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Ingy döt Net 2023-07-01 11:58:00 -04:00
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3
Task/Zig-zag-matrix/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Zig-zag_matrix
note: Matrices

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Task/Zig-zag-matrix/00-TASK.txt Normal file
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;Task:
Produce a zig-zag array.
A &nbsp; ''zig-zag'' &nbsp; array is a square arrangement of the first &nbsp; <big>N<sup>2</sup></big> &nbsp; natural numbers, &nbsp; where the
<br>numbers increase sequentially as you zig-zag along the array's &nbsp; [https://en.wiktionary.org/wiki/antidiagonal anti-diagonals].
For a graphical representation, see &nbsp; [[wp:Image:JPEG_ZigZag.svg|JPG zigzag]] &nbsp; (JPG uses such arrays to encode images).
For example, given &nbsp; '''5''', &nbsp; produce this array:
<pre>
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24
</pre>
;Related tasks:
* &nbsp; [[Spiral matrix]]
* &nbsp; [[Identity matrix]]
* &nbsp; [[Ulam spiral (for primes)]]
;See also:
* &nbsp; Wiktionary entry: &nbsp; [https://en.wiktionary.org/wiki/antidiagonal anti-diagonals]
<br><br>

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Task/Zig-zag-matrix/11l/zig-zag-matrix.11l Normal file
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F zigzag(n)
F compare(xy)
V (x, y) = xy
R (x + y, I (x + y) % 2 {-y} E y)
V xs = 0 .< n
R Dict(enumerate(sorted((multiloop(xs, xs, (x, y) -> (x, y))), key' compare)), (n, index) -> (index, n))
F printzz(myarray)
V n = Int(myarray.len ^ 0.5 + 0.5)
V xs = 0 .< n
print((xs.map(y -> @xs.map(x -> ‘#3’.format(@@myarray[(x, @y)])).join(‘’))).join("\n"))
printzz(zigzag(6))

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Task/Zig-zag-matrix/360-Assembly/zig-zag-matrix.360 Normal file
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* Zig-zag matrix 15/08/2015
ZIGZAGMA CSECT
USING ZIGZAGMA,R12 set base register
LR R12,R15 establish addressability
LA R9,N n : matrix size
LA R6,1 i=1
LA R7,1 j=1
LR R11,R9 n
MR R10,R9 *n
BCTR R11,0 R11=n**2-1
SR R8,R8 k=0
LOOPK CR R8,R11 do k=0 to n**2-1
BH ELOOPK k>limit
LR R1,R6 i
BCTR R1,0 -1
MR R0,R9 *n
LR R2,R7 j
BCTR R2,0 -1
AR R1,R2 (i-1)*n+(j-1)
SLA R1,1 index=((i-1)*n+j-1)*2
STH R8,T(R1) t(i,j)=k
LR R2,R6 i
AR R2,R7 i+j
LA R1,2 2
SRDA R2,32 shift right r1 to r2
DR R2,R1 (i+j)/2
LTR R2,R2 if mod(i+j,2)=0
BNZ ELSEMOD
CR R7,R9 if j<n
BNL ELSE1
LA R7,1(R7) j=j+1
B EIF1
ELSE1 LA R6,2(R6) i=i+2
EIF1 CH R6,=H'1' if i>1
BNH NOT1
BCTR R6,0 i=i-1
NOT1 B NOT2
ELSEMOD CR R6,R9 if i<n
BNL ELSE2
LA R6,1(R6) i=i+1
B EIF2
ELSE2 LA R7,2(R7) j=j+2
EIF2 CH R7,=H'1' if j>1
BNH NOT2
BCTR R7,0 j=j-1
NOT2 LA R8,1(R8) k=k+1
B LOOPK
ELOOPK LA R6,1 end k; i=1
LOOPI CR R6,R9 do i=1 to n
BH ELOOPI i>n
LA R10,0 ibuf=0 buffer index
MVC BUFFER,=CL80' '
LA R7,1 j=1
LOOPJ CR R7,R9 do j=1 to n
BH ELOOPJ j>n
LR R1,R6 i
BCTR R1,0 -1
MR R0,R9 *n
LR R2,R7 j
BCTR R2,0 -1
AR R1,R2 (i-1)*n+(j-1)
SLA R1,1 index=((i-1)*n+j-1)*2
LH R2,T(R1) t(i,j)
LA R3,BUFFER
AR R3,R10
XDECO R2,XDEC edit t(i,j) length=12
MVC 0(4,R3),XDEC+8 move in buffer length=4
LA R10,4(R10) ibuf=ibuf+1
LA R7,1(R7) j=j+1
B LOOPJ
ELOOPJ XPRNT BUFFER,80 end j
LA R6,1(R6) i=i+1
B LOOPI
ELOOPI XR R15,R15 end i; return_code=0
BR R14 return to caller
N EQU 5 matrix size
BUFFER DS CL80
XDEC DS CL12
T DS (N*N)H t(n,n) matrix
YREGS
END ZIGZAGMA

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Task/Zig-zag-matrix/ALGOL-68/zig-zag-matrix.alg Normal file
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PROC zig zag = (INT n)[,]INT: (
PROC move = (REF INT i, j)VOID: (
IF j < n THEN
i := ( i <= 1 | 1 | i-1 );
j +:= 1
ELSE
i +:= 1
FI
);
[n, n]INT a;
INT x:=LWB a, y:=LWB a;
FOR v FROM 0 TO n**2-1 DO
a[y, x] := v;
IF ODD (x + y) THEN
move(x, y)
ELSE
move(y, x)
FI
OD;
a
);
INT dim = 5;
#IF formatted transput possible THEN
FORMAT d = $z-d$;
FORMAT row = $"("n(dim-1)(f(d)",")f(d)")"$;
FORMAT block = $"("n(dim-1)(f(row)","lx)f(row)")"l$;
printf((block, zig zag(dim)))
ELSE#
[,]INT result = zig zag(dim);
FOR i TO dim DO
print((result[i,], new line))
OD
#FI#

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Task/Zig-zag-matrix/ALGOL-W/zig-zag-matrix.alg Normal file
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begin % zig-zag matrix %
% z is returned holding a zig-zag matrix of order n, z must be at least n x n %
procedure makeZigZag ( integer value n
; integer array z( *, * )
) ;
begin
procedure move ;
begin
if y = n then begin
upRight := not upRight;
x := x + 1
end
else if x = 1 then begin
upRight := not upRight;
y := y + 1
end
else begin
x := x - 1;
y := y + 1
end
end move ;
procedure swapXY ;
begin
integer swap;
swap := x;
x := y;
y := swap;
end swapXY ;
integer x, y;
logical upRight;
% initialise the n x n matrix in z %
for i := 1 until n do for j := 1 until n do z( i, j ) := 0;
% fill in the zig-zag matrix %
x := y := 1;
upRight := true;
for i := 1 until n * n do begin
z( x, y ) := i - 1;
if upRight then move
else begin
swapXY;
move;
swapXY
end;
end;
end makeZigZap ;
begin
integer array zigZag( 1 :: 10, 1 :: 10 );
for n := 5 do begin
makeZigZag( n, zigZag );
for i := 1 until n do begin
write( i_w := 4, s_w := 1, zigZag( i, 1 ) );
for j := 2 until n do writeon( i_w := 4, s_w := 1, zigZag( i, j ) );
end
end
end
end.

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Task/Zig-zag-matrix/APL/zig-zag-matrix.apl Normal file
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zz ← {⍵⍴⎕IO-⍨⍋⊃,/{(2|⍴⍵):⌽⍵⋄⍵}¨(⊂w)/¨⍨w{↓⍵∘.=⍨∪⍵}+/[1]⍵⊤w←⎕IO-⍨⍳×/⍵} ⍝ General zigzag (any rectangle)
zzSq ← {zz,⍨⍵} ⍝ Square zigzag
zzSq 5
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24

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Task/Zig-zag-matrix/ATS/zig-zag-matrix.ats Normal file
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(* ****** ****** *)
//
#include
"share/atspre_define.hats" // defines some names
#include
"share/atspre_staload.hats" // for targeting C
#include
"share/HATS/atspre_staload_libats_ML.hats" // for ...
//
(* ****** ****** *)
//
extern
fun
Zig_zag_matrix(n: int): void
//
(* ****** ****** *)
fun max(a: int, b: int): int =
if a > b then a else b
fun movex(n: int, x: int, y: int): int =
if y < n-1 then max(0, x-1) else x+1
fun movey(n: int, x: int, y: int): int =
if y < n-1 then y+1 else y
fun zigzag(n: int, i: int, row: int, x: int, y: int): void =
if i = n*n then ()
else
let
val () = (if x = row then begin print i; print ','; end else ())
//val () = (begin print x; print ' '; print y; print ' '; print i; print ' '; end)
val nextX: int = if ((x+y) % 2) = 0 then movex(n, x, y) else movey(n, y, x)
val nextY: int = if ((x+y) % 2) = 0 then movey(n, x, y) else movex(n, y, x)
in
zigzag(n, i+1, row, nextX, nextY)
end
implement
Zig_zag_matrix(n) =
let
fun loop(row: int): void =
if row = n then () else
let
val () = zigzag(n, 0, row, 0, 0)
val () = println!(" ")
in
loop(row + 1)
end
in
loop(0)
end
(* ****** ****** *)
implement
main0() = () where
{
val () = Zig_zag_matrix(5)
} (* end of [main0] *)
(* ****** ****** *)

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Task/Zig-zag-matrix/AWK/zig-zag-matrix.awk Normal file
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# syntax: GAWK -f ZIG-ZAG_MATRIX.AWK [-v offset={0|1}] [size]
BEGIN {
# offset: "0" prints 0 to size^2-1 while "1" prints 1 to size^2
offset = (offset == "") ? 0 : offset
size = (ARGV[1] == "") ? 5 : ARGV[1]
if (offset !~ /^[01]$/) { exit(1) }
if (size !~ /^[0-9]+$/) { exit(1) }
width = length(size ^ 2 - 1 + offset) + 1
i = j = 1
for (n=0; n<=size^2-1; n++) { # build array
arr[i-1,j-1] = n + offset
if ((i+j) % 2 == 0) {
if (j < size) { j++ } else { i+=2 }
if (i > 1) { i-- }
}
else {
if (i < size) { i++ } else { j+=2 }
if (j > 1) { j-- }
}
}
for (row=0; row<size; row++) { # show array
for (col=0; col<size; col++) {
printf("%*d",width,arr[row,col])
}
printf("\n")
}
exit(0)
}

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Task/Zig-zag-matrix/Action-/zig-zag-matrix.action Normal file
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DEFINE MAX_SIZE="10"
DEFINE MAX_MATRIX_SIZE="100"
INT FUNC Index(BYTE size,x,y)
RETURN (x+y*size)
PROC PrintMatrix(BYTE ARRAY a BYTE size)
BYTE i,j,v
FOR j=0 TO size-1
DO
FOR i=0 TO size-1
DO
v=a(Index(size,i,j))
IF v<10 THEN
Print(" ")
ELSE
Print(" ")
FI
PrintB(v)
OD
PutE()
OD
RETURN
PROC FillMatrix(BYTE ARRAY a BYTE size)
BYTE start,end
INT dir,i,j
start=0 end=size*size-1
i=0 j=0 dir=1
DO
a(Index(size,i,j))=start
a(Index(size,size-1-i,size-1-j))=end
start==+1 end==-1
i==+dir j==-dir
IF i<0 THEN
i==+1 dir=-dir
ELSEIF j<0 THEN
j==+1 dir=-dir
FI
UNTIL start>=end
OD
IF start=end THEN
a(Index(size,i,j))=start
FI
RETURN
PROC Test(BYTE size)
BYTE ARRAY mat(MAX_MATRIX_SIZE)
PrintF("Matrix size: %B%E",size)
FillMatrix(mat,size)
PrintMatrix(mat,size)
PutE()
RETURN
PROC Main()
Test(5)
Test(6)
RETURN

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Task/Zig-zag-matrix/ActionScript/zig-zag-matrix.as Normal file
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package
{
public class ZigZagMatrix extends Array
{
private var height:uint;
private var width:uint;
public var mtx:Array = [];
public function ZigZagMatrix(size:uint)
{
this.height = size;
this.width = size;
this.mtx = [];
for (var i:uint = 0; i < size; i++) {
this.mtx[i] = [];
}
i = 1;
var j:uint = 1;
for (var e:uint = 0; e < size*size; e++) {
this.mtx[i-1][j-1] = e;
if ((i + j) % 2 == 0) {
// Even stripes
if (j < size) j ++;
else i += 2;
if (i > 1) i --;
} else {
// Odd stripes
if (i < size) i ++;
else j += 2;
if (j > 1) j --;
}
}
}
}
}

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Task/Zig-zag-matrix/Ada/zig-zag-matrix.ada Normal file
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with Ada.Text_IO; use Ada.Text_IO;
procedure Test_Zig_Zag is
type Matrix is array (Positive range <>, Positive range <>) of Natural;
function Zig_Zag (Size : Positive) return Matrix is
Data : Matrix (1..Size, 1..Size);
I, J : Integer := 1;
begin
Data (1, 1) := 0;
for Element in 1..Size**2 - 1 loop
if (I + J) mod 2 = 0 then
-- Even stripes
if J < Size then
J := J + 1;
else
I := I + 2;
end if;
if I > 1 then
I := I - 1;
end if;
else
-- Odd stripes
if I < Size then
I := I + 1;
else
J := J + 2;
end if;
if J > 1 then
J := J - 1;
end if;
end if;
Data (I, J) := Element;
end loop;
return Data;
end Zig_Zag;
procedure Put (Data : Matrix) is
begin
for I in Data'Range (1) loop
for J in Data'Range (2) loop
Put (Integer'Image (Data (I, J)));
end loop;
New_Line;
end loop;
end Put;
begin
Put (Zig_Zag (5));
end Test_Zig_Zag;

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Task/Zig-zag-matrix/Agena/zig-zag-matrix.agena Normal file
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# zig-zag matrix
makeZigZag := proc( n :: number ) :: table is
local move := proc( x :: number, y :: number, upRight :: boolean ) is
if y = n then
upRight := not upRight;
x := x + 1
elif x = 1 then
upRight := not upRight;
y := y + 1
else
x := x - 1;
y := y + 1
fi;
return x, y, upRight
end ;
# create empty table
local result := [];
for i to n do
result[ i ] := [];
for j to n do result[ i, j ] := 0 od
od;
# fill the table
local x, y, upRight := 1, 1, true;
for i to n * n do
result[ x, y ] := i - 1;
if upRight then
x, y, upRight := move( x, y, upRight )
else
y, x, upRight := move( y, x, upRight )
fi
od;
return result
end;
scope
local m := makeZigZag( 5 );
for i to size m do
for j to size m do
printf( " %3d", m[ i, j ] )
od;
print()
od
epocs

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Task/Zig-zag-matrix/AppleScript/zig-zag-matrix-1.applescript Normal file
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set n to 5 -- Size of zig-zag matrix (n^2 cells).
-- Create an empty matrix.
set m to {}
repeat with i from 1 to n
set R to {}
repeat with j from 1 to n
set end of R to 0
end repeat
set end of m to R
end repeat
-- Populate the matrix in a zig-zag manner.
set {x, y, v, d} to {1, 1, 0, 1}
repeat while v < (n ^ 2)
if 1 ≤ x and x ≤ n and 1 ≤ y and y ≤ n then
set {m's item y's item x, x, y, v} to {v, x + d, y - d, v + 1}
else if x > n then
set {x, y, d} to {n, y + 2, -d}
else if y > n then
set {x, y, d} to {x + 2, n, -d}
else if x < 1 then
set {x, y, d} to {1, y, -d}
else if y < 1 then
set {x, y, d} to {x, 1, -d}
end if
end repeat
--> R = {{0, 1, 5, 6, 14}, {2, 4, 7, 13, 15}, {3, 8, 12, 16, 21}, {9, 11, 17, 20, 22}, {10, 18, 19, 23, 24}}
-- Reformat the matrix into a table for viewing.
repeat with i in m
repeat with j in i
set j's contents to (characters -(length of (n ^ 2 as string)) thru -1 of (" " & j)) as string
end repeat
set end of i to return
end repeat
return return & m as string

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Task/Zig-zag-matrix/AppleScript/zig-zag-matrix-2.applescript Normal file
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set n to 5
set m to {}
repeat with i from 1 to n
set end of m to {} -- Built a foundation for the matrix out of n empty lists.
end repeat
set {v, d, i} to {0, -1, 1}
repeat while v < n ^ 2
if length of m's item i < n then
set {end of m's item i, i, v} to {f(v, n), i + d, v + 1}
if i < 1 then
set {i, d} to {1, -d}
else if i > n then
set {i, d} to {n, -d}
else if i > 1 and (count of m's item (i - 1)) = 1 then
set d to -d
end if
else
set {i, d} to {i + 1, 1}
end if
end repeat
-- Handler/function to format the cells on the fly.
on f(v, n)
return (characters -(length of (n ^ 2 as string)) thru -1 of (" " & v)) as string
end f
-- Reformat the matrix into a table for viewing.
set text item delimiters to ""
repeat with i in m
set i's contents to (i as string) & return
end repeat
return return & m as string

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Task/Zig-zag-matrix/AppleScript/zig-zag-matrix-3.applescript Normal file
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-- zigzagMatrix
on zigzagMatrix(n)
-- diagonals :: n -> [[n]]
script diagonals
on |λ|(n)
script mf
on diags(xs, iCol, iRow)
if (iCol < length of xs) then
if iRow < n then
set iNext to iCol + 1
else
set iNext to iCol - 1
end if
set {headList, tail} to splitAt(iCol, xs)
{headList} & diags(tail, iNext, iRow + 1)
else
{xs}
end if
end diags
end script
diags(enumFromTo(0, n * n - 1), 1, 1) of mf
end |λ|
end script
-- oddReversed :: [a] -> Int -> [a]
script oddReversed
on |λ|(lst, i)
if i mod 2 = 0 then
lst
else
reverse of lst
end if
end |λ|
end script
rowsFromDiagonals(n, map(oddReversed, |λ|(n) of diagonals))
end zigzagMatrix
-- Rows of given length from list of diagonals
-- rowsFromDiagonals :: Int -> [[a]] -> [[a]]
on rowsFromDiagonals(n, lst)
if length of lst > 0 then
-- lengthOverOne :: [a] -> Bool
script lengthOverOne
on |λ|(lst)
length of lst > 1
end |λ|
end script
set {edge, residue} to splitAt(n, lst)
{map(my head, edge)} & ¬
rowsFromDiagonals(n, ¬
map(my tail, ¬
filter(lengthOverOne, edge)) & residue)
else
{}
end if
end rowsFromDiagonals
-- TEST -----------------------------------------------------------------------
on run
zigzagMatrix(5)
end run
-- GENERIC FUNCTIONS ----------------------------------------------------------
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if n < m then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- filter :: (a -> Bool) -> [a] -> [a]
on filter(f, xs)
tell mReturn(f)
set lst to {}
set lng to length of xs
repeat with i from 1 to lng
set v to item i of xs
if |λ|(v, i, xs) then set end of lst to v
end repeat
return lst
end tell
end filter
-- head :: [a] -> a
on head(xs)
if length of xs > 0 then
item 1 of xs
else
missing value
end if
end head
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- splitAt:: n -> list -> {n items from start of list, rest of list}
-- splitAt :: Int -> [a] -> ([a], [a])
on splitAt(n, xs)
if n > 0 and n < length of xs then
{items 1 thru n of xs, items (n + 1) thru -1 of xs}
else
if n < 1 then
{{}, xs}
else
{xs, {}}
end if
end if
end splitAt
-- tail :: [a] -> [a]
on tail(xs)
if length of xs > 1 then
items 2 thru -1 of xs
else
{}
end if
end tail

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Task/Zig-zag-matrix/AppleScript/zig-zag-matrix-4.applescript Normal file
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on zigzagMatrix(n)
script o
property matrix : {} -- Matrix list.
property row : missing value -- Row sublist.
end script
repeat n times
set end of o's matrix to {} -- Build a foundation for the matrix out of n empty lists.
end repeat
set {r, d} to {1, -1} -- Row index and direction to next insertion row (negative = row above).
repeat with v from 0 to (n ^ 2) - 1 -- Values to insert.
set o's row to o's matrix's item r
repeat while ((count o's row) = n)
set r to r + 1
set d to 1
set o's row to o's matrix's item r
end repeat
set end of o's row to v
set r to r + d
if (r < 1) then
set r to 1
set d to -d
else if (r > n) then
set r to n
set d to -d
else if ((r > 1) and ((count o's matrix's item (r - 1)) = 1)) then
set d to -d
end if
end repeat
return o's matrix
end zigzagMatrix
-- Demo:
on matrixToText(matrix, w)
script o
property matrix : missing value
property row : missing value
end script
set o's matrix to matrix
set padding to " "
repeat with r from 1 to (count o's matrix)
set o's row to o's matrix's item r
repeat with i from 1 to (count o's row)
set o's row's item i to text -w thru end of (padding & o's row's item i)
end repeat
set o's matrix's item r to join(o's row, "")
end repeat
return join(o's matrix, linefeed)
end matrixToText
on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join
set n to 5
set matrix to zigzagMatrix(n)
linefeed & matrixToText(matrix, (count (n ^ 2 - 1 as integer as text)) + 2) & linefeed

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Task/Zig-zag-matrix/Applesoft-BASIC/zig-zag-matrix.basic Normal file
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100 S = 5
110 S2 = S ^ 2 : REM SQUARED
120 H = S2 / 2 : REM HALFWAY
130 S2 = S2 - 1
140 DX = 1 : REM INITIAL
150 DY = 0 : REM DIRECTION
160 N = S - 1
170 DIM A%(N, N)
200 FOR I = 0 TO H
210 A%(X, Y) = I
220 A%(N - X, N - Y) = S2 - I
230 X = X + DX
240 Y = Y + DY
250 IF Y = 0 THEN DY = DY + 1 : IF DY THEN DX = -DX
260 IF X = 0 THEN DX = DX + 1 : IF DX THEN DY = -DY
270 NEXT I
300 FOR Y = 0 TO N
310 FOR X = 0 TO N
320 IF X THEN PRINT TAB(X * (LEN(STR$(S2)) + 1) + 1);
330 PRINT A%(X, Y);
340 NEXT X
350 PRINT
360 NEXT Y

24
Task/Zig-zag-matrix/Arturo/zig-zag-matrix.arturo Normal file
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zigzag: function [n][
result: map 1..n 'x -> map 1..n => 0
x: 1, y: 1, v: 0, d: 1
while [v < n^2][
if? all? @[1 =< x x =< n 1 =< y y =< n][
set get result (y-1) (x-1) v
x: x + d, y: y - d, v: v + 1
]
else[if? x > n [x: n, y: y + 2, d: neg d]
else[if? y > n [x: x + 2, y: n, d: neg d]
else[if? x < 1 [x: 1, d: neg d]
else[if y < 1 [y: 1, d: neg d]
]
]
]
]
]
result
]
zz: zigzag 5
loop zz 'row -> print map row 'col [pad to :string col 3]

21
Task/Zig-zag-matrix/AutoHotkey/zig-zag-matrix.ahk Normal file
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n = 5 ; size
v := x := y := 1 ; initial values
Loop % n*n { ; for every array element
a_%x%_%y% := v++ ; assign the next index
If ((x+y)&1) ; odd diagonal
If (x < n) ; while inside the square
y -= y<2 ? 0 : 1, x++ ; move right-up
Else y++ ; on the edge increment y, but not x: to even diagonal
Else ; even diagonal
If (y < n) ; while inside the square
x -= x<2 ? 0 : 1, y++ ; move left-down
Else x++ ; on the edge increment x, but not y: to odd diagonal
}
Loop %n% { ; generate printout
x := A_Index ; for each row
Loop %n% ; and for each column
t .= a_%x%_%A_Index% "`t" ; attach stored index
t .= "`n" ; row is complete
}
MsgBox %t% ; show output

27
Task/Zig-zag-matrix/AutoIt/zig-zag-matrix.autoit Normal file
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#include <Array.au3>
$Array = ZigZag(5)
_ArrayDisplay($Array)
Func ZigZag($int)
Local $av_array[$int][$int]
Local $x = 1, $y = 1
For $I = 0 To $int ^ 2 -1
$av_array[$x-1][$y-1] = $I
If Mod(($x + $y), 2) = 0 Then ;Even
if ($y < $int) Then
$y += 1
Else
$x += 2
EndIf
if ($x > 1) Then $x -= 1
Else ; ODD
if ($x < $int) Then
$x += 1
Else
$y += 2
EndIf
If $y > 1 Then $y -= 1
EndIf
Next
Return $av_array
EndFunc ;==>ZigZag

23
Task/Zig-zag-matrix/BBC-BASIC/zig-zag-matrix.basic Normal file
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Size% = 5
DIM array%(Size%-1,Size%-1)
i% = 1
j% = 1
FOR e% = 0 TO Size%^2-1
array%(i%-1,j%-1) = e%
IF ((i% + j%) AND 1) = 0 THEN
IF j% < Size% j% += 1 ELSE i% += 2
IF i% > 1 i% -= 1
ELSE
IF i% < Size% i% += 1 ELSE j% += 2
IF j% > 1 j% -= 1
ENDIF
NEXT
@% = &904
FOR row% = 0 TO Size%-1
FOR col% = 0 TO Size%-1
PRINT array%(row%,col%);
NEXT
PRINT
NEXT row%

2
Task/Zig-zag-matrix/BQN/zig-zag-matrix-1.bqn Normal file
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Flip ← {m←2|+⌜˜↕≠𝕩 ⋄ (⍉𝕩׬m)+𝕩×m}
Zz ← {Flip ⍋∘⍋⌾⥊+⌜˜↕𝕩}

1
Task/Zig-zag-matrix/BQN/zig-zag-matrix-2.bqn Normal file
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@ -0,0 +1 @@
Zz 5

50
Task/Zig-zag-matrix/Beads/zig-zag-matrix.beads Normal file
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beads 1 program 'Zig-zag Matrix'
calc main_init
var test : array^2 of num = create_array(5)
printMatrix(test)
calc create_array(
dimension:num
):array^2 of num
var
result : array^2 of num
lastValue = dimension^2 - 1
loopFrom
loopTo
row
col
currDiag = 0
currNum = 0
loop
if (currDiag < dimension) // if doing the upper-left triangular half
loopFrom = 1
loopTo = currDiag + 1
else // doing the bottom-right triangular half
loopFrom = currDiag - dimension + 2
loopTo = dimension
loop count:c from:loopFrom to:loopTo
var i = loopFrom + c - 1
if (rem(currDiag, 2) == 0) // want to fill upwards
row = loopTo - i + loopFrom
col = i
else // want to fill downwards
row = i
col = loopTo - i + loopFrom
result[row][col] = currNum
inc currNum
inc currDiag
if (currNum > lastValue)
exit
return result
calc printMatrix(
matrix:array^2 of num
)
var dimension = tree_count(matrix)
var maxDigits = 1 + lg((dimension^2-1), base:10)
loop across:matrix ptr:rowp index:row
var tempstr : str
loop across:rowp index:col
tempstr = tempstr & " " & to_str(matrix[row][col], min:maxDigits)
log(tempstr)

3
Task/Zig-zag-matrix/Befunge/zig-zag-matrix.bf Normal file
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>> 5 >>00p0010p:1:>20p030pv >0g-:0`*:*-:00g:*1-55+/>\55+/:v v:,*84<
v:++!\**2p01:+1g01:g02$$_>>#^4#00#+p#1:#+1#g0#0g#3<^/+ 55\_$:>55+/\|
>55+,20g!00g10g`>#^_$$$@^!`g03g00!g04++**2p03:+1g03!\*+1*2g01:g04.$<

81
Task/Zig-zag-matrix/C++/zig-zag-matrix.cpp Normal file
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#include <vector>
#include <memory> // for auto_ptr
#include <cmath> // for the log10 and floor functions
#include <iostream>
#include <iomanip> // for the setw function
using namespace std;
typedef vector< int > IntRow;
typedef vector< IntRow > IntTable;
auto_ptr< IntTable > getZigZagArray( int dimension )
{
auto_ptr< IntTable > zigZagArrayPtr( new IntTable(
dimension, IntRow( dimension ) ) );
// fill along diagonal stripes (oriented as "/")
int lastValue = dimension * dimension - 1;
int currNum = 0;
int currDiag = 0;
int loopFrom;
int loopTo;
int i;
int row;
int col;
do
{
if ( currDiag < dimension ) // if doing the upper-left triangular half
{
loopFrom = 0;
loopTo = currDiag;
}
else // doing the bottom-right triangular half
{
loopFrom = currDiag - dimension + 1;
loopTo = dimension - 1;
}
for ( i = loopFrom; i <= loopTo; i++ )
{
if ( currDiag % 2 == 0 ) // want to fill upwards
{
row = loopTo - i + loopFrom;
col = i;
}
else // want to fill downwards
{
row = i;
col = loopTo - i + loopFrom;
}
( *zigZagArrayPtr )[ row ][ col ] = currNum++;
}
currDiag++;
}
while ( currDiag <= lastValue );
return zigZagArrayPtr;
}
void printZigZagArray( const auto_ptr< IntTable >& zigZagArrayPtr )
{
size_t dimension = zigZagArrayPtr->size();
int fieldWidth = static_cast< int >( floor( log10(
static_cast< double >( dimension * dimension - 1 ) ) ) ) + 2;
size_t col;
for ( size_t row = 0; row < dimension; row++ )
{
for ( col = 0; col < dimension; col++ )
cout << setw( fieldWidth ) << ( *zigZagArrayPtr )[ row ][ col ];
cout << endl;
}
}
int main()
{
printZigZagArray( getZigZagArray( 5 ) );
}

25
Task/Zig-zag-matrix/C-sharp/zig-zag-matrix.cs Normal file
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public static int[,] ZigZag(int n)
{
int[,] result = new int[n, n];
int i = 0, j = 0;
int d = -1; // -1 for top-right move, +1 for bottom-left move
int start = 0, end = n * n - 1;
do
{
result[i, j] = start++;
result[n - i - 1, n - j - 1] = end--;
i += d; j -= d;
if (i < 0)
{
i++; d = -d; // top reached, reverse
}
else if (j < 0)
{
j++; d = -d; // left reached, reverse
}
} while (start < end);
if (start == end)
result[i, j] = start;
return result;
}

23
Task/Zig-zag-matrix/C/zig-zag-matrix.c Normal file
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#include <stdio.h>
#include <stdlib.h>
int main(int c, char **v)
{
int i, j, m, n, *s;
/* default size: 5 */
if (c < 2 || ((m = atoi(v[1]))) <= 0) m = 5;
/* alloc array*/
s = malloc(sizeof(int) * m * m);
for (i = n = 0; i < m * 2; i++)
for (j = (i < m) ? 0 : i-m+1; j <= i && j < m; j++)
s[(i&1)? j*(m-1)+i : (i-j)*m+j ] = n++;
for (i = 0; i < m * m; putchar((++i % m) ? ' ':'\n'))
printf("%3d", s[i]);
/* free(s) */
return 0;
}

50
Task/Zig-zag-matrix/Ceylon/zig-zag-matrix.ceylon Normal file
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class ZigZag(Integer size) {
value data = Array {
for (i in 0:size)
Array.ofSize(size, 0)
};
variable value i = 1;
variable value j = 1;
for (element in 0 : size^2) {
data[j - 1]?.set(i - 1, element);
if ((i + j).even) {
if (j < size) {
j++;
}
else {
i += 2;
}
if (i > 1) {
i--;
}
}
else {
if (i < size) {
i++;
}
else {
j += 2;
}
if (j > 1) {
j--;
}
}
}
shared void display() {
for (row in data) {
for (element in row) {
process.write(element.string.pad(3));
}
print(""); //newline
}
}
}
shared void run() {
value zz = ZigZag(5);
zz.display();
}

33
Task/Zig-zag-matrix/Clojure/zig-zag-matrix.clj Normal file
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(defn partitions [sizes coll]
(lazy-seq
(when-let [n (first sizes)]
(when-let [s (seq coll)]
(cons (take n coll)
(partitions (next sizes) (drop n coll)))))))
(defn take-from [n colls]
(lazy-seq
(when-let [s (seq colls)]
(let [[first-n rest-n] (split-at n s)]
(cons (map first first-n)
(take-from n (concat (filter seq (map rest first-n)) rest-n)))))))
(defn zig-zag [n]
(->> (partitions (concat (range 1 (inc n)) (range (dec n) 0 -1)) (range (* n n)))
(map #(%1 %2) (cycle [reverse identity]) ,)
(take-from n ,)))
user> (zig-zag 5)
(( 0 1 5 6 14)
( 2 4 7 13 15)
( 3 8 12 16 21)
( 9 11 17 20 22)
(10 18 19 23 24))
user> (zig-zag 6)
(( 0 1 5 6 14 15)
( 2 4 7 13 16 25)
( 3 8 12 17 24 26)
( 9 11 18 23 27 32)
(10 19 22 28 31 33)
(20 21 29 30 34 35))

41
Task/Zig-zag-matrix/CoffeeScript/zig-zag-matrix.coffee Normal file
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# Calculate a zig-zag pattern of numbers like so:
# 0 1 5
# 2 4 6
# 3 7 8
#
# There are many interesting ways to solve this; we
# try for an algebraic approach, calculating triangle
# areas, so that me minimize space requirements.
zig_zag_value = (x, y, n) ->
upper_triangle_zig_zag = (x, y) ->
# calculate the area of the triangle from the prior
# diagonals
diag = x + y
triangle_area = diag * (diag+1) / 2
# then add the offset along the diagonal
if diag % 2 == 0
triangle_area + y
else
triangle_area + x
if x + y < n
upper_triangle_zig_zag x, y
else
# For the bottom right part of the matrix, we essentially
# use reflection to count backward.
bottom_right_cell = n * n - 1
n -= 1
v = upper_triangle_zig_zag(n-x, n-y)
bottom_right_cell - v
zig_zag_matrix = (n) ->
row = (i) -> (zig_zag_value i, j, n for j in [0...n])
(row i for i in [0...n])
do ->
for n in [4..6]
console.log "---- n=#{n}"
console.log zig_zag_matrix(n)
console.log "\n"

14
Task/Zig-zag-matrix/Common-Lisp/zig-zag-matrix-1.lisp Normal file
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(defun zigzag (n)
(flet ((move (i j)
(if (< j (1- n))
(values (max 0 (1- i)) (1+ j))
(values (1+ i) j))))
(loop with a = (make-array (list n n) :element-type 'integer)
with x = 0
with y = 0
for v from 0 below (* n n)
do (setf (aref a x y) v)
(if (evenp (+ x y))
(setf (values x y) (move x y))
(setf (values y x) (move y x)))
finally (return a))))

17
Task/Zig-zag-matrix/Common-Lisp/zig-zag-matrix-2.lisp Normal file
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; ZigZag
;
; Nigel Galloway.
; June 4th., 2012
;
(defun ZigZag (COLS)
(let ((cs 2) (st '(1 2)) (dx '(-1 1)))
(defun new_cx (i)
(setq st (append st (list (setq cs (+ cs (* 2 i))) (setq cs (+ 1 cs))))
dx (append dx '(-1 1))))
(do ((i 2 (+ 2 i))) ((>= i COLS)) (new_cx i))
(do ((i (- COLS 1 (mod COLS 2)) (+ -2 i))) ((<= i 0)) (new_cx i))
(do ((i 0 (+ 1 i))) ((>= i COLS))
(format t "~%")
(do ((j i (+ 1 j))) ((>= j (+ COLS i)))
(format t "~3d" (nth j st))
(setf (nth j st) (+ (nth j st) (nth j dx)))))))

12
Task/Zig-zag-matrix/Crystal/zig-zag-matrix.crystal Normal file
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def zigzag(n)
(seq=(0...n).to_a).product(seq)
.sort_by {|x,y| [x+y, (x+y).even? ? y : -y]}
.map_with_index{|v, i| {v, i}}.sort.map(&.last).each_slice(n).to_a
end
def print_matrix(m)
format = "%#{m.flatten.max.to_s.size}d " * m[0].size
m.each {|row| puts format % row}
end
print_matrix zigzag(5)

24
Task/Zig-zag-matrix/D/zig-zag-matrix-1.d Normal file
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int[][] zigZag(in int n) pure nothrow @safe {
static void move(in int n, ref int i, ref int j)
pure nothrow @safe @nogc {
if (j < n - 1) {
if (i > 0) i--;
j++;
} else
i++;
}
auto a = new int[][](n, n);
int x, y;
foreach (v; 0 .. n ^^ 2) {
a[y][x] = v;
(x + y) % 2 ? move(n, x, y) : move(n, y, x);
}
return a;
}
void main() {
import std.stdio;
writefln("%(%(%2d %)\n%)", 5.zigZag);
}

18
Task/Zig-zag-matrix/D/zig-zag-matrix-2.d Normal file
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import std.stdio, std.algorithm, std.range, std.array;
int[][] zigZag(in int n) pure nothrow {
static struct P2 { int x, y; }
const L = iota(n ^^ 2).map!(i => P2(i % n, i / n)).array
.sort!q{ (a.x + a.y == b.x + b.y) ?
((a.x + a.y) % 2 ? a.y < b.y : a.x < b.x) :
(a.x + a.y) < (b.x + b.y) }.release;
auto result = new typeof(return)(n, n);
foreach (immutable i, immutable p; L)
result[p.y][p.x] = i;
return result;
}
void main() {
writefln("%(%(%2d %)\n%)", 5.zigZag);
}

56
Task/Zig-zag-matrix/Delphi/zig-zag-matrix.delphi Normal file
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type TMatrix = array of array of double;
procedure DisplayMatrix(Memo: TMemo; Mat: TMatrix);
{Display specified matrix}
var X,Y: integer;
var S: string;
begin
S:='';
for Y:=0 to High(Mat[0]) do
begin
S:=S+'[';
for X:=0 to High(Mat) do
S:=S+Format('%4.0f',[Mat[X,Y]]);
S:=S+']'+#$0D#$0A;
end;
Memo.Lines.Add(S);
end;
procedure ZigzagMatrix(Memo: TMemo);
var Mat: TMatrix;
var X,Y,Inx,Dir: integer;
const Size = 10;
procedure Toggle(var I: integer);
{Toggle Direction and increment I}
begin
Dir:=-Dir;
Inc(I);
end;
procedure Step(var X,Y: integer);
{Take one step "Dir" direction}
begin
X:=X+Dir;
Y:=Y-Dir;
end;
begin
SetLength(Mat,Size,Size);
Inx:=0; X:=0; Y:=0; Dir:=1;
repeat
begin
Mat[X,Y]:=Inx;
if (X+Dir)>=Size then Toggle(Y)
else if (Y-Dir)>=Size then Toggle(X)
else if (X+Dir)<0 then Toggle(Y)
else if (Y-Dir)<0 then Toggle(X)
else Step(X,Y);
Inc(Inx);
end
until Inx>=Size*Size;
DisplayMatrix(Memo,Mat);
end;

24
Task/Zig-zag-matrix/E/zig-zag-matrix.e Normal file
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def zigZag(n) {
def move(&i, &j) {
if (j < (n - 1)) {
i := 0.max(i - 1)
j += 1
} else {
i += 1
}
}
def array := makeFlex2DArray(n, n)
var x := 0
var y := 0
for i in 1..n**2 {
array[y, x] := i
if ((x + y) % 2 == 0) {
move(&x, &y)
} else {
move(&y, &x)
}
}
return array
}

30
Task/Zig-zag-matrix/EMal/zig-zag-matrix.emal Normal file
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fun zigzag = List by int n
List matrix = List[].with(n)
for int y = 0; y < n; y++ do matrix[y] = int[].with(n) end
int y, x = 1
for int value = 0; value < n * n; value++
matrix[y - 1][x - 1] = value
if (y + x) % 2 == 0
if x < n do x++
else do y += 2 end
if y > 1 do y-- end
else
if y < n do y++
else do x += 2 end
if x > 1 do x-- end
end
end
return matrix
end
fun dump = void by List matrix
int max = length(text!(matrix.length ** 2)) + 1
for each List row in matrix
for each int value in row
write(" " * (max - length(text!value)) + value)
end
writeLine()
end
end
dump(zigzag(5))
writeLine()
dump(zigzag(10))

29
Task/Zig-zag-matrix/ERRE/zig-zag-matrix.erre Normal file
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PROGRAM ZIG_ZAG
!$DYNAMIC
DIM ARRAY%[0,0]
BEGIN
SIZE%=5
!$DIM ARRAY%[SIZE%-1,SIZE%-1]
I%=1
J%=1
FOR E%=0 TO SIZE%^2-1 DO
ARRAY%[I%-1,J%-1]=E%
IF ((I%+J%) AND 1)=0 THEN
IF J%<SIZE% THEN J%+=1 ELSE I%+=2 END IF
IF I%>1 THEN I%-=1 END IF
ELSE
IF I%<SIZE% THEN I%+=1 ELSE J%+=2 END IF
IF J%>1 THEN J%-=1 END IF
END IF
END FOR
FOR ROW%=0 TO SIZE%-1 DO
FOR COL%=0 TO SIZE%-1 DO
WRITE("###";ARRAY%[ROW%,COL%];)
END FOR
PRINT
END FOR
END PROGRAM

44
Task/Zig-zag-matrix/Elena/zig-zag-matrix.elena Normal file
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import extensions;
extension op : IntNumber
{
zigzagMatrix()
{
auto result := IntMatrix.allocate(self, self);
int i := 0;
int j := 0;
int d := -1;
int start := 0;
int end := self*self - 1;
while (start < end)
{
result.setAt(i, j, start); start += 1;
result.setAt(self - i - 1, self - j - 1, end); end -= 1;
i := i + d;
j := j - d;
if (i < 0)
{
i:=i+1; d := d.Negative
}
else if (j < 0)
{
j := j + 1; d := d.Negative
}
};
if (start == end)
{
result.setAt(i, j, start)
};
^ result
}
}
public program()
{
console.printLine(5.zigzagMatrix()).readChar()
}

15
Task/Zig-zag-matrix/Elixir/zig-zag-matrix.elixir Normal file
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defmodule RC do
require Integer
def zigzag(n) do
fmt = "~#{to_char_list(n*n-1) |> length}w "
(for x <- 1..n, y <- 1..n, do: {x,y})
|> Enum.sort_by(fn{x,y}->{x+y, if(Integer.is_even(x+y), do: y, else: x)} end)
|> Enum.with_index |> Enum.sort
|> Enum.each(fn {{_x,y},i} ->
:io.format fmt, [i]
if y==n, do: IO.puts ""
end)
end
end
RC.zigzag(5)

28
Task/Zig-zag-matrix/Erlang/zig-zag-matrix.erl Normal file
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-module( zigzag ).
-export( [matrix/1, task/0] ).
matrix( N ) ->
{{_X_Y, N}, Proplist} = lists:foldl( fun matrix_as_proplist/2, {{{0, 0}, N}, []}, lists:seq(0, (N * N) - 1) ),
[columns( X, Proplist ) || X <- lists:seq(0, N - 1)].
task() -> matrix( 5 ).
columns( Column, Proplist ) -> lists:sort( [Value || {{_X, Y}, Value} <- Proplist, Y =:= Column] ).
matrix_as_proplist( N, {{X_Y, Max}, Acc} ) ->
Next = next_indexes( X_Y, Max ),
{{Next, Max}, [{X_Y, N} | Acc]}.
next_indexes( {X, Y}, Max ) when Y + 1 =:= Max, (X + Y) rem 2 =:= 0 -> {X + 1, Y - 1};
next_indexes( {X, Y}, Max ) when Y + 1 =:= Max, (X + Y) rem 2 =:= 1 -> {X + 1, Y};
next_indexes( {X, Y}, Max ) when X + 1 =:= Max, (X + Y) rem 2 =:= 0 -> {X, Y + 1};
next_indexes( {X, Y}, Max ) when X + 1 =:= Max, (X + Y) rem 2 =:= 1 -> {X - 1, Y + 1};
next_indexes( {X, 0}, _Max ) when X rem 2 =:= 0 -> {X + 1, 0};
next_indexes( {X, 0}, _Max ) when X rem 2 =:= 1 -> {X - 1, 1};
next_indexes( {0, Y}, _Max ) when Y rem 2 =:= 0 -> {1, Y - 1};
next_indexes( {0, Y}, _Max ) when Y rem 2 =:= 1 -> {0, Y + 1};
next_indexes( {X, Y}, _Max ) when (X + Y) rem 2 =:= 0 -> {X + 1, Y - 1};
next_indexes( {X, Y}, _Max ) when (X + Y) rem 2 =:= 1 -> {X - 1, Y + 1}.

20
Task/Zig-zag-matrix/Euphoria/zig-zag-matrix.euphoria Normal file
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function zigzag(integer size)
sequence s
integer i, j, d, max
s = repeat(repeat(0,size),size)
i = 1 j = 1 d = -1
max = size*size
for n = 1 to floor(max/2)+1 do
s[i][j] = n
s[size-i+1][size-j+1] = max-n+1
i += d j-= d
if i < 1 then
i += 1 d = -d
elsif j < 1 then
j += 1 d = -d
end if
end for
return s
end function
? zigzag(5)

14
Task/Zig-zag-matrix/F-Sharp/zig-zag-matrix-1.fs Normal file
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//Produce a zig zag matrix - Nigel Galloway: April 7th., 2015
let zz l a =
let N = Array2D.create l a 0
let rec gng (n, i, g, e) =
N.[n,i] <- g
match e with
| _ when i=a-1 && n=l-1 -> N
| 1 when n = l-1 -> gng (n, i+1, g+1, 2)
| 2 when i = a-1 -> gng (n+1, i, g+1, 1)
| 1 when i = 0 -> gng (n+1, 0, g+1, 2)
| 2 when n = 0 -> gng (0, i+1, g+1, 1)
| 1 -> gng (n+1, i-1, g+1, 1)
| _ -> gng (n-1, i+1, g+1, 2)
gng (0, 0, 0, 2)

1
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zz 5 5

1
Task/Zig-zag-matrix/F-Sharp/zig-zag-matrix-3.fs Normal file
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@ -0,0 +1 @@
zz 8 8

1
Task/Zig-zag-matrix/F-Sharp/zig-zag-matrix-4.fs Normal file
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@ -0,0 +1 @@
zz 5 8

25
Task/Zig-zag-matrix/Factor/zig-zag-matrix-1.factor Normal file
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USING: columns fry kernel make math math.ranges prettyprint
sequences sequences.cords sequences.extras ;
IN: rosetta-code.zig-zag-matrix
: [1,b,1] ( n -- seq )
[1,b] dup but-last-slice <reversed> cord-append ;
: <reversed-evens> ( seq -- seq' )
[ even? [ <reversed> ] when ] map-index ;
: diagonals ( n -- seq )
[ sq <iota> ] [ [1,b,1] ] bi
[ [ cut [ , ] dip ] each ] { } make nip <reversed-evens> ;
: zig-zag-matrix ( n -- seq )
[ diagonals ] [ dup ] bi '[
[
dup 0 <column> _ head ,
[ _ < [ rest-slice ] when ] map-index harvest
] until-empty
] { } make ;
: zig-zag-demo ( -- ) 5 zig-zag-matrix simple-table. ;
MAIN: zig-zag-demo

11
Task/Zig-zag-matrix/Factor/zig-zag-matrix-2.factor Normal file
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USING: assocs assocs.extras grouping io kernel math
math.combinatorics math.matrices prettyprint sequences ;
: <zig-zag-matrix> ( n -- matrix )
[
dup [ + ] <matrix-by-indices> concat zip-index
expand-keys-push-at values [ even? [ reverse ] when ]
map-index concat inverse-permutation
] [ group ] bi ;
5 <zig-zag-matrix> simple-table.

91
Task/Zig-zag-matrix/Fan/zig-zag-matrix.fan Normal file
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using gfx // for Point; convenient x/y wrapper
**
** A couple methods for generating a 'zigzag' array like
**
** 0 1 5 6
** 2 4 7 12
** 3 8 11 13
** 9 10 14 15
**
class ZigZag
{
** return an n x n array of uninitialized Int
static Int[][] makeSquareArray(Int n)
{
Int[][] grid := Int[][,] {it.size=n}
n.times |i| { grid[i] = Int[,] {it.size=n} }
return grid
}
Int[][] zig(Int n)
{
grid := makeSquareArray(n)
move := |Int i, Int j->Point|
{ return j < n - 1 ? Point(i <= 0 ? 0 : i-1, j+1) : Point(i+1, j) }
pt := Point(0,0)
(n*n).times |i| {
grid[pt.y][pt.x] = i
if ((pt.x+pt.y)%2 != 0) pt = move(pt.x,pt.y)
else {tmp:= move(pt.y,pt.x); pt = Point(tmp.y, tmp.x) }
}
return grid
}
public static Int[][] zag(Int size)
{
data := makeSquareArray(size)
Int i := 1
Int j := 1
for (element:=0; element < size * size; element++)
{
data[i - 1][j - 1] = element
if((i + j) % 2 == 0) {
// Even stripes
if (j < size) {
j++
} else {
i += 2
}
if (i > 1) {
i--
}
} else {
// Odd stripes
if (i < size) {
i++;
} else {
j += 2
}
if (j > 1) {
j--
}
}
}
return data;
}
Void print(Int[][] data)
{
data.each |row|
{
buf := StrBuf()
row.each |num|
{
buf.add(num.toStr.justr(3))
}
echo(buf)
}
}
Void main()
{
echo("zig method:")
print(zig(8))
echo("\nzag method:")
print(zag(8))
}
}

50
Task/Zig-zag-matrix/Forth/zig-zag-matrix.fth Normal file
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0 value diag
: south diag abs + cell+ ;
' cell+ value zig
' south value zag
: init ( n -- )
1- cells negate to diag
['] cell+ to zig
['] south to zag ;
: swap-diag zig zag to zig to zag ;
: put ( n addr -- n+1 addr )
2dup ! swap 1+ swap ;
: turn ( addr -- addr+E/S )
zig execute swap-diag
diag negate to diag ;
: zigzag ( matrix n -- )
{ n } n init
0 swap
n 1 ?do
put turn
i 0 do put diag + loop
loop
swap-diag
n 1 ?do
put turn
n i 1+ ?do put diag + loop
loop
! ;
: .matrix ( n matrix -- )
over 0 do
cr
over 0 do
dup @ 3 .r cell+
loop
loop 2drop ;
: test ( n -- ) here over zigzag here .matrix ;
5 test
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24 ok

38
Task/Zig-zag-matrix/Fortran/zig-zag-matrix.f Normal file
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PROGRAM ZIGZAG
IMPLICIT NONE
INTEGER, PARAMETER :: size = 5
INTEGER :: zzarray(size,size), x(size*size), y(size*size), i, j
! index arrays
x = (/ ((j, i = 1, size), j = 1, size) /)
y = (/ ((i, i = 1, size), j = 1, size) /)
! Sort indices
DO i = 2, size*size
j = i - 1
DO WHILE (j>=1 .AND. (x(j)+y(j)) > (x(i)+y(i)))
j = j - 1
END DO
x(j+1:i) = cshift(x(j+1:i),-1)
y(j+1:i) = cshift(y(j+1:i),-1)
END DO
! Create zig zag array
DO i = 1, size*size
IF (MOD(x(i)+y(i), 2) == 0) THEN
zzarray(x(i),y(i)) = i - 1
ELSE
zzarray(y(i),x(i)) = i - 1
END IF
END DO
! Print zig zag array
DO j = 1, size
DO i = 1, size
WRITE(*, "(I5)", ADVANCE="NO") zzarray(i,j)
END DO
WRITE(*,*)
END DO
END PROGRAM ZIGZAG

74
Task/Zig-zag-matrix/FreeBASIC/zig-zag-matrix.basic Normal file
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' FB 1.05.0 Win64
Dim As Integer n
Do
Input "Enter size of matrix "; n
Loop Until n > 0
Dim zigzag(1 To n, 1 To n) As Integer '' all zero by default
' enter the numbers 0 to (n^2 - 1) in the matrix's anti-diagonals
zigzag(1, 1) = 0
If n > 1 Then
Dim As Integer row = 0, col = 3
Dim As Boolean down = true, increment = true
Dim As Integer i = 0, j = 2, k
Do
If down Then
For k = 1 To j
i += 1
row += 1
col -= 1
zigzag(row, col) = i
Next
down = false
Else
For k = 1 To j
i += 1
row -= 1
col += 1
zigzag(row, col) = i
Next
down = true
End If
If increment Then
j += 1
If j > n Then
j = n - 1
increment = false
End If
Else
j -= 1
If j = 0 Then Exit Do
End If
If down AndAlso increment Then
col += 2
row -= 1
ElseIf Not Down AndAlso increment Then
row += 2
col -= 1
ElseIf down AndAlso Not increment Then
col += 1
Else '' Not down AndAlso NotIncrement
row += 1
End If
Loop
End If
' print zigzag matrix if n < 20
Print
If n < 20 Then
For i As Integer = 1 To n
For j As Integer = 1 To n
Print Using "####"; zigzag(i, j);
Next j
Print
Next i
Else
Print "Matrix is too big to display on 80 column console"
End If
Print
Print "Press any key to quit"
Sleep

36
Task/Zig-zag-matrix/GAP/zig-zag-matrix.gap Normal file
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ZigZag := function(n)
local a, i, j, k;
a := NullMat(n, n);
i := 1;
j := 1;
for k in [0 .. n*n - 1] do
a[i][j] := k;
if (i + j) mod 2 = 0 then
if j < n then
j := j + 1;
else
i := i + 2;
fi;
if i > 1 then
i := i - 1;
fi;
else
if i < n then
i := i + 1;
else
j := j + 2;
fi;
if j > 1 then
j := j - 1;
fi;
fi;
od;
return a;
end;
PrintArray(ZigZag(5));
# [ [ 0, 1, 5, 6, 14 ],
# [ 2, 4, 7, 13, 15 ],
# [ 3, 8, 12, 16, 21 ],
# [ 9, 11, 17, 20, 22 ],
# [ 10, 18, 19, 23, 24 ] ]

47
Task/Zig-zag-matrix/Go/zig-zag-matrix.go Normal file
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package main
import (
"fmt"
"strconv"
)
func zz(n int) []int {
r := make([]int, n*n)
i := 0
n2 := n * 2
for d := 1; d <= n2; d++ {
x := d - n
if x < 0 {
x = 0
}
y := d - 1
if y > n-1 {
y = n - 1
}
j := n2 - d
if j > d {
j = d
}
for k := 0; k < j; k++ {
if d&1 == 0 {
r[(x+k)*n+y-k] = i
} else {
r[(y-k)*n+x+k] = i
}
i++
}
}
return r
}
func main() {
const n = 5
w := len(strconv.Itoa(n*n - 1))
for i, e := range zz(n) {
fmt.Printf("%*d ", w, e)
if i%n == n-1 {
fmt.Println("")
}
}
}

11
Task/Zig-zag-matrix/Groovy/zig-zag-matrix-1.groovy Normal file
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def zz = { n ->
grid = new int[n][n]
i = 0
for (d in 1..n*2) {
(x, y) = [Math.max(0, d - n), Math.min(n - 1, d - 1)]
Math.min(d, n*2 - d).times {
grid[d%2?y-it:x+it][d%2?x+it:y-it] = i++;
}
}
grid
}

11
Task/Zig-zag-matrix/Groovy/zig-zag-matrix-2.groovy Normal file
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def zz = { n->
move = { i, j -> j < n - 1 ? [i <= 0 ? 0 : i-1, j+1] : [i+1, j] }
grid = new int[n][n]
(x, y) = [0, 0]
(n**2).times {
grid[y][x] = it
if ((x+y)%2) (x,y) = move(x,y)
else (y,x) = move(y,x)
}
grid
}

5
Task/Zig-zag-matrix/Groovy/zig-zag-matrix-3.groovy Normal file
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def zz = { n ->
(0..<n*n).collect { [x:it%n,y:(int)(it/n)] }.sort { c->
[c.x+c.y, (((c.x+c.y)%2) ? c.y : -c.y)]
}.with { l -> l.inject(new int[n][n]) { a, c -> a[c.y][c.x] = l.indexOf(c); a } }
}

15
Task/Zig-zag-matrix/Haskell/zig-zag-matrix-1.hs Normal file
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import Data.Array (Array, array, bounds, range, (!))
import Text.Printf (printf)
import Data.List (sortBy)
compZig :: (Int, Int) -> (Int, Int) -> Ordering
compZig (x, y) (x_, y_) = compare (x + y) (x_ + y_) <> go x y
where
go x y
| even (x + y) = compare x x_
| otherwise = compare y y_
zigZag :: (Int, Int) -> Array (Int, Int) Int
zigZag upper = array b $ zip (sortBy compZig (range b)) [0 ..]
where
b = ((0, 0), upper)

12
Task/Zig-zag-matrix/Haskell/zig-zag-matrix-2.hs Normal file
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-- format a 2d array of integers neatly
show2d a =
unlines
[ unwords
[ printf "%3d" (a ! (x, y) :: Integer)
| x <- axis fst ]
| y <- axis snd ]
where
(l, h) = bounds a
axis f = [f l .. f h]
main = mapM_ (putStr . ('\n' :) . show2d . zigZag) [(3, 3), (4, 4), (10, 2)]

26
Task/Zig-zag-matrix/Haskell/zig-zag-matrix-3.hs Normal file
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import Data.Text (justifyRight, pack, unpack)
import Data.List (mapAccumL)
import Data.Bool (bool)
zigZag :: Int -> [[Int]]
zigZag = go <*> diagonals
where
go _ [] = []
go n xss = (head <$> edge) : go n (dropWhile null (tail <$> edge) <> rst)
where
(edge, rst) = splitAt n xss
diagonals :: Int -> [[Int]]
diagonals n =
snd $ mapAccumL go [0 .. (n * n) - 1] (slope <> [n] <> reverse slope)
where
slope = [1 .. n - 1]
go xs h = (rst, bool id reverse (0 /= mod h 2) grp)
where
(grp, rst) = splitAt h xs
main :: IO ()
main =
putStrLn $
unlines $
concatMap unpack . fmap (justifyRight 3 ' ' . pack . show) <$> zigZag 5

28
Task/Zig-zag-matrix/IS-BASIC/zig-zag-matrix.basic Normal file
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100 PROGRAM "ZigZag.bas"
110 LET SIZE=5
120 NUMERIC A(1 TO SIZE,1 TO SIZE)
130 LET I,J=1
140 FOR E=0 TO SIZE^2-1
150 LET A(I,J)=E
160 IF ((I+J) BAND 1)=0 THEN
170 IF J<SIZE THEN
180 LET J=J+1
190 ELSE
200 LET I=I+2
210 END IF
220 IF I>1 THEN LET I=I-1
230 ELSE
240 IF I<SIZE THEN
250 LET I=I+1
260 ELSE
270 LET J=J+2
280 END IF
290 IF J>1 THEN LET J=J-1
300 END IF
310 NEXT
320 FOR ROW=1 TO SIZE
330 FOR COL=1 TO SIZE
340 PRINT USING " ##":A(ROW,COL);
350 NEXT
360 PRINT
370 NEXT

25
Task/Zig-zag-matrix/Icon/zig-zag-matrix.icon Normal file
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procedure main(args)
n := integer(!args) | 5
every !(A := list(n)) := list(n)
A := zigzag(A)
show(A)
end
procedure show(A)
every writes(right(!A,5) | "\n")
end
procedure zigzag(A)
x := [0,0]
every i := 0 to (*A^2 -1) do {
x := nextIndices(*A, x)
A[x[1]][x[2]] := i
}
return A
end
procedure nextIndices(n, x)
return if (x[1]+x[2])%2 = 0
then if x[2] = n then [x[1]+1, x[2]] else [max(1, x[1]-1), x[2]+1]
else if x[1] = n then [x[1], x[2]+1] else [x[1]+1, max(1, x[2]-1)]
end

6
Task/Zig-zag-matrix/J/zig-zag-matrix-1.j Normal file
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($ [: /:@; <@|.`</.@i.)@,~ 5
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24

6
Task/Zig-zag-matrix/J/zig-zag-matrix-2.j Normal file
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($ [: /:@; [: <@(A.~_2|#)/. i.)@,~ 5
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24

6
Task/Zig-zag-matrix/J/zig-zag-matrix-3.j Normal file
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($ ([: /:@;@(+/"1 <@|.`</. ]) (#: i.@(*/))))@,~ 5
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24

6
Task/Zig-zag-matrix/J/zig-zag-matrix-4.j Normal file
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($ [: /:@; [: <@|.`</. i.) 5 3
0 1 5
2 4 6
3 7 11
8 10 12
9 13 14

31
Task/Zig-zag-matrix/Java/zig-zag-matrix.java Normal file
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public static int[][] Zig_Zag(final int size)
{
int[][] data = new int[size][size];
int i = 1;
int j = 1;
for (int element = 0; element < size * size; element++)
{
data[i - 1][j - 1] = element;
if ((i + j) % 2 == 0)
{
// Even stripes
if (j < size)
j++;
else
i+= 2;
if (i > 1)
i--;
}
else
{
// Odd stripes
if (i < size)
i++;
else
j+= 2;
if (j > 1)
j--;
}
}
return data;
}

32
Task/Zig-zag-matrix/JavaScript/zig-zag-matrix-1.js Normal file
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function ZigZagMatrix(n) {
this.height = n;
this.width = n;
this.mtx = [];
for (var i = 0; i < n; i++)
this.mtx[i] = [];
var i=1, j=1;
for (var e = 0; e < n*n; e++) {
this.mtx[i-1][j-1] = e;
if ((i + j) % 2 == 0) {
// Even stripes
if (j < n) j ++;
else i += 2;
if (i > 1) i --;
} else {
// Odd stripes
if (i < n) i ++;
else j += 2;
if (j > 1) j --;
}
}
}
ZigZagMatrix.prototype = Matrix.prototype;
var z = new ZigZagMatrix(5);
print(z);
print();
z = new ZigZagMatrix(4);
print(z);

97
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(function (n) {
// Read range of values into a series of 'diagonal rows'
// for a square of given dimension,
// starting at diagonal row i.
// [
// [0],
// [1, 2],
// [3, 4, 5],
// [6, 7, 8, 9],
// [10, 11, 12, 13, 14],
// [15, 16, 17, 18],
// [19, 20, 21],
// [22, 23],
// [24]
// ]
// diagonals :: n -> [[n]]
function diagonals(n) {
function diags(xs, iCol, iRow) {
if (iCol < xs.length) {
var xxs = splitAt(iCol, xs);
return [xxs[0]].concat(diags(
xxs[1],
(iCol + (iRow < n ? 1 : -1)),
iRow + 1
));
} else return [xs];
}
return diags(range(0, n * n - 1), 1, 1);
}
// Recursively read off n heads from the diagonals (as rows)
// n -> [[n]] -> [[n]]
function nHeads(n, lst) {
var zipEdge = lst.slice(0, n);
return lst.length ? [zipEdge.map(function (x) {
return x[0];
})].concat(nHeads(n, [].concat.apply([], zipEdge.map(function (
x) {
return x.length > 1 ? [x.slice(1)] : [];
}))
.concat(lst.slice(n)))) : [];
}
// range(intFrom, intTo, optional intStep)
// Int -> Int -> Maybe Int -> [Int]
function range(m, n, delta) {
var d = delta || 1,
blnUp = n > m,
lng = Math.floor((blnUp ? n - m : m - n) / d) + 1,
a = Array(lng),
i = lng;
if (blnUp)
while (i--) a[i] = (d * i) + m;
else
while (i--) a[i] = m - (d * i);
return a;
}
// splitAt :: Int -> [a] -> ([a],[a])
function splitAt(n, xs) {
return [xs.slice(0, n), xs.slice(n)];
}
// Recursively take n heads from the alternately reversed diagonals
// [ [
// [0], -> [0, 1, 5, 6, 14] and:
// [1, 2], [2],
// [5, 4, 3], [4, 3],
// [6, 7, 8, 9], [7, 8, 9],
// [14, 13, 12, 11, 10], [13, 12, 11, 10],
// [15, 16, 17, 18], [15, 16, 17, 18],
// [21, 20, 19], [21, 20, 19],
// [22, 23], [22, 23],
// [24] [24]
// ] ]
//
// In the next recursion with the remnant on the right, the next
// 5 heads will be [2, 4, 7, 13, 15] - the second row of our zig zag matrix.
// (and so forth)
return nHeads(n, diagonals(n)
.map(function (x, i) {
i % 2 || x.reverse();
return x;
}));
})(5);

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(n => {
// diagonals :: n -> [[n]]
function diagonals(n) {
let diags = (xs, iCol, iRow) => {
if (iCol < xs.length) {
let xxs = splitAt(iCol, xs);
return [xxs[0]].concat(diags(
xxs[1],
iCol + (iRow < n ? 1 : -1),
iRow + 1
));
} else return [xs];
}
return diags(range(0, n * n - 1), 1, 1);
}
// Recursively read off n heads of diagonal lists
// rowsFromDiagonals :: n -> [[n]] -> [[n]]
function rowsFromDiagonals(n, lst) {
if (lst.length) {
let [edge, rest] = splitAt(n, lst);
return [edge.map(x => x[0])]
.concat(rowsFromDiagonals(n,
edge.filter(x => x.length > 1)
.map(x => x.slice(1))
.concat(rest)
));
} else return [];
}
// GENERIC FUNCTIONS
// splitAt :: Int -> [a] -> ([a],[a])
function splitAt(n, xs) {
return [xs.slice(0, n), xs.slice(n)];
}
// range :: From -> To -> Maybe Step -> [Int]
// range :: Int -> Int -> Maybe Int -> [Int]
function range(m, n, step) {
let d = (step || 1) * (n >= m ? 1 : -1);
return Array.from({
length: Math.floor((n - m) / d) + 1
}, (_, i) => m + (i * d));
}
// ZIG-ZAG MATRIX
return rowsFromDiagonals(n,
diagonals(n)
.map((x, i) => (i % 2 || x.reverse()) && x)
);
})(5);

51
Task/Zig-zag-matrix/Joy/zig-zag-matrix.joy Normal file
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(*
From the library.
*)
DEFINE reverse == [] swap shunt;
shunt == [swons] step.
(*
Split according to the parameter given.
*)
DEFINE take-drop == [dup] swap dup [[] cons [take swap] concat concat] dip []
cons concat [drop] concat.
(*
Take the first of a list of lists.
*)
DEFINE take-first == [] cons 3 [dup] times [dup] swap concat [take [first] map
swap dup] concat swap concat [drop swap] concat swap
concat [take [rest] step []] concat swap concat [[cons]
times swap concat 1 drop] concat.
DEFINE zigzag ==
(*
Use take-drop to generate a list of lists.
*)
4 [dup] times 1 swap from-to-list swap pred 1 swap from-to-list reverse concat
swap dup * pred 0 swap from-to-list swap [take-drop i] step [pop list] [cons]
while
(*
The odd numbers must be modified with reverse.
*)
[dup size 2 div popd [1 =] [pop reverse] [pop] ifte] map
(*
Take the first of the first of n lists.
*)
swap dup take-first [i] cons times pop
(*
Merge the n separate lists.
*)
[] [pop list] [cons] while
(*
And print them.
*)
swap dup * pred 'd 1 1 format size succ [] cons 'd swons [1 format putchars]
concat [step '\n putch] cons step.
11 zigzag.

18
Task/Zig-zag-matrix/Jq/zig-zag-matrix-1.jq Normal file
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# Create an m x n matrix
def matrix(m; n; init):
if m == 0 then []
elif m == 1 then [range(0;n)] | map(init)
elif m > 0 then
matrix(1;n;init) as $row
| [range(0;m)] | map( $row )
else error("matrix\(m);_;_) invalid")
end ;
# Print a matrix neatly, each cell occupying n spaces
def neatly(n):
def right: tostring | ( " " * (n-length) + .);
. as $in
| length as $length
| reduce range (0;$length) as $i
(""; . + reduce range(0;$length) as $j
(""; "\(.) \($in[$i][$j] | right )" ) + "\n" ) ;

19
Task/Zig-zag-matrix/Jq/zig-zag-matrix-2.jq Normal file
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def zigzag(n):
# unless m == n*n, place m at (i,j), pointing
# in the direction d, where d = [drow, dcolumn]:
def _next(i; j; m; d):
if m == (n*n) then . else .[i][j] = m end
| if m == (n*n) - 1 then .
elif i == n-1 then if j+1 < n then .[i][j+1] = m+1 | _next(i-1; j+2; m+2; [-1, 1]) else . end
elif i == 0 then if j+1 < n then .[i][j+1] = m+1 | _next(i+1; j ; m+2; [ 1,-1])
else .[i+1][j] = m+1 | _next(i+2; j-1; m+2; [ 1,-1]) end
elif j == n-1 then if i+1 < n then .[i+1][j] = m+1 | _next(i+2; j-1; m+2; [ 1,-1]) else . end
elif j == 0 then if i+1 < n then .[i+1][j] = m+1 | _next(i; j+1; m+2; [-1, 1])
else .[i][j+1] = m+1 | _next(i-1; j+1; m+2; [-1, 1]) end
else _next(i+ d[0]; j+ d[1]; m+1; d)
end ;
matrix(n;n;-1) | _next(0;0; 0; [0,1]) ;
# Example
zigzag(5) | neatly(4)

65
Task/Zig-zag-matrix/Jq/zig-zag-matrix-3.jq Normal file
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#!/usr/bin/env jq -Mnrc -f
#
# solve zigzag matrix by constructing list of 2n+1 column "runs"
# and then shifting them into final form.
#
# e.g. for n=3 initial runs are [[0],[1,2],[3,4,5],[6,7],[8]]
# runs below are shown as columns:
#
# initial column runs 0 1 3 6 8
# 2 4 7
# 5
#
# reverse cols 0,2,4 0 1 5 6 8
# 2 4 7
# 3
#
# shift cols 3,4 down 0 1 5
# 2 4 6
# 3 7 8
#
# shift rows left 0 1 5
# to get final zigzag 2 4 6
# 3 7 8
def N: $n ; # size of matrix
def NR: 2*N - 1; # number of runs
def abs: if .<0 then -. else . end ; # absolute value
def runlen: N-(N-.|abs) ; # length of run
def makeruns: [
foreach range(1;NR+1) as $r ( # for each run
{c:0} # state counter
; .l = ($r|runlen) # length of this run
| .r = [range(.c;.c+.l)] # values in this run
| .c += .l # increment counter
; .r # produce run
) ] ; # collect into array
def even: .%2==0 ; # is input even?
def reverseruns: # reverse alternate runs
.[keys|map(select(even))[]] |= reverse ;
def zeros: [range(.|N-length)|0] ; # array of padding zeros
def shiftdown:
def pad($r): # pad run with zeros
if $r < N # determine where zeros go
then . = . + zeros # at back for left runs
else . = zeros + . # at front for right runs
end ;
reduce keys[] as $r (.;.[$r] |= pad($r)); # shift rows down with pad
def shiftleft: [
range(N) as $r
| [ range($r;$r+N) as $c
| .[$c][$r]
]
] ;
def width: [.[][]]|max|tostring|1+length; # width of largest value
def justify($w): (($w-length)*" ") + . ; # leading spaces
def format:
width as $w # compute width
| map(map(tostring | justify($w)))[] # justify values
| join(" ")
;
makeruns # create column runs
| reverseruns # reverse alternate runs
| shiftdown # shift right runs down
| shiftleft # shift rows left
| format # format final result

25
Task/Zig-zag-matrix/Julia/zig-zag-matrix-1.julia Normal file
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function zigzag_matrix(n::Int)
matrix = zeros(Int, n, n)
x, y = 1, 1
for i = 0:(n*n-1)
matrix[y,x] = i
if (x + y) % 2 == 0
# Even stripes
if x < n
x += 1
y -= (y > 1)
else
y += 1
end
else
# Odd stripes
if y < n
x -= (x > 1)
y += 1
else
x += 1
end
end
end
return matrix
end

59
Task/Zig-zag-matrix/Julia/zig-zag-matrix-2.julia Normal file
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immutable ZigZag
m::Int
n::Int
diag::Array{Int,1}
cmax::Int
numd::Int
lohi::(Int,Int)
end
function zigzag(m::Int, n::Int)
0<m && 0<n || error("The matrix dimensions must be positive.")
ZigZag(m, n, [-1,1], m*n, m+n-1, extrema([m,n]))
end
zigzag(n::Int) = zigzag(n, n)
type ZZState
cnt::Int
cell::Array{Int,1}
dir::Int
dnum::Int
dlen::Int
dcnt::Int
end
Base.length(zz::ZigZag) = zz.cmax
Base.start(zz::ZigZag) = ZZState(1, [1,1], 1, 1, 1, 1)
Base.done(zz::ZigZag, zzs::ZZState) = zzs.cnt > zz.cmax
function Base.next(zz::ZigZag, zzs::ZZState)
s = sub2ind((zz.m, zz.n), zzs.cell[1], zzs.cell[2])
if zzs.dcnt == zzs.dlen
if isodd(zzs.dnum)
if zzs.cell[2] < zz.n
zzs.cell[2] += 1
else
zzs.cell[1] += 1
end
else
if zzs.cell[1] < zz.m
zzs.cell[1] += 1
else
zzs.cell[2] += 1
end
end
zzs.dcnt = 1
zzs.dnum += 1
zzs.dir = -zzs.dir
if zzs.dnum <= zz.lohi[1]
zzs.dlen += 1
elseif zz.lohi[2] < zzs.dnum
zzs.dlen -= 1
end
else
zzs.cell += zzs.dir*zz.diag
zzs.dcnt += 1
end
zzs.cnt += 1
return (s, zzs)
end

24
Task/Zig-zag-matrix/Julia/zig-zag-matrix-3.julia Normal file
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using Formatting
function width{T<:Integer}(n::T)
w = ndigits(n)
n < 0 || return w
return w + 1
end
function pretty{T<:Integer}(a::Array{T,2}, indent::Int=4)
lo, hi = extrema(a)
w = max(width(lo), width(hi))
id = " "^indent
fe = FormatExpr(@sprintf(" {:%dd}", w))
s = id
nrow = size(a)[1]
for i in 1:nrow
for j in a[i,:]
s *= format(fe, j)
end
i != nrow || continue
s *= "\n"*id
end
return s
end

26
Task/Zig-zag-matrix/Julia/zig-zag-matrix-4.julia Normal file
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n = 5
println("The n = ", n, " zig-zag matrix:")
a = zeros(Int, (n, n))
for (i, s) in enumerate(zigzag(n))
a[s] = i-1
end
println(pretty(a))
m = 3
println()
println("Generalize to a non-square matrix (", m, "x", n, "):")
a = zeros(Int, (m, n))
for (i, s) in enumerate(zigzag(m, n))
a[s] = i-1
end
println(pretty(a))
p = primes(10^3)
n = 7
println()
println("An n = ", n, " prime spiral matrix:")
a = zeros(Int, (n, n))
for (i, s) in enumerate(zigzag(n))
a[s] = p[i]
end
println(pretty(a))

4
Task/Zig-zag-matrix/K/zig-zag-matrix.k Normal file
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f:{grid:+x#<<a,'(!#a)*- 2!a:+/!x,:x
padded:(-#$-1+*/x)$$grid
`0:" "/'padded}
f 5

31
Task/Zig-zag-matrix/Klingphix/zig-zag-matrix.klingphix Normal file
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include ..\Utilitys.tlhy
%Size 5 !Size
0 ( $Size dup ) dim
%i 1 !i %j 1 !j
$Size 2 power [
1 -
( $i $j ) set
$i $j + 1 band 0 == (
[$j $Size < ( [$j 1 + !j] [$i 2 + !i] ) if
$i 1 > [ $i 1 - !i] if ]
[$i $Size < ( [$i 1 + !i] [$j 2 + !j] ) if
$j 1 > [ $j 1 - !j] if ]
) if
] for
$Size [
%row !row
$Size [
%col !col
( $row $col ) get tostr 32 32 chain chain 1 3 slice print drop
] for
nl
] for
nl "End " input

37
Task/Zig-zag-matrix/Kotlin/zig-zag-matrix.kotlin Normal file
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// version 1.1.3
typealias Vector = IntArray
typealias Matrix = Array<Vector>
fun zigzagMatrix(n: Int): Matrix {
val result = Matrix(n) { Vector(n) }
var down = false
var count = 0
for (col in 0 until n) {
if (down)
for (row in 0..col) result[row][col - row] = count++
else
for (row in col downTo 0) result[row][col - row] = count++
down = !down
}
for (row in 1 until n) {
if (down)
for (col in n - 1 downTo row) result[row + n - 1 - col][col] = count++
else
for (col in row until n) result[row + n - 1 - col][col] = count++
down = !down
}
return result
}
fun printMatrix(m: Matrix) {
for (i in 0 until m.size) {
for (j in 0 until m.size) print("%2d ".format(m[i][j]))
println()
}
println()
}
fun main(args: Array<String>) {
printMatrix(zigzagMatrix(5))
printMatrix(zigzagMatrix(10))
}

32
Task/Zig-zag-matrix/Ksh/zig-zag-matrix.ksh Normal file
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#!/bin/ksh
# Produce a zig-zag array.
# # Variables:
#
integer DEF_SIZE=5 # Default size = 5
arr_size=${1:-$DEF_SIZE} # $1 = size, or default
# # Externals:
#
# # Functions:
#
######
# main #
######
integer i j n
typeset -a zzarr
for (( i=n=0; i<arr_size*2; i++ )); do
for (( j= (i<arr_size) ? 0 : i-arr_size+1; j<=i && j<arr_size; j++ )); do
(( zzarr[(i&1) ? j*(arr_size-1)+i : (i-j)*arr_size+j] = n++ ))
done
done
for ((i=0; i<arr_size*arr_size; i++)); do
printf "%3d " ${zzarr[i]}
(( (i+1)%arr_size == 0 )) && printf "\n"
done

75
Task/Zig-zag-matrix/Lasso/zig-zag-matrix.lasso Normal file
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var(
'square' = array
,'size' = integer( 5 )// for a 5 X 5 square
,'row' = array
,'x' = integer( 1 )
,'y' = integer( 1 )
,'counter' = integer( 1 )
);
// create place-holder matrix
loop( $size );
$row = array;
loop( $size );
$row->insert( 0 );
/loop;
$square->insert( $row );
/loop;
while( $counter < $size * $size );
// check downward diagonal
if(
$x > 1
&&
$y < $square->size
&&
$square->get( $y + 1 )->get( $x - 1 ) == 0
);
$x -= 1;
$y += 1;
// check upward diagonal
else(
$x < $square->size
&&
$y > 1
&&
$square->get( $y - 1 )->get( $x + 1 ) == 0
);
$x += 1;
$y -= 1;
// check right
else(
(
$y == 1
||
$y == $square->size
)
&&
$x < $square->size
&&
$square->get( $y )->get( $x + 1 ) == 0
);
$x += 1;
// down
else;
$y += 1;
/if;
$square->get( $y )->get( $x ) = loop_count;
$counter += 1;
/while;
$square;

76
Task/Zig-zag-matrix/Lua/zig-zag-matrix.lua Normal file
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local zigzag = {}
function zigzag.new(n)
local a = {}
local i -- cols
local j -- rows
a.n = n
a.val = {}
for j = 1, n do
a.val[j] = {}
for i = 1, n do
a.val[j][i] = 0
end
end
i = 1
j = 1
local di
local dj
local k = 0
while k < n * n do
a.val[j][i] = k
k = k + 1
if i == n then
j = j + 1
a.val[j][i] = k
k = k + 1
di = -1
dj = 1
end
if j == 1 then
i = i + 1
a.val[j][i] = k
k = k + 1
di = -1
dj = 1
end
if j == n then
i = i + 1
a.val[j][i] = k
k = k + 1
di = 1
dj = -1
end
if i == 1 then
j = j + 1
a.val[j][i] = k
k = k + 1
di = 1
dj = -1
end
i = i + di
j = j + dj
end
setmetatable(a, {__index = zigzag, __tostring = zigzag.__tostring})
return a
end
function zigzag:__tostring()
local s = {}
for j = 1, self.n do
local row = {}
for i = 1, self.n do
row[i] = string.format('%d', self.val[j][i])
end
s[j] = table.concat(row, ' ')
end
return table.concat(s, '\n')
end
print(zigzag.new(5))

48
Task/Zig-zag-matrix/M2000-Interpreter/zig-zag-matrix.m2000 Normal file
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Module Lib1 {
Module Global PrintArray(&Ar()) {
if dimension(Ar())<>2 then Error "This is for 2D arrays"
integer i, j, n=dimension(Ar(),1), n1=dimension(Ar(),2)
for i=1 to n
for j=1 to n1
print Ar(i, j),
next
print
next
}
Function Global MakeArray(n as integer=5) {
dim a(1 to n, 1 to n) as integer=0
integer i=1, j=1, z, t1=1
boolean ch=true
for z=0 to n*n-1
if ch then a(i,j)=z else a(j,i)=z
j++
if j>t1 then t1++: j=1:i=t1: ch~ else i--
if i<1 then i=t1 else.if i>n then i=n: j++
if j>n then j=i+2: i=n:ch~
next
=a() // return array (as a pointer)
}
}
Module Zig_Zag_Matrix (n as integer=5) {
Pen 15 {Report "matrix "+n+"x"+n}
integer old_column=tab
Print $(,4) // set column to 4 chars
if random(1,2)=2 then
dim ret()
ret()=makeArray(n) // this get a copy
else
object a=makeArray(n) // but this get the copy of pointer
link a to ret() // ret() is reference to a, to array
end if
PrintArray &ret()
Print $(,old_column)
}
Inline Code Lib1 // just execute the code from module lib1 like was here
Form 60, 36 \\ console 60x36 characters
Report 2, "Zig-zag matrix" // 2 for center
Pen 14 {Zig_Zag_Matrix 1}
Pen 11 {Zig_Zag_Matrix 2}
Pen 14 {Zig_Zag_Matrix 3}
Pen 11 {Zig_Zag_Matrix 4}
Pen 14 {Zig_Zag_Matrix 5}
Pen 11 {Zig_Zag_Matrix 10}

30
Task/Zig-zag-matrix/M4/zig-zag-matrix.m4 Normal file
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divert(-1)
define(`set2d',`define(`$1[$2][$3]',`$4')')
define(`get2d',`defn(`$1[$2][$3]')')
define(`for',
`ifelse($#,0,``$0'',
`ifelse(eval($2<=$3),1,
`pushdef(`$1',$2)$4`'popdef(`$1')$0(`$1',incr($2),$3,`$4')')')')
define(`show2d',
`for(`x',0,decr($2),
`for(`y',0,decr($3),`format(`%2d',get2d($1,x,y)) ')
')')
dnl <name>,<size>
define(`zigzag',
`define(`j',1)`'define(`k',1)`'for(`e',0,eval($2*$2-1),
`set2d($1,decr(j),decr(k),e)`'ifelse(eval((j+k)%2),0,
`ifelse(eval(k<$2),1,
`define(`k',incr(k))',
`define(`j',eval(j+2))')`'ifelse(eval(j>1),1,
`define(`j',decr(j))')',
`ifelse(eval(j<$2),1,
`define(`j',incr(j))',
`define(`k',eval(k+2))')`'ifelse(eval(k>1),1,
`define(`k',decr(k))')')')')
divert
zigzag(`a',5)
show2d(`a',5,5)

66
Task/Zig-zag-matrix/MATLAB/zig-zag-matrix.m Normal file
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function matrix = zigZag(n)
%This is very unintiutive. This algorithm parameterizes the
%zig-zagging movement along the matrix indicies. The easiest way to see
%what this algorithm does is to go through line-by-line and write out
%what the algorithm does on a peace of paper.
matrix = zeros(n);
counter = 1;
flipCol = true;
flipRow = false;
%This for loop does the top-diagonal of the matrix
for i = (2:n)
row = (1:i);
column = (1:i);
%Causes the zig-zagging. Without these conditionals,
%you would end up with a diagonal matrix.
%To see what happens, comment these conditionals out.
if flipCol
column = fliplr(column);
flipRow = true;
flipCol = false;
elseif flipRow
row = fliplr(row);
flipRow = false;
flipCol = true;
end
%Selects a diagonal of the zig-zag matrix and places the
%correct integer value in each index along that diagonal
for j = (1:numel(row))
matrix(row(j),column(j)) = counter;
counter = counter + 1;
end
end
%This for loop does the bottom-diagonal of the matrix
for i = (2:n)
row = (i:n);
column = (i:n);
%Causes the zig-zagging. Without these conditionals,
%you would end up with a diagonal matrix.
%To see what happens comment these conditionals out.
if flipCol
column = fliplr(column);
flipRow = true;
flipCol = false;
elseif flipRow
row = fliplr(row);
flipRow = false;
flipCol = true;
end
%Selects a diagonal of the zig-zag matrix and places the
%correct integer value in each index along that diagonal
for j = (1:numel(row))
matrix(row(j),column(j)) = counter;
counter = counter + 1;
end
end
end

23
Task/Zig-zag-matrix/Maple/zig-zag-matrix-1.maple Normal file
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zigzag1:=proc(n)
uses ArrayTools;
local i,u,v,a;
u:=Replicate(<-1,1>,n):
v:=Vector[row](1..n,i->i*(2*i-3)):
v:=Reshape(<v+~1,v+~2>,2*n):
a:=Matrix(n,n):
for i to n do
a[...,i]:=v[i+1..i+n];
v+=u
od:
a
end:
zigzag2:=proc(n)
local i,v,a;
a:=zigzag1(n);
v:=Vector(1..n-1,i->i^2);
for i from 2 to n do
a[n+2-i..n,i]-=v[1..i-1]
od;
a
end:

1
Task/Zig-zag-matrix/Maple/zig-zag-matrix-2.maple Normal file
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zigzag1(6);

1
Task/Zig-zag-matrix/Maple/zig-zag-matrix-3.maple Normal file
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@ -0,0 +1 @@
zigzag2(6);

4
Task/Zig-zag-matrix/Mathematica/zig-zag-matrix-1.math Normal file
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ZigZag[size_Integer/;size>0]:=Module[{empty=ConstantArray[0,{size,size}]},
empty=ReplacePart[empty,{i_,j_}:>1/2 (i+j)^2-(i+j)/2-i (1-Mod[i+j,2])-j Mod[i+j,2]];
ReplacePart[empty,{i_,j_}/;i+j>size+1:> size^2-tmp[[size-i+1,size-j+1]]-1]
]

15
Task/Zig-zag-matrix/Mathematica/zig-zag-matrix-2.math Normal file
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ZigZag2[size_] := Module[{data, i, j, elem},
data = ConstantArray[0, {size, size}];
i = j = 1;
For[elem = 0, elem < size^2, elem++,
data[[i, j]] = elem;
If[Mod[i + j, 2] == 0,
If[j < size, j++, i += 2];
If[i > 1, i--]
,
If[i < size, i++, j += 2];
If[j > 1, j--];
];
];
data
]

2
Task/Zig-zag-matrix/Mathematica/zig-zag-matrix-3.math Normal file
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ZigZag[5] // MatrixForm
ZigZag2[6] // MatrixForm

22
Task/Zig-zag-matrix/Maxima/zig-zag-matrix.maxima Normal file
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zigzag(n) := block([a, i, j],
a: zeromatrix(n, n),
i: 1,
j: 1,
for k from 0 thru n*n - 1 do (
a[i, j]: k,
if evenp(i + j) then (
if j < n then j: j + 1 else i: i + 2,
if i > 1 then i: i - 1
) else (
if i < n then i: i + 1 else j: j + 2,
if j > 1 then j: j - 1
)
),
a)$
zigzag(5);
/* matrix([ 0, 1, 5, 6, 14],
[ 2, 4, 7, 13, 15],
[ 3, 8, 12, 16, 21],
[ 9, 11, 17, 20, 22],
[10, 18, 19, 23, 24]) */

9
Task/Zig-zag-matrix/MiniZinc/zig-zag-matrix.minizinc Normal file
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%Zigzag Matrix. Nigel Galloway, February 3rd., 2020
int: Size;
array [1..Size,1..Size] of var 1..Size*Size: zigzag;
constraint zigzag[1,1]=1 /\ zigzag[Size,Size]=Size*Size;
constraint forall(n in {2*g | g in 1..Size div 2})(zigzag[1,n]=zigzag[1,n-1]+1 /\ forall(g in 2..n)(zigzag[g,n-g+1]=zigzag[g-1,n-g+2]+1));
constraint forall(n in {2*g + ((Size-1) mod 2) | g in 1..(Size-1) div 2})(zigzag[n,Size]=zigzag[n-1,Size]+1 /\ forall(g in 1..Size-n)(zigzag[n+g,Size-g]=zigzag[n+g-1,Size-g+1]+1));
constraint forall(n in {2*g+1 | g in 1..(Size-1) div 2})(zigzag[n,1]=zigzag[n-1,1]+1 /\ forall(g in 2..n)(zigzag[n-g+1,g]=zigzag[n-g+2,g-1]+1));
constraint forall(n in {2*g+((Size) mod 2) | g in 1..(Size-1) div 2})(zigzag[Size,n]=zigzag[Size,n-1]+1 /\ forall(g in 1..Size-n)(zigzag[Size-g,n+g]=zigzag[Size-g+1,n+g-1]+1));
output [show2d(zigzag)];

48
Task/Zig-zag-matrix/Modula-3/zig-zag-matrix.mod3 Normal file
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MODULE ZigZag EXPORTS Main;
IMPORT IO, Fmt;
TYPE Matrix = REF ARRAY OF ARRAY OF CARDINAL;
PROCEDURE Create(size: CARDINAL): Matrix =
PROCEDURE move(VAR i, j: INTEGER) =
BEGIN
IF j < (size - 1) THEN
IF (i - 1) < 0 THEN
i := 0;
ELSE
i := i - 1;
END;
INC(j);
ELSE
INC(i);
END;
END move;
VAR data := NEW(Matrix, size, size);
x, y: INTEGER := 0;
BEGIN
FOR v := 0 TO size * size - 1 DO
data[y, x] := v;
IF (x + y) MOD 2 = 0 THEN
move(y, x);
ELSE
move(x, y);
END;
END;
RETURN data;
END Create;
PROCEDURE Print(data: Matrix) =
BEGIN
FOR i := FIRST(data^) TO LAST(data^) DO
FOR j := FIRST(data[0]) TO LAST(data[0]) DO
IO.Put(Fmt.F("%3s", Fmt.Int(data[i, j])));
END;
IO.Put("\n");
END;
END Print;
BEGIN
Print(Create(5));
END ZigZag.

41
Task/Zig-zag-matrix/NetRexx/zig-zag-matrix.netrexx Normal file
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/* NetRexx */
options replace format comments java crossref savelog symbols binary
zigzag(5)
return
method zigzag(msize) public static
row = 1
col = 1
ziggy = Rexx(0)
loop j_ = 0 for msize * msize
ziggy[row, col] = j_
if (row + col) // 2 == 0 then do
if col < msize then -
col = col + 1
else row = row + 2
if row \== 1 then -
row = row - 1
end
else do
if row < msize then -
row = row + 1
else col = col + 2
if col \== 1 then -
col = col - 1
end
end j_
L = (msize * msize - 1).length /*for a constant element width. */
loop row = 1 for msize /*show all the matrix's rows. */
rowOut = ''
loop col = 1 for msize
rowOut = rowOut ziggy[row, col].right(L)
end col
say rowOut
end row
return

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