->SetRight(RotateRight(n->GetRight()));
return RotateLeft(n);
}
method : SetBalance(n : AVLNode) ~ Nil {
Reheight(n);
n->SetBalance(Height(n->GetRight()) - Height(n->GetLeft()));
}
method : Reheight(node : AVLNode) ~ Nil {
if(node <> Nil) {
node->SetHeight(1 + Int->Max(Height(node->GetLeft()), Height(node->GetRight())));
};
}
method : Height(n : AVLNode) ~ Int {
if(n = Nil) {
return -1;
};
return n->GetHeight();
}
method : public : PrintBalance() ~ Nil {
PrintBalance(@root);
}
method : PrintBalance(n : AVLNode) ~ Nil {
if (n <> Nil) {
PrintBalance(n->GetLeft());
balance := n->GetBalance();
"{$balance} "->Print();
PrintBalance(n->GetRight());
};
}
}
class Test {
function : Main(args : String[]) ~ Nil {
tree := AVLTree->New();
"Inserting values 1 to 10"->PrintLine();
for(i := 1; i < 10; i+=1;) {
tree->Insert(i);
};
"Printing balance: "->Print();
tree->PrintBalance();
}
}

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@implementation AVLTree
-(BOOL)insertWithKey:(NSInteger)key {
if (self.root == nil) {
self.root = [[AVLTreeNode alloc]initWithKey:key andParent:nil];
} else {
AVLTreeNode *n = self.root;
AVLTreeNode *parent;
while (true) {
if (n.key == key) {
return false;
}
parent = n;
BOOL goLeft = n.key > key;
n = goLeft ? n.left : n.right;
if (n == nil) {
if (goLeft) {
parent.left = [[AVLTreeNode alloc]initWithKey:key andParent:parent];
} else {
parent.right = [[AVLTreeNode alloc]initWithKey:key andParent:parent];
}
[self rebalanceStartingAtNode:parent];
break;
}
}
}
return true;
}
-(void)rebalanceStartingAtNode:(AVLTreeNode*)n {
[self setBalance:@[n]];
if (n.balance == -2) {
if ([self height:(n.left.left)] >= [self height:n.left.right]) {
n = [self rotateRight:n];
} else {
n = [self rotateLeftThenRight:n];
}
} else if (n.balance == 2) {
if ([self height:n.right.right] >= [self height:n.right.left]) {
n = [self rotateLeft:n];
} else {
n = [self rotateRightThenLeft:n];
}
}
if (n.parent != nil) {
[self rebalanceStartingAtNode:n.parent];
} else {
self.root = n;
}
}
-(AVLTreeNode*)rotateRight:(AVLTreeNode*)a {
AVLTreeNode *b = a.left;
b.parent = a.parent;
a.left = b.right;
if (a.left != nil) {
a.left.parent = a;
}
b.right = a;
a.parent = b;
if (b.parent != nil) {
if (b.parent.right == a) {
b.parent.right = b;
} else {
b.parent.left = b;
}
}
[self setBalance:@[a,b]];
return b;
}
-(AVLTreeNode*)rotateLeftThenRight:(AVLTreeNode*)n {
n.left = [self rotateLeft:n.left];
return [self rotateRight:n];
}
-(AVLTreeNode*)rotateRightThenLeft:(AVLTreeNode*)n {
n.right = [self rotateRight:n.right];
return [self rotateLeft:n];
}
-(AVLTreeNode*)rotateLeft:(AVLTreeNode*)a {
//set a's right node as b
AVLTreeNode* b = a.right;
//set b's parent as a's parent (which could be nil)
b.parent = a.parent;
//in case b had a left child transfer it to a
a.right = b.left;
// after changing a's reference to the right child, make sure the parent is set too
if (a.right != nil) {
a.right.parent = a;
}
// switch a over to the left to be b's left child
b.left = a;
a.parent = b;
if (b.parent != nil) {
if (b.parent.right == a) {
b.parent.right = b;
} else {
b.parent.right = b;
}
}
[self setBalance:@[a,b]];
return b;
}
-(void) setBalance:(NSArray*)nodesArray {
for (AVLTreeNode* n in nodesArray) {
n.balance = [self height:n.right] - [self height:n.left];
}
}
-(int)height:(AVLTreeNode*)n {
if (n == nil) {
return -1;
}
return 1 + MAX([self height:n.left], [self height:n.right]);
}
-(void)printKey:(AVLTreeNode*)n {
if (n != nil) {
[self printKey:n.left];
NSLog(@"%ld", n.key);
[self printKey:n.right];
}
}
-(void)printBalance:(AVLTreeNode*)n {
if (n != nil) {
[self printBalance:n.left];
NSLog(@"%ld", n.balance);
[self printBalance:n.right];
}
}
@end
-- test
int main(int argc, const char * argv[]) {
@autoreleasepool {
AVLTree *tree = [AVLTree new];
NSLog(@"inserting values 1 to 6");
[tree insertWithKey:1];
[tree insertWithKey:2];
[tree insertWithKey:3];
[tree insertWithKey:4];
[tree insertWithKey:5];
[tree insertWithKey:6];
NSLog(@"printing balance: ");
[tree printBalance:tree.root];
NSLog(@"printing key: ");
[tree printKey:tree.root];
}
return 0;
}

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(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">KEY</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">LEFT</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">HEIGHT</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (NB +/-1 gives LEFT or RIGHT)</span>
<span style="color: #000000;">RIGHT</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">tree</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">freelist</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">newNode</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">node</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">freelist</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">node</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">tree</span> <span style="color: #0000FF;">&=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">key</span><span style="color: #0000FF;">,</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">node</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">freelist</span>
<span style="color: #000000;">freelist</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">freelist</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">..</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">key</span><span style="color: #0000FF;">,</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">node</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">height</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">node</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">?</span><span style="color: #000000;">0</span><span style="color: #0000FF;">:</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">HEIGHT</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">setHeight</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">HEIGHT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">height</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">]),</span> <span style="color: #000000;">height</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">]))+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">rotate</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">idirection</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">LEFT</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">-</span><span style="color: #000000;">direction</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">pivot</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">idirection</span><span style="color: #0000FF;">]</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">pivot</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">],</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">idirection</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">node</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">pivot</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">]}</span>
<span style="color: #000000;">setHeight</span><span style="color: #0000FF;">(</span><span style="color: #000000;">node</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">setHeight</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pivot</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">pivot</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">getBalance</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">N</span><span style="color: #0000FF;">==</span><span style="color: #004600;">NULL</span> <span style="color: #0000FF;">?</span> <span style="color: #000000;">0</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">height</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">+</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">])-</span><span style="color: #000000;">height</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">]))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">insertNode</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">==</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">newNode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">key</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">compare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">key</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">direction</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">HEIGHT</span><span style="color: #0000FF;">+</span><span style="color: #000000;">c</span> <span style="color: #000080;font-style:italic;">-- LEFT or RIGHT
-- note this crashes under p2js... (easy to fix, not so easy to find)
-- tree[node+direction] = insertNode(tree[node+direction], key)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">tnd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">insertNode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tnd</span>
<span style="color: #000000;">setHeight</span><span style="color: #0000FF;">(</span><span style="color: #000000;">node</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">balance</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trunc</span><span style="color: #0000FF;">(</span><span style="color: #000000;">getBalance</span><span style="color: #0000FF;">(</span><span style="color: #000000;">node</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- +/-1 (or 0)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">balance</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">direction</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">HEIGHT</span><span style="color: #0000FF;">-</span><span style="color: #000000;">balance</span> <span style="color: #000080;font-style:italic;">-- LEFT or RIGHT</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">compare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">key</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">balance</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rotate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">],</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">node</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rotate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">node</span><span style="color: #0000FF;">,</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">-</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">node</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">minValueNode</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">next</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">next</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">node</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">next</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">node</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">deleteNode</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">root</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">root</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">root</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">compare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">key</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">deleteNode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=+</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">deleteNode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">]==</span><span style="color: #004600;">NULL</span>
<span style="color: #008080;">or</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">]==</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">temp</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">?</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">temp</span><span style="color: #0000FF;">==</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- No child case</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">temp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">root</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">root</span><span style="color: #0000FF;">,</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">else</span> <span style="color: #000080;font-style:italic;">-- One child case</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">..</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">temp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">..</span><span style="color: #000000;">temp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">temp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">freelist</span>
<span style="color: #000000;">freelist</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">temp</span>
<span style="color: #008080;">else</span> <span style="color: #000080;font-style:italic;">-- Two child case</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">temp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">minValueNode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">temp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">deleteNode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">temp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">root</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">root</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">setHeight</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">balance</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">trunc</span><span style="color: #0000FF;">(</span><span style="color: #000000;">getBalance</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">balance</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">direction</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">HEIGHT</span><span style="color: #0000FF;">-</span><span style="color: #000000;">balance</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">compare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">getBalance</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">]),</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">balance</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rotate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">root</span><span style="color: #0000FF;">+</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">],</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">root</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rotate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">,</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">-</span><span style="color: #000000;">direction</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">root</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">inOrder</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">!=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">inOrder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">LEFT</span><span style="color: #0000FF;">])</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"%d "</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">KEY</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">inOrder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">node</span><span style="color: #0000FF;">+</span><span style="color: #000000;">RIGHT</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">root</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">test</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">shuffle</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">50003</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">test</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">root</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">insertNode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">,</span><span style="color: #000000;">test</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">test</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">shuffle</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">50000</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">test</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">root</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">deleteNode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">,</span><span style="color: #000000;">test</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">inOrder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">)</span>
<!--

51
Task/AVL-tree/Picat/avl-tree.picat Normal file
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main =>
T = nil,
foreach (X in 1..10)
T := insert(X,T)
end,
output(T,0).
insert(X, nil) = {1,nil,X,nil}.
insert(X, T@{H,L,V,R}) = Res =>
if X < V then
Res = rotate({H, insert(X,L) ,V,R})
elseif X > V then
Res = rotate({H,L,V, insert(X,R)})
else
Res = T
end.
rotate(nil) = nil.
rotate({H, {LH,LL,LV,LR}, V, R}) = Res,
LH - height(R) > 1,
height(LL) - height(LR) > 0
=> % Left Left.
Res = {LH,LL,LV, {depth(R,LR), LR,V,R}}.
rotate({H,L,V, {RH,RL,RV,RR}}) = Res,
RH - height(L) > 1,
height(RR) - height(RL) > 0
=> % Right Right.
Res = {RH, {depth(L,RL),L,V,RL}, RV,RR}.
rotate({H, {LH,LL,LV, {RH,RL,RV,RR}, V,R}}) = Res,
LH - height(R) > 1
=> % Left Right.
Res = {H, {RH + 1, {LH - 1, LL, LV, RL}, RV, RR}, V, R}.
rotate({H,L,V, {RH, {LH,LL,LV,LR},RV,RR}}) = Res,
RH - height(L) > 1
=> % Right Left.
Res = {H,L,V, {LH+1, LL, LV, {RH-1, LR, RV, RR}}}.
rotate({H,L,V,R}) = Res => % Re-weighting.
L1 = rotate(L),
R1 = rotate(R),
Res = {depth(L1,R1), L1,V,R1}.
height(nil) = -1.
height({H,_,_,_}) = H.
depth(A,B) = max(height(A), height(B)) + 1.
output(nil,Indent) => printf("%*w\n",Indent,nil).
output({_,L,V,R},Indent) =>
output(L,Indent+6),
printf("%*w\n",Indent,V),
output(R,Indent+6).

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281
Task/AVL-tree/Raku/avl-tree.raku Normal file
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class AVL-Tree {
has $.root is rw = 0;
class Node {
has $.key is rw = '';
has $.parent is rw = 0;
has $.data is rw = 0;
has $.left is rw = 0;
has $.right is rw = 0;
has Int $.balance is rw = 0;
has Int $.height is rw = 0;
}
#=====================================================
# public methods
#=====================================================
#| returns a node object or 0 if not found
method find($key) {
return 0 if !$.root;
self!find: $key, $.root;
}
#| returns a list of tree keys
method keys() {
return () if !$.root;
my @list;
self!keys: $.root, @list;
@list;
}
#| returns a list of tree nodes
method nodes() {
return () if !$.root;
my @list;
self!nodes: $.root, @list;
@list;
}
#| insert a node key, optionally add data (the `parent` arg is for
#| internal use only)
method insert($key, :$data = 0, :$parent = 0,) {
return $.root = Node.new: :$key, :$parent, :$data if !$.root;
my $n = $.root;
while True {
return False if $n.key eq $key;
my $parent = $n;
my $goLeft = $n.key > $key;
$n = $goLeft ?? $n.left !! $n.right;
if !$n {
if $goLeft {
$parent.left = Node.new: :$key, :$parent, :$data;
}
else {
$parent.right = Node.new: :$key, :$parent, :$data;
}
self!rebalance: $parent;
last
}
}
True
}
#| delete one or more nodes by key
method delete(*@del-key) {
return if !$.root;
for @del-key -> $del-key {
my $child = $.root;
while $child {
my $node = $child;
$child = $del-key >= $node.key ?? $node.right !! $node.left;
if $del-key eq $node.key {
self!delete: $node;
next;
}
}
}
}
#| show a list of all nodes by key
method show-keys {
self!show-keys: $.root;
say()
}
#| show a list of all nodes' balances (not normally needed)
method show-balances {
self!show-balances: $.root;
say()
}
#=====================================================
# private methods
#=====================================================
method !delete($node) {
if !$node.left && !$node.right {
if !$node.parent {
$.root = 0;
}
else {
my $parent = $node.parent;
if $parent.left === $node {
$parent.left = 0;
}
else {
$parent.right = 0;
}
self!rebalance: $parent;
}
return
}
if $node.left {
my $child = $node.left;
while $child.right {
$child = $child.right;
}
$node.key = $child.key;
self!delete: $child;
}
else {
my $child = $node.right;
while $child.left {
$child = $child.left;
}
$node.key = $child.key;
self!delete: $child;
}
}
method !rebalance($n is copy) {
self!set-balance: $n;
if $n.balance == -2 {
if self!height($n.left.left) >= self!height($n.left.right) {
$n = self!rotate-right: $n;
}
else {
$n = self!rotate-left'right: $n;
}
}
elsif $n.balance == 2 {
if self!height($n.right.right) >= self!height($n.right.left) {
$n = self!rotate-left: $n;
}
else {
$n = self!rotate-right'left: $n;
}
}
if $n.parent {
self!rebalance: $n.parent;
}
else {
$.root = $n;
}
}
method !rotate-left($a) {
my $b = $a.right;
$b.parent = $a.parent;
$a.right = $b.left;
if $a.right {
$a.right.parent = $a;
}
$b.left = $a;
$a.parent = $b;
if $b.parent {
if $b.parent.right === $a {
$b.parent.right = $b;
}
else {
$b.parent.left = $b;
}
}
self!set-balance: $a, $b;
$b;
}
method !rotate-right($a) {
my $b = $a.left;
$b.parent = $a.parent;
$a.left = $b.right;
if $a.left {
$a.left.parent = $a;
}
$b.right = $a;
$a.parent = $b;
if $b.parent {
if $b.parent.right === $a {
$b.parent.right = $b;
}
else {
$b.parent.left = $b;
}
}
self!set-balance: $a, $b;
$b;
}
method !rotate-left'right($n) {
$n.left = self!rotate-left: $n.left;
self!rotate-right: $n;
}
method !rotate-right'left($n) {
$n.right = self!rotate-right: $n.right;
self!rotate-left: $n;
}
method !height($n) {
$n ?? $n.height !! -1;
}
method !set-balance(*@n) {
for @n -> $n {
self!reheight: $n;
$n.balance = self!height($n.right) - self!height($n.left);
}
}
method !show-balances($n) {
if $n {
self!show-balances: $n.left;
printf "%s ", $n.balance;
self!show-balances: $n.right;
}
}
method !reheight($node) {
if $node {
$node.height = 1 + max self!height($node.left), self!height($node.right);
}
}
method !show-keys($n) {
if $n {
self!show-keys: $n.left;
printf "%s ", $n.key;
self!show-keys: $n.right;
}
}
method !nodes($n, @list) {
if $n {
self!nodes: $n.left, @list;
@list.push: $n if $n;
self!nodes: $n.right, @list;
}
}
method !keys($n, @list) {
if $n {
self!keys: $n.left, @list;
@list.push: $n.key if $n;
self!keys: $n.right, @list;
}
}
method !find($key, $n) {
if $n {
self!find: $key, $n.left;
return $n if $n.key eq $key;
self!find: $key, $n.right;
}
}
}

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import scala.collection.mutable
class AVLTree[A](implicit val ordering: Ordering[A]) extends mutable.SortedSet[A] {
if (ordering eq null) throw new NullPointerException("ordering must not be null")
private var _root: AVLNode = _
private var _size = 0
override def size: Int = _size
override def foreach[U](f: A => U): Unit = {
val stack = mutable.Stack[AVLNode]()
var current = root
var done = false
while (!done) {
if (current != null) {
stack.push(current)
current = current.left
} else if (stack.nonEmpty) {
current = stack.pop()
f.apply(current.key)
current = current.right
} else {
done = true
}
}
}
def root: AVLNode = _root
override def isEmpty: Boolean = root == null
override def min[B >: A](implicit cmp: Ordering[B]): A = minNode().key
def minNode(): AVLNode = {
if (root == null) throw new UnsupportedOperationException("empty tree")
var node = root
while (node.left != null) node = node.left
node
}
override def max[B >: A](implicit cmp: Ordering[B]): A = maxNode().key
def maxNode(): AVLNode = {
if (root == null) throw new UnsupportedOperationException("empty tree")
var node = root
while (node.right != null) node = node.right
node
}
def next(node: AVLNode): Option[AVLNode] = {
var successor = node
if (successor != null) {
if (successor.right != null) {
successor = successor.right
while (successor != null && successor.left != null) {
successor = successor.left
}
} else {
successor = node.parent
var n = node
while (successor != null && successor.right == n) {
n = successor
successor = successor.parent
}
}
}
Option(successor)
}
def prev(node: AVLNode): Option[AVLNode] = {
var predecessor = node
if (predecessor != null) {
if (predecessor.left != null) {
predecessor = predecessor.left
while (predecessor != null && predecessor.right != null) {
predecessor = predecessor.right
}
} else {
predecessor = node.parent
var n = node
while (predecessor != null && predecessor.left == n) {
n = predecessor
predecessor = predecessor.parent
}
}
}
Option(predecessor)
}
override def rangeImpl(from: Option[A], until: Option[A]): mutable.SortedSet[A] = ???
override def +=(key: A): AVLTree.this.type = {
insert(key)
this
}
def insert(key: A): AVLNode = {
if (root == null) {
_root = new AVLNode(key)
_size += 1
return root
}
var node = root
var parent: AVLNode = null
var cmp = 0
while (node != null) {
parent = node
cmp = ordering.compare(key, node.key)
if (cmp == 0) return node // duplicate
node = node.matchNextChild(cmp)
}
val newNode = new AVLNode(key, parent)
if (cmp <= 0) parent._left = newNode
else parent._right = newNode
while (parent != null) {
cmp = ordering.compare(parent.key, key)
if (cmp < 0) parent.balanceFactor -= 1
else parent.balanceFactor += 1
parent = parent.balanceFactor match {
case -1 | 1 => parent.parent
case x if x < -1 =>
if (parent.right.balanceFactor == 1) rotateRight(parent.right)
val newRoot = rotateLeft(parent)
if (parent == root) _root = newRoot
null
case x if x > 1 =>
if (parent.left.balanceFactor == -1) rotateLeft(parent.left)
val newRoot = rotateRight(parent)
if (parent == root) _root = newRoot
null
case _ => null
}
}
_size += 1
newNode
}
override def -=(key: A): AVLTree.this.type = {
remove(key)
this
}
override def remove(key: A): Boolean = {
var node = findNode(key).orNull
if (node == null) return false
if (node.left != null) {
var max = node.left
while (max.left != null || max.right != null) {
while (max.right != null) max = max.right
node._key = max.key
if (max.left != null) {
node = max
max = max.left
}
}
node._key = max.key
node = max
}
if (node.right != null) {
var min = node.right
while (min.left != null || min.right != null) {
while (min.left != null) min = min.left
node._key = min.key
if (min.right != null) {
node = min
min = min.right
}
}
node._key = min.key
node = min
}
var current = node
var parent = node.parent
while (parent != null) {
parent.balanceFactor += (if (parent.left == current) -1 else 1)
current = parent.balanceFactor match {
case x if x < -1 =>
if (parent.right.balanceFactor == 1) rotateRight(parent.right)
val newRoot = rotateLeft(parent)
if (parent == root) _root = newRoot
newRoot
case x if x > 1 =>
if (parent.left.balanceFactor == -1) rotateLeft(parent.left)
val newRoot = rotateRight(parent)
if (parent == root) _root = newRoot
newRoot
case _ => parent
}
parent = current.balanceFactor match {
case -1 | 1 => null
case _ => current.parent
}
}
if (node.parent != null) {
if (node.parent.left == node) {
node.parent._left = null
} else {
node.parent._right = null
}
}
if (node == root) _root = null
_size -= 1
true
}
def findNode(key: A): Option[AVLNode] = {
var node = root
while (node != null) {
val cmp = ordering.compare(key, node.key)
if (cmp == 0) return Some(node)
node = node.matchNextChild(cmp)
}
None
}
private def rotateLeft(node: AVLNode): AVLNode = {
val rightNode = node.right
node._right = rightNode.left
if (node.right != null) node.right._parent = node
rightNode._parent = node.parent
if (rightNode.parent != null) {
if (rightNode.parent.left == node) {
rightNode.parent._left = rightNode
} else {
rightNode.parent._right = rightNode
}
}
node._parent = rightNode
rightNode._left = node
node.balanceFactor += 1
if (rightNode.balanceFactor < 0) {
node.balanceFactor -= rightNode.balanceFactor
}
rightNode.balanceFactor += 1
if (node.balanceFactor > 0) {
rightNode.balanceFactor += node.balanceFactor
}
rightNode
}
private def rotateRight(node: AVLNode): AVLNode = {
val leftNode = node.left
node._left = leftNode.right
if (node.left != null) node.left._parent = node
leftNode._parent = node.parent
if (leftNode.parent != null) {
if (leftNode.parent.left == node) {
leftNode.parent._left = leftNode
} else {
leftNode.parent._right = leftNode
}
}
node._parent = leftNode
leftNode._right = node
node.balanceFactor -= 1
if (leftNode.balanceFactor > 0) {
node.balanceFactor -= leftNode.balanceFactor
}
leftNode.balanceFactor -= 1
if (node.balanceFactor < 0) {
leftNode.balanceFactor += node.balanceFactor
}
leftNode
}
override def contains(elem: A): Boolean = findNode(elem).isDefined
override def iterator: Iterator[A] = ???
override def keysIteratorFrom(start: A): Iterator[A] = ???
class AVLNode private[AVLTree](k: A, p: AVLNode = null) {
private[AVLTree] var _key: A = k
private[AVLTree] var _parent: AVLNode = p
private[AVLTree] var _left: AVLNode = _
private[AVLTree] var _right: AVLNode = _
private[AVLTree] var balanceFactor: Int = 0
def parent: AVLNode = _parent
private[AVLTree] def selectNextChild(key: A): AVLNode = matchNextChild(ordering.compare(key, this.key))
def key: A = _key
private[AVLTree] def matchNextChild(cmp: Int): AVLNode = cmp match {
case x if x < 0 => left
case x if x > 0 => right
case _ => null
}
def left: AVLNode = _left
def right: AVLNode = _right
}
}

803
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(cond-expand
(r7rs)
(chicken (import r7rs)))
(define-library (avl-trees)
;;
;; This library implements ‘persistent’ (that is, ‘immutable’) AVL
;; trees for R7RS Scheme.
;;
;; Included are generators of the key-data pairs in a tree. Because
;; the trees are persistent (‘immutable’), these generators are safe
;; from alterations of the tree.
;;
;; References:
;;
;; * Niklaus Wirth, 1976. Algorithms + Data Structures =
;; Programs. Prentice-Hall, Englewood Cliffs, New Jersey.
;;
;; * Niklaus Wirth, 2004. Algorithms and Data Structures. Updated
;; by Fyodor Tkachov, 2014.
;;
;; Note that the references do not discuss persistent
;; implementations. It seems worthwhile to compare the methods of
;; implementation.
;;
(export avl)
(export alist->avl)
(export avl->alist)
(export avl?)
(export avl-empty?)
(export avl-size)
(export avl-insert)
(export avl-delete)
(export avl-delete-values)
(export avl-has-key?)
(export avl-search)
(export avl-search-values)
(export avl-make-generator)
(export avl-pretty-print)
(export avl-check-avl-condition)
(export avl-check-usage)
(import (scheme base))
(import (scheme case-lambda))
(import (scheme process-context))
(import (scheme write))
(cond-expand
(chicken
(import (only (chicken base) define-record-printer))
(import (only (chicken format) format))) ; For debugging.
(else))
(begin
;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
;;
;; Tools for making generators. These use call/cc and so might be
;; inefficient in your Scheme. I am using CHICKEN, in which
;; call/cc is not so inefficient.
;;
;; Often I have made &fail a unique object rather than #f, but in
;; this case #f will suffice.
;;
(define &fail #f)
(define *suspend*
(make-parameter (lambda (x) x)))
(define (suspend v)
((*suspend*) v))
(define (fail-forever)
(let loop ()
(suspend &fail)
(loop)))
(define (make-generator-procedure thunk)
;; Make a suspendable procedure that takes no arguments. The
;; result is a simple generator of values. (This can be
;; elaborated upon for generators to take values on resumption,
;; in the manner of Icon co-expressions.)
(define (next-run return)
(define (my-suspend v)
(set! return (call/cc (lambda (resumption-point)
(set! next-run resumption-point)
(return v)))))
(parameterize ((*suspend* my-suspend))
(suspend (thunk))
(fail-forever)))
(lambda () (call/cc next-run)))
;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
(define-syntax avl-check-usage
(syntax-rules ()
((_ pred msg)
(or pred (usage-error msg)))))
;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
(define-record-type <avl>
(%avl key data bal left right)
avl?
(key %key)
(data %data)
(bal %bal)
(left %left)
(right %right))
(cond-expand
(chicken (define-record-printer (<avl> rt out)
(display "#<avl " out)
(display (%key rt) out)
(display " " out)
(display (%data rt) out)
(display " " out)
(display (%bal rt) out)
(display " " out)
(display (%left rt) out)
(display " " out)
(display (%right rt) out)
(display ">" out)))
(else))
;; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
(define avl
(case-lambda
(() (%avl #f #f #f #f #f))
((pred<? . args) (alist->avl pred<? args))))
(define (avl-empty? tree)
(avl-check-usage
(avl? tree)
"avl-empty? expects an AVL tree as argument")
(not (%bal tree)))
(define (avl-size tree)
(define (traverse p sz)
(if (not p)
sz
(traverse (%left p) (traverse (%right p) (+ sz 1)))))
(if (avl-empty? tree)
0
(traverse tree 0)))
(define (avl-has-key? pred<? tree key)
(define (search p)
(and p
(let ((k (%key p)))
(cond ((pred<? key k) (search (%left p)))
((pred<? k key) (search (%right p)))
(else #t)))))
(avl-check-usage
(procedure? pred<?)
"avl-has-key? expects a procedure as first argument")
(and (not (avl-empty? tree))
(search tree)))
(define (avl-search pred<? tree key)
;; Return the data matching a key, or #f if the key is not
;; found. (Note that the data matching the key might be #f.)
(define (search p)
(and p
(let ((k (%key p)))
(cond ((pred<? key k) (search (%left p)))
((pred<? k key) (search (%right p)))
(else (%data p))))))
(avl-check-usage
(procedure? pred<?)
"avl-search expects a procedure as first argument")
(and (not (avl-empty? tree))
(search tree)))
(define (avl-search-values pred<? tree key)
;; Return two values: the data matching the key, or #f is the
;; key is not found; and a second value that is either #f or #t,
;; depending on whether the key is found.
(define (search p)
(if (not p)
(values #f #f)
(let ((k (%key p)))
(cond ((pred<? key k) (search (%left p)))
((pred<? k key) (search (%right p)))
(else (values (%data p) #t))))))
(avl-check-usage
(procedure? pred<?)
"avl-search-values expects a procedure as first argument")
(if (avl-empty? tree)
(values #f #f)
(search tree)))
(define (alist->avl pred<? alst)
;; Go from association list to AVL tree.
(avl-check-usage
(procedure? pred<?)
"alist->avl expects a procedure as first argument")
(let loop ((tree (avl))
(lst alst))
(if (null? lst)
tree
(let ((head (car lst)))
(loop (avl-insert pred<? tree (car head) (cdr head))
(cdr lst))))))
(define (avl->alist tree)
;; Go from AVL tree to association list. The output will be in
;; order.
(define (traverse p lst)
;; Reverse in-order traversal of the tree, to produce an
;; in-order cons-list.
(if (not p)
lst
(traverse (%left p) (cons (cons (%key p) (%data p))
(traverse (%right p) lst)))))
(if (avl-empty? tree)
'()
(traverse tree '())))
(define (avl-insert pred<? tree key data)
(define (search p fix-balance?)
(cond
((not p)
;; The key was not found. Make a new node and set
;; fix-balance?
(values (%avl key data 0 #f #f) #t))
((pred<? key (%key p))
;; Continue searching.
(let-values (((p1 fix-balance?)
(search (%left p) fix-balance?)))
(cond
((not fix-balance?)
(let ((p^ (%avl (%key p) (%data p) (%bal p)
p1 (%right p))))
(values p^ #f)))
(else
;; A new node has been inserted on the left side.
(case (%bal p)
((1)
(let ((p^ (%avl (%key p) (%data p) 0
p1 (%right p))))
(values p^ #f)))
((0)
(let ((p^ (%avl (%key p) (%data p) -1
p1 (%right p))))
(values p^ fix-balance?)))
((-1)
;; Rebalance.
(case (%bal p1)
((-1)
;; A single LL rotation.
(let* ((p^ (%avl (%key p) (%data p) 0
(%right p1) (%right p)))
(p1^ (%avl (%key p1) (%data p1) 0
(%left p1) p^)))
(values p1^ #f)))
((0 1)
;; A double LR rotation.
(let* ((p2 (%right p1))
(bal2 (%bal p2))
(p^ (%avl (%key p) (%data p)
(- (min bal2 0))
(%right p2) (%right p)))
(p1^ (%avl (%key p1) (%data p1)
(- (max bal2 0))
(%left p1) (%left p2)))
(p2^ (%avl (%key p2) (%data p2) 0
p1^ p^)))
(values p2^ #f)))
(else (internal-error))))
(else (internal-error)))))))
((pred<? (%key p) key)
;; Continue searching.
(let-values (((p1 fix-balance?)
(search (%right p) fix-balance?)))
(cond
((not fix-balance?)
(let ((p^ (%avl (%key p) (%data p) (%bal p)
(%left p) p1)))
(values p^ #f)))
(else
;; A new node has been inserted on the right side.
(case (%bal p)
((-1)
(let ((p^ (%avl (%key p) (%data p) 0
(%left p) p1)))
(values p^ #f)))
((0)
(let ((p^ (%avl (%key p) (%data p) 1
(%left p) p1)))
(values p^ fix-balance?)))
((1)
;; Rebalance.
(case (%bal p1)
((1)
;; A single RR rotation.
(let* ((p^ (%avl (%key p) (%data p) 0
(%left p) (%left p1)))
(p1^ (%avl (%key p1) (%data p1) 0
p^ (%right p1))))
(values p1^ #f)))
((-1 0)
;; A double RL rotation.
(let* ((p2 (%left p1))
(bal2 (%bal p2))
(p^ (%avl (%key p) (%data p)
(- (max bal2 0))
(%left p) (%left p2)))
(p1^ (%avl (%key p1) (%data p1)
(- (min bal2 0))
(%right p2) (%right p1)))
(p2^ (%avl (%key p2) (%data p2) 0
p^ p1^)))
(values p2^ #f)))
(else (internal-error))))
(else (internal-error)))))))
(else
;; The key was found; p is an existing node.
(values (%avl key data (%bal p) (%left p) (%right p))
#f))))
(avl-check-usage
(procedure? pred<?)
"avl-insert expects a procedure as first argument")
(if (avl-empty? tree)
(%avl key data 0 #f #f)
(let-values (((p fix-balance?) (search tree #f)))
p)))
(define (avl-delete pred<? tree key)
;; If one is not interested in whether the key was in the tree,
;; then throw away that information.
(let-values (((tree had-key?)
(avl-delete-values pred<? tree key)))
tree))
(define (balance-for-shrunken-left p)
;; Returns two values: a new p and a new fix-balance?
(case (%bal p)
((-1) (values (%avl (%key p) (%data p) 0
(%left p) (%right p))
#t))
((0) (values (%avl (%key p) (%data p) 1
(%left p) (%right p))
#f))
((1)
;; Rebalance.
(let* ((p1 (%right p))
(bal1 (%bal p1)))
(case bal1
((0)
;; A single RR rotation.
(let* ((p^ (%avl (%key p) (%data p) 1
(%left p) (%left p1)))
(p1^ (%avl (%key p1) (%data p1) -1
p^ (%right p1))))
(values p1^ #f)))
((1)
;; A single RR rotation.
(let* ((p^ (%avl (%key p) (%data p) 0
(%left p) (%left p1)))
(p1^ (%avl (%key p1) (%data p1) 0
p^ (%right p1))))
(values p1^ #t)))
((-1)
;; A double RL rotation.
(let* ((p2 (%left p1))
(bal2 (%bal p2))
(p^ (%avl (%key p) (%data p) (- (max bal2 0))
(%left p) (%left p2)))
(p1^ (%avl (%key p1) (%data p1) (- (min bal2 0))
(%right p2) (%right p1)))
(p2^ (%avl (%key p2) (%data p2) 0 p^ p1^)))
(values p2^ #t)))
(else (internal-error)))))
(else (internal-error))))
(define (balance-for-shrunken-right p)
;; Returns two values: a new p and a new fix-balance?
(case (%bal p)
((1) (values (%avl (%key p) (%data p) 0
(%left p) (%right p))
#t))
((0) (values (%avl (%key p) (%data p) -1
(%left p) (%right p))
#f))
((-1)
;; Rebalance.
(let* ((p1 (%left p))
(bal1 (%bal p1)))
(case bal1
((0)
;; A single LL rotation.
(let* ((p^ (%avl (%key p) (%data p) -1
(%right p1) (%right p)))
(p1^ (%avl (%key p1) (%data p1) 1
(%left p1) p^)))
(values p1^ #f)))
((-1)
;; A single LL rotation.
(let* ((p^ (%avl (%key p) (%data p) 0
(%right p1) (%right p)))
(p1^ (%avl (%key p1) (%data p1) 0
(%left p1) p^)))
(values p1^ #t)))
((1)
;; A double LR rotation.
(let* ((p2 (%right p1))
(bal2 (%bal p2))
(p^ (%avl (%key p) (%data p) (- (min bal2 0))
(%right p2) (%right p)))
(p1^ (%avl (%key p1) (%data p1) (- (max bal2 0))
(%left p1) (%left p2)))
(p2^ (%avl (%key p2) (%data p2) 0 p1^ p^)))
(values p2^ #t)))
(else (internal-error)))))
(else (internal-error))))
(define (avl-delete-values pred<? tree key)
(define-syntax balance-L
(syntax-rules ()
((_ p fix-balance?)
(if fix-balance?
(balance-for-shrunken-left p)
(values p #f)))))
(define-syntax balance-R
(syntax-rules ()
((_ p fix-balance?)
(if fix-balance?
(balance-for-shrunken-right p)
(values p #f)))))
(define (del r fix-balance?)
;; Returns a new r, a new fix-balance?, and key and data to be
;; ‘moved up the tree’.
(if (%right r)
(let*-values
(((q fix-balance? key^ data^)
(del (%right r) fix-balance?))
((r fix-balance?)
(balance-R (%avl (%key r) (%data r) (%bal r)
(%left r) q)
fix-balance?)))
(values r fix-balance? key^ data^))
(values (%left r) #t (%key r) (%data r))))
(define (search p fix-balance?)
;; Return three values: a new p, a new fix-balance, and
;; whether the key was found.
(cond
((not p) (values #f #f #f))
((pred<? key (%key p))
;; Recursive search down the left branch.
(let*-values
(((q fix-balance? found?)
(search (%left p) fix-balance?))
((p fix-balance?)
(balance-L (%avl (%key p) (%data p) (%bal p)
q (%right p))
fix-balance?)))
(values p fix-balance? found?)))
((pred<? (%key p) key)
;; Recursive search down the right branch.
(let*-values
(((q fix-balance? found?)
(search (%right p) fix-balance?))
((p fix-balance?)
(balance-R (%avl (%key p) (%data p) (%bal p)
(%left p) q)
fix-balance?)))
(values p fix-balance? found?)))
((not (%right p))
;; Delete p, replace it with its left branch, then
;; rebalance.
(values (%left p) #t #t))
((not (%left p))
;; Delete p, replace it with its right branch, then
;; rebalance.
(values (%right p) #t #t))
(else
;; Delete p, but it has both left and right branches,
;; and therefore may have complicated branch structure.
(let*-values
(((q fix-balance? key^ data^)
(del (%left p) fix-balance?))
((p fix-balance?)
(balance-L (%avl key^ data^ (%bal p) q (%right p))
fix-balance?)))
(values p fix-balance? #t)))))
(avl-check-usage
(procedure? pred<?)
"avl-delete-values expects a procedure as first argument")
(if (avl-empty? tree)
(values tree #f)
(let-values (((tree fix-balance? found?)
(search tree #f)))
(if found?
(values (or tree (avl)) #t)
(values tree #f)))))
(define avl-make-generator
(case-lambda
((tree) (avl-make-generator tree 1))
((tree direction)
(if (negative? direction)
(make-generator-procedure
(lambda ()
(define (traverse p)
(unless (or (not p) (avl-empty? p))
(traverse (%right p))
(suspend (cons (%key p) (%data p)))
(traverse (%left p)))
&fail)
(traverse tree)))
(make-generator-procedure
(lambda ()
(define (traverse p)
(unless (or (not p) (avl-empty? p))
(traverse (%left p))
(suspend (cons (%key p) (%data p)))
(traverse (%right p)))
&fail)
(traverse tree)))))))
(define avl-pretty-print
(case-lambda
((tree)
(avl-pretty-print tree (current-output-port)))
((tree port)
(avl-pretty-print tree port
(lambda (port key data)
(display "(" port)
(write key port)
(display ", " port)
(write data port)
(display ")" port))))
((tree port key-data-printer)
;; In-order traversal, so the printing is done in
;; order. Reflect the display diagonally to get the more
;; usual orientation of left-to-right, top-to-bottom.
(define (pad depth)
(unless (zero? depth)
(display " " port)
(pad (- depth 1))))
(define (traverse p depth)
(when p
(traverse (%left p) (+ depth 1))
(pad depth)
(key-data-printer port (%key p) (%data p))
(display "\t\tdepth = " port)
(display depth port)
(display " bal = " port)
(display (%bal p) port)
(display "\n" port)
(traverse (%right p) (+ depth 1))))
(unless (avl-empty? tree)
(traverse (%left tree) 1)
(key-data-printer port (%key tree) (%data tree))
(display "\t\tdepth = 0 bal = " port)
(display (%bal tree) port)
(display "\n" port)
(traverse (%right tree) 1)))))
(define (avl-check-avl-condition tree)
;; Check that the AVL condition is satisfied.
(define (check-heights height-L height-R)
(when (<= 2 (abs (- height-L height-R)))
(display "*** AVL condition violated ***"
(current-error-port))
(internal-error)))
(define (get-heights p)
(if (not p)
(values 0 0)
(let-values (((height-LL height-LR)
(get-heights (%left p)))
((height-RL height-RR)
(get-heights (%right p))))
(check-heights height-LL height-LR)
(check-heights height-RL height-RR)
(values (+ height-LL height-LR)
(+ height-RL height-RR)))))
(unless (avl-empty? tree)
(let-values (((height-L height-R) (get-heights tree)))
(check-heights height-L height-R))))
(define (internal-error)
(display "internal error\n" (current-error-port))
(emergency-exit 123))
(define (usage-error msg)
(display "Procedure usage error:\n" (current-error-port))
(display " " (current-error-port))
(display msg (current-error-port))
(newline (current-error-port))
(exit 1))
)) ;; end library (avl-trees)
(cond-expand
(DEMONSTRATION
(begin
(import (avl-trees))
(import (scheme base))
(import (scheme time))
(import (scheme process-context))
(import (scheme write))
(cond-expand
(chicken
(import (only (chicken format) format))) ; For debugging.
(else))
(define 2**64 (expt 2 64))
(define seed (truncate-remainder (exact (current-second)) 2**64))
(define random
;; A really slow (but presumably highly portable)
;; implementation of Donald Knuth’s linear congruential random
;; number generator, returning a rational number in [0,1). See
;; https://en.wikipedia.org/w/index.php?title=Linear_congruential_generator&oldid=1076681286
(let ((a 6364136223846793005)
(c 1442695040888963407))
(lambda ()
(let ((result (/ seed 2**64)))
(set! seed (truncate-remainder (+ (* a seed) c) 2**64))
result))))
(do ((i 0 (+ i 1)))
((= i 10))
(random))
(define (fisher-yates-shuffle keys)
(let ((n (vector-length keys)))
(do ((i 1 (+ i 1)))
((= i n))
(let* ((randnum (random))
(j (+ i (floor (* randnum (- n i)))))
(xi (vector-ref keys i))
(xj (vector-ref keys j)))
(vector-set! keys i xj)
(vector-set! keys j xi)))))
(define (display-key-data key data)
(display "(")
(write key)
(display ", ")
(write data)
(display ")"))
(define (display-tree-contents tree)
(do ((p (avl->alist tree) (cdr p)))
((null? p))
(display-key-data (caar p) (cdar p))
(newline)))
(define (error-stop)
(display "*** ERROR STOP ***\n" (current-error-port))
(emergency-exit 1))
(define n 20)
(define keys (make-vector (+ n 1)))
(do ((i 0 (+ i 1)))
((= i n))
;; To keep things more like Fortran, do not use index zero.
(vector-set! keys (+ i 1) (+ i 1)))
(fisher-yates-shuffle keys)
;; Insert key-data pairs in the shuffled order.
(define tree (avl))
(avl-check-avl-condition tree)
(do ((i 1 (+ i 1)))
((= i (+ n 1)))
(let ((ix (vector-ref keys i)))
(set! tree (avl-insert < tree ix (inexact ix)))
(avl-check-avl-condition tree)
(do ((j 1 (+ j 1)))
((= j (+ n 1)))
(let*-values (((k) (vector-ref keys j))
((has-key?) (avl-has-key? < tree k))
((data) (avl-search < tree k))
((data^ has-key?^)
(avl-search-values < tree k)))
(unless (exact? k) (error-stop))
(if (<= j i)
(unless (and has-key? data data^ has-key?^
(inexact? data) (= data k)
(inexact? data^) (= data^ k))
(error-stop))
(when (or has-key? data data^ has-key?^)
(error-stop)))))))
(display "----------------------------------------------------------------------\n")
(display "keys = ")
(write (cdr (vector->list keys)))
(newline)
(display "----------------------------------------------------------------------\n")
(avl-pretty-print tree)
(display "----------------------------------------------------------------------\n")
(display "tree size = ")
(display (avl-size tree))
(newline)
(display-tree-contents tree)
(display "----------------------------------------------------------------------\n")
;;
;; Reshuffle the keys, and change the data from inexact numbers
;; to strings.
;;
(fisher-yates-shuffle keys)
(do ((i 1 (+ i 1)))
((= i (+ n 1)))
(let ((ix (vector-ref keys i)))
(set! tree (avl-insert < tree ix (number->string ix)))
(avl-check-avl-condition tree)))
(avl-pretty-print tree)
(display "----------------------------------------------------------------------\n")
(display "tree size = ")
(display (avl-size tree))
(newline)
(display-tree-contents tree)
(display "----------------------------------------------------------------------\n")
;;
;; Reshuffle the keys, and delete the contents of the tree, but
;; also keep the original tree by saving it in a variable. Check
;; persistence of the tree.
;;
(fisher-yates-shuffle keys)
(define saved-tree tree)
(do ((i 1 (+ i 1)))
((= i (+ n 1)))
(let ((ix (vector-ref keys i)))
(set! tree (avl-delete < tree ix))
(avl-check-avl-condition tree)
(unless (= (avl-size tree) (- n i)) (error-stop))
;; Try deleting a second time.
(set! tree (avl-delete < tree ix))
(avl-check-avl-condition tree)
(unless (= (avl-size tree) (- n i)) (error-stop))
(do ((j 1 (+ j 1)))
((= j (+ n 1)))
(let ((jx (vector-ref keys j)))
(unless (eq? (avl-has-key? < tree jx) (< i j))
(error-stop))
(let ((data (avl-search < tree jx)))
(unless (eq? (not (not data)) (< i j))
(error-stop))
(unless (or (not data)
(= (string->number data) jx))
(error-stop)))
(let-values (((data found?)
(avl-search-values < tree jx)))
(unless (eq? found? (< i j)) (error-stop))
(unless (or (and (not data) (<= j i))
(and data (= (string->number data) jx)))
(error-stop)))))))
(do ((i 1 (+ i 1)))
((= i (+ n 1)))
;; Is save-tree the persistent value of the tree we just
;; deleted?
(let ((ix (vector-ref keys i)))
(unless (equal? (avl-search < saved-tree ix)
(number->string ix))
(error-stop))))
(display "forwards generator:\n")
(let ((gen (avl-make-generator saved-tree)))
(do ((pair (gen) (gen)))
((not pair))
(display-key-data (car pair) (cdr pair))
(newline)))
(display "----------------------------------------------------------------------\n")
(display "backwards generator:\n")
(let ((gen (avl-make-generator saved-tree -1)))
(do ((pair (gen) (gen)))
((not pair))
(display-key-data (car pair) (cdr pair))
(newline)))
(display "----------------------------------------------------------------------\n")
))
(else))

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class AVLtree {
has root = nil
struct Node {
Number key,
Number balance = 0,
Node left = nil,
Node right = nil,
Node parent = nil,
}
method insert(key) {
if (root == nil) {
root = Node(key)
return true
}
var n = root
var parent = nil
loop {
if (n.key == key) {
return false
}
parent = n
var goLeft = (n.key > key)
n = (goLeft ? n.left : n.right)
if (n == nil) {
var tn = Node(key, parent: parent)
if (goLeft) {
parent.left = tn
}
else {
parent.right = tn
}
self.rebalance(parent)
break
}
}
return true
}
method delete_key(delKey) {
if (root == nil) { return nil }
var n = root
var parent = root
var delNode = nil
var child = root
while (child != nil) {
parent = n
n = child
child = (delKey >= n.key ? n.right : n.left)
if (delKey == n.key) {
delNode = n
}
}
if (delNode != nil) {
delNode.key = n.key
child = (n.left != nil ? n.left : n.right)
if (root.key == delKey) {
root = child
}
else {
if (parent.left == n) {
parent.left = child
}
else {
parent.right = child
}
self.rebalance(parent)
}
}
}
method rebalance(n) {
if (n == nil) { return nil }
self.setBalance(n)
given (n.balance) {
when (-2) {
if (self.height(n.left.left) >= self.height(n.left.right)) {
n = self.rotate(n, :right)
}
else {
n = self.rotate_twice(n, :left, :right)
}
}
when (2) {
if (self.height(n.right.right) >= self.height(n.right.left)) {
n = self.rotate(n, :left)
}
else {
n = self.rotate_twice(n, :right, :left)
}
}
}
if (n.parent != nil) {
self.rebalance(n.parent)
}
else {
root = n
}
}
method rotate(a, dir) {
var b = (dir == :left ? a.right : a.left)
b.parent = a.parent
(dir == :left) ? (a.right = b.left)
: (a.left = b.right)
if (a.right != nil) {
a.right.parent = a
}
b.$dir = a
a.parent = b
if (b.parent != nil) {
if (b.parent.right == a) {
b.parent.right = b
}
else {
b.parent.left = b
}
}
self.setBalance(a, b)
return b
}
method rotate_twice(n, dir1, dir2) {
n.left = self.rotate(n.left, dir1)
self.rotate(n, dir2)
}
method height(n) {
if (n == nil) { return -1 }
1 + Math.max(self.height(n.left), self.height(n.right))
}
method setBalance(*nodes) {
nodes.each { |n|
n.balance = (self.height(n.right) - self.height(n.left))
}
}
method printBalance {
self.printBalance(root)
}
method printBalance(n) {
if (n != nil) {
self.printBalance(n.left)
print(n.balance, ' ')
self.printBalance(n.right)
}
}
}
var tree = AVLtree()
say "Inserting values 1 to 10"
{|i| tree.insert(i) } << 1..10
print "Printing balance: "
tree.printBalance

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CLASS AVL;
BEGIN
! AVL TREE ADAPTED FROM JULIENNE WALKER'S PRESENTATION AT ;
! HTTP://ETERNALLYCONFUZZLED.COM/TUTS/DATASTRUCTURES/JSW_TUT_AVL.ASPX. ;
! THIS PORT USES SIMILAR INDENTIFIER NAMES. ;
! THE KEY INTERFACE MUST BE SUPPORTED BY DATA STORED IN THE AVL TREE. ;
CLASS KEY;
VIRTUAL:
PROCEDURE LESS IS BOOLEAN PROCEDURE LESS (K); REF(KEY) K;;
PROCEDURE EQUAL IS BOOLEAN PROCEDURE EQUAL(K); REF(KEY) K;;
BEGIN
END KEY;
! NODE IS A NODE IN AN AVL TREE. ;
CLASS NODE(DATA); REF(KEY) DATA; ! ANYTHING COMPARABLE WITH LESS AND EQUAL. ;
BEGIN
INTEGER BALANCE; ! BALANCE FACTOR ;
REF(NODE) ARRAY LINK(0:1); ! CHILDREN, INDEXED BY "DIRECTION", 0 OR 1. ;
END NODE;
! A LITTLE READABILITY FUNCTION FOR RETURNING THE OPPOSITE OF A DIRECTION, ;
! WHERE A DIRECTION IS 0 OR 1. ;
! WHERE JW WRITES !DIR, THIS CODE HAS OPP(DIR). ;
INTEGER PROCEDURE OPP(DIR); INTEGER DIR;
BEGIN
OPP := 1 - DIR;
END OPP;
! SINGLE ROTATION ;
REF(NODE) PROCEDURE SINGLE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
BEGIN
REF(NODE) SAVE;
SAVE :- ROOT.LINK(OPP(DIR));
ROOT.LINK(OPP(DIR)) :- SAVE.LINK(DIR);
SAVE.LINK(DIR) :- ROOT;
SINGLE :- SAVE;
END SINGLE;
! DOUBLE ROTATION ;
REF(NODE) PROCEDURE DOUBLE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
BEGIN
REF(NODE) SAVE;
SAVE :- ROOT.LINK(OPP(DIR)).LINK(DIR);
ROOT.LINK(OPP(DIR)).LINK(DIR) :- SAVE.LINK(OPP(DIR));
SAVE.LINK(OPP(DIR)) :- ROOT.LINK(OPP(DIR));
ROOT.LINK(OPP(DIR)) :- SAVE;
SAVE :- ROOT.LINK(OPP(DIR));
ROOT.LINK(OPP(DIR)) :- SAVE.LINK(DIR);
SAVE.LINK(DIR) :- ROOT;
DOUBLE :- SAVE;
END DOUBLE;
! ADJUST BALANCE FACTORS AFTER DOUBLE ROTATION ;
PROCEDURE ADJUSTBALANCE(ROOT, DIR, BAL); REF(NODE) ROOT; INTEGER DIR, BAL;
BEGIN
REF(NODE) N, NN;
N :- ROOT.LINK(DIR);
NN :- N.LINK(OPP(DIR));
IF NN.BALANCE = 0 THEN BEGIN ROOT.BALANCE := 0; N.BALANCE := 0; END ELSE
IF NN.BALANCE = BAL THEN BEGIN ROOT.BALANCE := -BAL; N.BALANCE := 0; END
ELSE BEGIN ROOT.BALANCE := 0; N.BALANCE := BAL; END;
NN.BALANCE := 0;
END ADJUSTBALANCE;
REF(NODE) PROCEDURE INSERTBALANCE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
BEGIN REF(NODE) N; INTEGER BAL;
N :- ROOT.LINK(DIR);
BAL := 2*DIR - 1;
IF N.BALANCE = BAL THEN
BEGIN
ROOT.BALANCE := 0;
N.BALANCE := 0;
INSERTBALANCE :- SINGLE(ROOT, OPP(DIR));
END ELSE
BEGIN
ADJUSTBALANCE(ROOT, DIR, BAL);
INSERTBALANCE :- DOUBLE(ROOT, OPP(DIR));
END;
END INSERTBALANCE;
CLASS TUPLE(N,B); REF(NODE) N; BOOLEAN B;;
REF(TUPLE) PROCEDURE INSERTR(ROOT, DATA); REF(NODE) ROOT; REF(KEY) DATA;
BEGIN
IF ROOT == NONE THEN
INSERTR :- NEW TUPLE(NEW NODE(DATA), FALSE)
ELSE
BEGIN
REF(TUPLE) T; BOOLEAN DONE; INTEGER DIR;
DIR := 0;
IF ROOT.DATA.LESS(DATA) THEN
DIR := 1;
T :- INSERTR(ROOT.LINK(DIR), DATA);
ROOT.LINK(DIR) :- T.N;
DONE := T.B;
IF DONE THEN INSERTR :- NEW TUPLE(ROOT, TRUE) ELSE
BEGIN
ROOT.BALANCE := ROOT.BALANCE + 2*DIR - 1;
IF ROOT.BALANCE = 0 THEN
INSERTR :- NEW TUPLE(ROOT, TRUE) ELSE
IF ROOT.BALANCE = 1 OR ROOT.BALANCE = -1 THEN
INSERTR :- NEW TUPLE(ROOT, FALSE)
ELSE
INSERTR :- NEW TUPLE(INSERTBALANCE(ROOT, DIR), TRUE);
END;
END;
END INSERTR;
! INSERT A NODE INTO THE AVL TREE. ;
! DATA IS INSERTED EVEN IF OTHER DATA WITH THE SAME KEY ALREADY EXISTS. ;
PROCEDURE INSERT(TREE, DATA); NAME TREE; REF(NODE) TREE; REF(KEY) DATA;
BEGIN
REF(TUPLE) T;
T :- INSERTR(TREE, DATA);
TREE :- T.N;
END INSERT;
REF(TUPLE) PROCEDURE REMOVEBALANCE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
BEGIN REF(NODE) N; INTEGER BAL;
N :- ROOT.LINK(OPP(DIR));
BAL := 2*DIR - 1;
IF N.BALANCE = -BAL THEN
BEGIN ROOT.BALANCE := 0; N.BALANCE := 0;
REMOVEBALANCE :- NEW TUPLE(SINGLE(ROOT, DIR), FALSE);
END ELSE
IF N.BALANCE = BAL THEN
BEGIN ADJUSTBALANCE(ROOT, OPP(DIR), -BAL);
REMOVEBALANCE :- NEW TUPLE(DOUBLE(ROOT, DIR), FALSE);
END ELSE
BEGIN ROOT.BALANCE := -BAL; N.BALANCE := BAL;
REMOVEBALANCE :- NEW TUPLE(SINGLE(ROOT, DIR), TRUE);
END
END REMOVEBALANCE;
REF(TUPLE) PROCEDURE REMOVER(ROOT, DATA); REF(NODE) ROOT; REF(KEY) DATA;
BEGIN INTEGER DIR; BOOLEAN DONE; REF(TUPLE) T;
IF ROOT == NONE THEN
REMOVER :- NEW TUPLE(NONE, FALSE)
ELSE
IF ROOT.DATA.EQUAL(DATA) THEN
BEGIN
IF ROOT.LINK(0) == NONE THEN
BEGIN
REMOVER :- NEW TUPLE(ROOT.LINK(1), FALSE);
GOTO L;
END
ELSE IF ROOT.LINK(1) == NONE THEN
BEGIN
REMOVER :- NEW TUPLE(ROOT.LINK(0), FALSE);
GOTO L;
END
ELSE
BEGIN REF(NODE) HEIR;
HEIR :- ROOT.LINK(0);
WHILE HEIR.LINK(1) =/= NONE DO
HEIR :- HEIR.LINK(1);
ROOT.DATA :- HEIR.DATA;
DATA :- HEIR.DATA;
END;
END;
DIR := 0;
IF ROOT.DATA.LESS(DATA) THEN
DIR := 1;
T :- REMOVER(ROOT.LINK(DIR), DATA); ROOT.LINK(DIR) :- T.N; DONE := T.B;
IF DONE THEN
BEGIN
REMOVER :- NEW TUPLE(ROOT, TRUE);
GOTO L;
END;
ROOT.BALANCE := ROOT.BALANCE + 1 - 2*DIR;
IF ROOT.BALANCE = 1 OR ROOT.BALANCE = -1 THEN
REMOVER :- NEW TUPLE(ROOT, TRUE)
ELSE IF ROOT.BALANCE = 0 THEN
REMOVER :- NEW TUPLE(ROOT, FALSE)
ELSE
REMOVER :- REMOVEBALANCE(ROOT, DIR);
L:
END REMOVER;
! REMOVE A SINGLE ITEM FROM AN AVL TREE. ;
! IF KEY DOES NOT EXIST, FUNCTION HAS NO EFFECT. ;
PROCEDURE REMOVE(TREE, DATA); NAME TREE; REF(NODE) TREE; REF(KEY) DATA;
BEGIN REF(TUPLE) T;
T :- REMOVER(TREE, DATA);
TREE :- T.N;
END REMOVEM;
END.

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EXTERNAL CLASS AVL;
AVL
BEGIN
KEY CLASS INTEGERKEY(I); INTEGER I;
BEGIN
BOOLEAN PROCEDURE LESS (K); REF(KEY) K; LESS := I < K QUA INTEGERKEY.I;
BOOLEAN PROCEDURE EQUAL(K); REF(KEY) K; EQUAL := I = K QUA INTEGERKEY.I;
END INTEGERKEY;
PROCEDURE DUMP(ROOT); REF(NODE) ROOT;
BEGIN
IF ROOT =/= NONE THEN
BEGIN
DUMP(ROOT.LINK(0));
OUTINT(ROOT.DATA QUA INTEGERKEY.I, 0); OUTTEXT(" ");
DUMP(ROOT.LINK(1));
END
END DUMP;
INTEGER I;
REF(NODE) TREE;
OUTTEXT("Empty tree: "); DUMP(TREE); OUTIMAGE;
FOR I := 3, 1, 4, 1, 5 DO
BEGIN OUTTEXT("Insert "); OUTINT(I, 0); OUTTEXT(": ");
INSERT(TREE, NEW INTEGERKEY(I)); DUMP(TREE); OUTIMAGE;
END;
FOR I := 3, 1 DO
BEGIN OUTTEXT("Remove "); OUTINT(I, 0); OUTTEXT(": ");
REMOVE(TREE, NEW INTEGERKEY(I)); DUMP(TREE); OUTIMAGE;
END;
END.

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package require TclOO
namespace eval AVL {
# Class for the overall tree; manages real public API
oo::class create Tree {
variable root nil class
constructor {{nodeClass AVL::Node}} {
set class [oo::class create Node [list superclass $nodeClass]]
# Create a nil instance to act as a leaf sentinel
set nil [my NewNode ""]
set root [$nil ref]
# Make nil be special
oo::objdefine $nil {
method height {} {return 0}
method key {} {error "no key possible"}
method value {} {error "no value possible"}
method destroy {} {
# Do nothing (doesn't prohibit destruction entirely)
}
method print {indent increment} {
# Do nothing
}
}
}
# How to actually manufacture a new node
method NewNode {key} {
if {![info exists nil]} {set nil ""}
$class new $key $nil [list [namespace current]::my NewNode]
}
# Create a new node in the tree and return it
method insert {key} {
set node [my NewNode $key]
if {$root eq $nil} {
set root $node
} else {
$root insert $node
}
return $node
}
# Find the node for a particular key
method lookup {key} {
for {set node $root} {$node ne $nil} {} {
if {[$node key] == $key} {
return $node
} elseif {[$node key] > $key} {
set node [$node left]
} else {
set node [$node right]
}
}
error "no such node"
}
# Print a tree out, one node per line
method print {{indent 0} {increment 1}} {
$root print $indent $increment
return
}
}
# Class of an individual node; may be subclassed
oo::class create Node {
variable key value left right 0 refcount newNode
constructor {n nil instanceFactory} {
set newNode $instanceFactory
set 0 [expr {$nil eq "" ? [self] : $nil}]
set key $n
set value {}
set left [set right $0]
set refcount 0
}
method ref {} {
incr refcount
return [self]
}
method destroy {} {
if {[incr refcount -1] < 1} next
}
method New {key value} {
set n [{*}$newNode $key]
$n setValue $value
return $n
}
# Getters
method key {} {return $key}
method value {} {return $value}
method left {} {return $left}
method right {args} {return $right}
# Setters
method setValue {newValue} {
set value $newValue
}
method setLeft {node} {
# Non-trivial because of reference management
$node ref
$left destroy
set left $node
return
}
method setRight {node} {
# Non-trivial because of reference management
$node ref
$right destroy
set right $node
return
}
# Print a node and its descendents
method print {indent increment} {
puts [format "%s%s => %s" [string repeat " " $indent] $key $value]
incr indent $increment
$left print $indent $increment
$right print $indent $increment
}
method height {} {
return [expr {max([$left height], [$right height]) + 1}]
}
method balanceFactor {} {
expr {[$left height] - [$right height]}
}
method insert {node} {
# Simple insertion
if {$key > [$node key]} {
if {$left eq $0} {
my setLeft $node
} else {
$left insert $node
}
} else {
if {$right eq $0} {
my setRight $node
} else {
$right insert $node
}
}
# Rebalance this node
if {[my balanceFactor] > 1} {
if {[$left balanceFactor] < 0} {
$left rotateLeft
}
my rotateRight
} elseif {[my balanceFactor] < -1} {
if {[$right balanceFactor] > 0} {
$right rotateRight
}
my rotateLeft
}
}
# AVL Rotations
method rotateLeft {} {
set new [my New $key $value]
set key [$right key]
set value [$right value]
$new setLeft $left
$new setRight [$right left]
my setLeft $new
my setRight [$right right]
}
method rotateRight {} {
set new [my New $key $value]
set key [$left key]
set value [$left value]
$new setLeft [$left right]
$new setRight $right
my setLeft [$left left]
my setRight $new
}
}
}

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# Create an AVL tree
AVL::Tree create tree
# Populate it with some semi-random data
for {set i 33} {$i < 127} {incr i} {
[tree insert $i] setValue \
[string repeat [format %c $i] [expr {1+int(rand()*5)}]]
}
# Print it out
tree print
# Look up a few values in the tree
for {set i 0} {$i < 10} {incr i} {
set k [expr {33+int((127-33)*rand())}]
puts $k=>[[tree lookup $k] value]
}
# Destroy the tree and all its nodes
tree destroy

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/** A single node in an AVL tree */
class AVLnode <T> {
balance: number
left: AVLnode<T>
right: AVLnode<T>
constructor(public key: T, public parent: AVLnode<T> = null) {
this.balance = 0
this.left = null
this.right = null
}
}
/** The balanced AVL tree */
class AVLtree <T> {
// public members organized here
constructor() {
this.root = null
}
insert(key: T): boolean {
if (this.root === null) {
this.root = new AVLnode<T>(key)
} else {
let n: AVLnode<T> = this.root,
parent: AVLnode<T> = null
while (true) {
if(n.key === key) {
return false
}
parent = n
let goLeft: boolean = n.key > key
n = goLeft ? n.left : n.right
if (n === null) {
if (goLeft) {
parent.left = new AVLnode<T>(key, parent)
} else {
parent.right = new AVLnode<T>(key, parent)
}
this.rebalance(parent)
break
}
}
}
return true
}
deleteKey(delKey: T): void {
if (this.root === null) {
return
}
let n: AVLnode<T> = this.root,
parent: AVLnode<T> = this.root,
delNode: AVLnode<T> = null,
child: AVLnode<T> = this.root
while (child !== null) {
parent = n
n = child
child = delKey >= n.key ? n.right : n.left
if (delKey === n.key) {
delNode = n
}
}
if (delNode !== null) {
delNode.key = n.key
child = n.left !== null ? n.left : n.right
if (this.root.key === delKey) {
this.root = child
} else {
if (parent.left === n) {
parent.left = child
} else {
parent.right = child
}
this.rebalance(parent)
}
}
}
treeBalanceString(n: AVLnode<T> = this.root): string {
if (n !== null) {
return `${this.treeBalanceString(n.left)} ${n.balance} ${this.treeBalanceString(n.right)}`
}
return ""
}
toString(n: AVLnode<T> = this.root): string {
if (n !== null) {
return `${this.toString(n.left)} ${n.key} ${this.toString(n.right)}`
}
return ""
}
// private members organized here
private root: AVLnode<T>
private rotateLeft(a: AVLnode<T>): AVLnode<T> {
let b: AVLnode<T> = a.right
b.parent = a.parent
a.right = b.left
if (a.right !== null) {
a.right.parent = a
}
b.left = a
a.parent = b
if (b.parent !== null) {
if (b.parent.right === a) {
b.parent.right = b
} else {
b.parent.left = b
}
}
this.setBalance(a)
this.setBalance(b)
return b
}
private rotateRight(a: AVLnode<T>): AVLnode<T> {
let b: AVLnode<T> = a.left
b.parent = a.parent
a.left = b.right
if (a.left !== null) {
a.left.parent = a
}
b.right = a
a.parent = b
if (b.parent !== null) {
if (b.parent.right === a) {
b.parent.right = b
} else {
b.parent.left = b
}
}
this.setBalance(a)
this.setBalance(b)
return b
}
private rotateLeftThenRight(n: AVLnode<T>): AVLnode<T> {
n.left = this.rotateLeft(n.left)
return this.rotateRight(n)
}
private rotateRightThenLeft(n: AVLnode<T>): AVLnode<T> {
n.right = this.rotateRight(n.right)
return this.rotateLeft(n)
}
private rebalance(n: AVLnode<T>): void {
this.setBalance(n)
if (n.balance === -2) {
if(this.height(n.left.left) >= this.height(n.left.right)) {
n = this.rotateRight(n)
} else {
n = this.rotateLeftThenRight(n)
}
} else if (n.balance === 2) {
if(this.height(n.right.right) >= this.height(n.right.left)) {
n = this.rotateLeft(n)
} else {
n = this.rotateRightThenLeft(n)
}
}
if (n.parent !== null) {
this.rebalance(n.parent)
} else {
this.root = n
}
}
private height(n: AVLnode<T>): number {
if (n === null) {
return -1
}
return 1 + Math.max(this.height(n.left), this.height(n.right))
}
private setBalance(n: AVLnode<T>): void {
n.balance = this.height(n.right) - this.height(n.left)
}
public showNodeBalance(n: AVLnode<T>): string {
if (n !== null) {
return `${this.showNodeBalance(n.left)} ${n.balance} ${this.showNodeBalance(n.right)}`
}
return ""
}
}

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class Node {
construct new(key, parent) {
_key = key
_parent = parent
_balance = 0
_left = null
_right = null
}
key { _key }
parent { _parent }
balance { _balance }
left { _left }
right { _right }
key=(k) { _key = k }
parent=(p) { _parent = p }
balance=(v) { _balance = v }
left=(n) { _left = n }
right= (n) { _right = n }
}
class AvlTree {
construct new() {
_root = null
}
insert(key) {
if (!_root) {
_root = Node.new(key, null)
} else {
var n = _root
while (true) {
if (n.key == key) return false
var parent = n
var goLeft = n.key > key
n = goLeft ? n.left : n.right
if (!n) {
if (goLeft) {
parent.left = Node.new(key, parent)
} else {
parent.right = Node.new(key, parent)
}
rebalance(parent)
break
}
}
}
return true
}
delete(delKey) {
if (!_root) return
var n = _root
var parent = _root
var delNode = null
var child = _root
while (child) {
parent = n
n = child
child = (delKey >= n.key) ? n.right : n.left
if (delKey == n.key) delNode = n
}
if (delNode) {
delNode.key = n.key
child = n.left ? n.left : n.right
if (_root.key == delKey) {
_root = child
if (_root) _root.parent = null
} else {
if (parent.left == n) {
parent.left = child
} else {
parent.right = child
}
if (child) child.parent = parent
rebalance(parent)
}
}
}
rebalance(n) {
setBalance([n])
var nn = n
if (nn.balance == -2) {
if (height(nn.left.left) >= height(nn.left.right)) {
nn = rotateRight(nn)
} else {
nn = rotateLeftThenRight(nn)
}
} else if (nn.balance == 2) {
if (height(nn.right.right) >= height(nn.right.left)) {
nn = rotateLeft(nn)
} else {
nn = rotateRightThenLeft(nn)
}
}
if (nn.parent) rebalance(nn.parent) else _root = nn
}
rotateLeft(a) {
var b = a.right
b.parent = a.parent
a.right = b.left
if (a.right) a.right.parent = a
b.left = a
a.parent = b
if (b.parent) {
if (b.parent.right == a) {
b.parent.right = b
} else {
b.parent.left = b
}
}
setBalance([a, b])
return b
}
rotateRight(a) {
var b = a.left
b.parent = a.parent
a.left = b.right
if (a.left) a.left.parent = a
b.right = a
a.parent = b
if (b.parent) {
if (b.parent.right == a) {
b.parent.right = b
} else {
b.parent.left = b
}
}
setBalance([a, b])
return b
}
rotateLeftThenRight(n) {
n.left = rotateLeft(n.left)
return rotateRight(n)
}
rotateRightThenLeft(n) {
n.right = rotateRight(n.right)
return rotateLeft(n)
}
height(n) {
if (!n) return -1
return 1 + height(n.left).max(height(n.right))
}
setBalance(nodes) {
for (n in nodes) n.balance = height(n.right) - height(n.left)
}
printKey() {
printKey(_root)
System.print()
}
printKey(n) {
if (n) {
printKey(n.left)
System.write("%(n.key) ")
printKey(n.right)
}
}
printBalance() {
printBalance(_root)
System.print()
}
printBalance(n) {
if (n) {
printBalance(n.left)
System.write("%(n.balance) ")
printBalance(n.right)
}
}
}
var tree = AvlTree.new()
System.print("Inserting values 1 to 10")
for (i in 1..10) tree.insert(i)
System.write("Printing key : ")
tree.printKey()
System.write("Printing balance : ")
tree.printBalance()

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// AVL-Tree C code, https://www.programiz.com/dsa/avl-tree
// Ported to Yabasic by Galileo 2022/07
KEY = 1 : LRIGHT = 2 : LLEFT = 3 : HEIGHT = 4
root = 0 : ramas = 5 : indice = 0
dim arbol(ramas, 4)
sub rotateRight(y)
local x, T2
x = arbol(y, LLEFT)
T2 = arbol(x, LRIGHT)
arbol(x, LRIGHT) = y
arbol(y, LLEFT) = T2
arbol(y, HEIGHT) = max(height(arbol(y, LLEFT)), height(arbol(y, LRIGHT))) + 1
arbol(x, HEIGHT) = max(height(arbol(x, LLEFT)), height(arbol(x, LRIGHT))) + 1
return x
end sub
sub rotateLeft(x)
local y, T2
y = arbol(x, LRIGHT)
T2 = arbol(y, LLEFT)
arbol(y, LLEFT) = x
arbol(x, LRIGHT) = T2
arbol(x, HEIGHT) = max(height(arbol(x, LLEFT)), height(arbol(x, LRIGHT))) + 1
arbol(y, HEIGHT) = max(height(arbol(y, LLEFT)), height(arbol(y, LRIGHT))) + 1
return y
end sub
sub Balance(current)
return height(arbol(current, LLEFT)) - height(arbol(current, LRIGHT))
end sub
sub height(current)
return arbol(current, HEIGHT)
end sub
sub insert(current, key)
local balance
if current = 0 indice = indice + 1 : if indice > ramas then ramas = ramas + 5 : redim arbol(ramas, 4) endif : arbol(indice, KEY) = key : arbol(indice, HEIGHT) = 1 : return indice
if key < arbol(current, KEY) then
arbol(current, LLEFT) = insert(arbol(current, LLEFT), key)
elsif key > arbol(current, KEY) then
arbol(current, LRIGHT) = insert(arbol(current, LRIGHT), key)
else
return current
endif
arbol(current, HEIGHT) = max(height(arbol(current, LLEFT)), height(arbol(current, LRIGHT))) + 1
balance = Balance(current)
if balance > 1 and key < arbol(arbol(current, LLEFT), KEY) return rotateRight(current)
if balance < -1 and key > arbol(arbol(current, LRIGHT), KEY) return rotateLeft(current)
if balance > 1 and key > arbol(arbol(current, LLEFT), KEY) then
arbol(current, LLEFT) = rotateLeft(arbol(current, LLEFT))
return rotateRight(current)
endif
if balance < -1 and key < arbol(arbol(current, LRIGHT), KEY) then
arbol(current, LRIGHT) = rotateRight(arbol(current, LRIGHT))
return rotateLeft(current)
endif
return current
end sub
sub minValueNode(current)
while arbol(current, LLEFT)
current = arbol(current, LLEFT)
wend
return current
end sub
// Delete a nodes
sub deleteNode(root, key)
local temp, balance
// Find the node and delete it
if root = 0 return root
if key < arbol(root, KEY) then
arbol(root, LLEFT) = deleteNode(arbol(root, LLEFT), key)
elsif key > arbol(root, KEY) then
arbol(root, LRIGHT) = deleteNode(arbol(root, LRIGHT), key)
else
if arbol(root, LLEFT) = 0 or arbol(root, LRIGHT) = 0 then
temp = max(arbol(root, LLEFT), arbol(root, LRIGHT))
if temp = 0 then
temp = root
root = 0
else
root = temp
endif
else
temp = minValueNode(arbol(root, LRIGHT))
arbol(root, KEY) = arbol(temp, KEY)
arbol(root, LRIGHT) = deleteNode(arbol(root, LRIGHT), arbol(temp, KEY))
endif
endif
if root = 0 return root
// Update the balance factor of each node and
// balance the tree
arbol(root, HEIGHT) = 1 + max(height(arbol(root, LLEFT)), height(arbol(root, LRIGHT)))
balance = Balance(root)
if balance > 1 and Balance(arbol(root, LLEFT)) >= 0 return rightRotate(root)
if balance > 1 and Balance(arbol(root, LLEFT)) < 0 arbol(root, LLEFT) = leftRotate(arbol(root, LLEFT)) : return rightRotate(root)
if balance < -1 and Balance(arbol(root, LRIGHT)) <= 0 return leftRotate(root)
if balance < -1 and Balance(arbol(root, LRIGHT)) > 0 arbol(root, LRIGHT) = rightRotate(arbol(root, LRIGHT)) : return leftRotate(root)
return root
end sub
sub preOrder(temp)
if temp then
print arbol(temp, KEY), " ", arbol(temp, HEIGHT), " ", Balance(temp)
preOrder(arbol(temp, LLEFT))
preOrder(arbol(temp, LRIGHT))
endif
end sub
root = insert(root, 2)
root = insert(root, 1)
root = insert(root, 7)
root = insert(root, 4)
root = insert(root, 5)
root = insert(root, 3)
root = insert(root, 8)
preOrder(root)
root = deleteNode(root, 3)
print "\nAfter deletion: "
preOrder(root)