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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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3
Task/Spiral-matrix/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Spiral_matrix
note: Matrices

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Task/Spiral-matrix/00-TASK.txt Normal file
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;Task:
Produce a spiral array.
A &nbsp; ''spiral array'' &nbsp; 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 go around the edges of the array spiraling inwards.
For example, given &nbsp; '''5''', &nbsp; produce this array:
<pre>
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8
</pre>
;Related tasks:
* &nbsp; [[Zig-zag matrix]]
* &nbsp; [[Identity_matrix]]
* &nbsp; [[Ulam_spiral_(for_primes)]]
<br><br>

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Task/Spiral-matrix/11l/spiral-matrix.11l Normal file
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F spiral_matrix(n)
V m = [[0] * n] *n
V d = [(0, 1), (1, 0), (0, -1), (-1, 0)]
V xy = (0, -1)
V c = 0
L(i) 0 .< n + n - 1
L 0 .< (n + n - i) I/ 2
xy += d[i % 4]
m[xy.x][xy.y] = c
c++
R m
F printspiral(myarray)
L(y) 0 .< myarray.len
L(x) 0 .< myarray.len
print(‘#2’.format(myarray[y][x]), end' ‘ ’)
print()
printspiral(spiral_matrix(5))

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Task/Spiral-matrix/360-Assembly/spiral-matrix.360 Normal file
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SPIRALM CSECT
USING SPIRALM,R13
SAVEAREA B STM-SAVEAREA(R15)
DC 17F'0'
DC CL8'SPIRALM'
STM STM R14,R12,12(R13)
ST R13,4(R15)
ST R15,8(R13)
LR R13,R15
* ---- CODE
LA R0,0
LA R1,1
LH R12,N n
LR R4,R1 Row=1
LR R5,R1 Col=1
LR R6,R1 BotRow=1
LR R7,R1 BotCol=1
LR R8,R12 TopRow=n
LR R9,R12 TopCol=n
LR R10,R0 Dir=0
LR R15,R12 n
MR R14,R12 R15=n*n
LA R11,1 k=1
LOOP CR R11,R15
BH ENDLOOP
LR R1,R4
BCTR R1,0
MH R1,N
AR R1,R5
LR R2,R11 k
BCTR R2,0
BCTR R1,0
SLA R1,1
STH R2,MATRIX(R1) Matrix(Row,Col)=k-1
CH R10,=H'0'
BE DIR0
CH R10,=H'1'
BE DIR1
CH R10,=H'2'
BE DIR2
CH R10,=H'3'
BE DIR3
B DIRX
DIR0 CR R5,R9 if Col<TopCol
BNL DIR0S
LA R5,1(R5) Col=Col+1
B DIRX
DIR0S LA R10,1 Dir=1
LA R4,1(R4) Row=Row+1
LA R6,1(R6) BotRow=BotRow+1
B DIRX
DIR1 CR R4,R8 if Row<TopRow
BNL DIR1S
LA R4,1(R4) Row=Row+1
B DIRX
DIR1S LA R10,2 Dir=2
BCTR R5,0 Col=Col-1
BCTR R9,0 TopCol=TopCol-1
B DIRX
DIR2 CR R5,R7 if Col>BotCol
BNH DIR2S
BCTR R5,0 Col=Col-1
B DIRX
DIR2S LA R10,3 Dir=3
BCTR R4,0 Row=Row-1
BCTR R8,0 TopRow=TopRow-1
B DIRX
DIR3 CR R4,R6 if Row>BotRow
BNH DIR3S
BCTR R4,0 Row=Row-1
B DIRX
DIR3S LA R10,0 Dir=0
LA R5,1(R5) Col=Col+1
LA R7,1(R7) BotCol=BotCol+1
DIRX EQU *
LA R11,1(R11) k=k+1
B LOOP
ENDLOOP EQU *
LA R4,1 i
LOOPI CR R4,R12
BH ENDLOOPI
XR R10,R10
LA R5,1 j
LOOPJ CR R5,R12
BH ENDLOOPJ
LR R1,R4
BCTR R1,0
MH R1,N
AR R1,R5
BCTR R1,0
SLA R1,1
LH R2,MATRIX(R1) Matrix(i,j)
LA R3,BUF
AR R3,R10
CVD R2,P8
MVC 0(4,R3),=X'40202120'
ED 0(4,R3),P8+6
LA R10,4(R10)
LA R5,1(R5)
B LOOPJ
ENDLOOPJ EQU *
WTO MF=(E,WTOMSG)
LA R4,1(R4)
B LOOPI
ENDLOOPI EQU *
* ---- END CODE
L R13,4(0,R13)
LM R14,R12,12(R13)
XR R15,R15
BR R14
* ---- DATA
N DC H'5' max=20 (20*4=80)
LTORG
P8 DS PL8
WTOMSG DS 0F
DC H'80',XL2'0000'
BUF DC CL80' '
MATRIX DS H Matrix(n,n)
YREGS
END SPIRALM

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REPORT zspiral_matrix.
CLASS lcl_spiral_matrix DEFINITION FINAL.
PUBLIC SECTION.
TYPES:
BEGIN OF ty_coordinates,
dy TYPE i,
dx TYPE i,
value TYPE i,
END OF ty_coordinates,
ty_t_coordinates TYPE STANDARD TABLE OF ty_coordinates WITH EMPTY KEY.
DATA mv_dimention TYPE i.
DATA mv_initial_value TYPE i.
METHODS:
constructor IMPORTING iv_dimention TYPE i
iv_initial_value TYPE i,
get_coordinates RETURNING VALUE(rv_result) TYPE ty_t_coordinates,
print.
PRIVATE SECTION.
DATA lt_coordinates TYPE ty_t_coordinates.
METHODS create RETURNING VALUE(ro_result) TYPE REF TO lcl_spiral_matrix.
ENDCLASS.
CLASS lcl_spiral_matrix IMPLEMENTATION.
METHOD constructor.
mv_dimention = iv_dimention.
mv_initial_value = iv_initial_value.
create( ).
ENDMETHOD.
METHOD create.
DATA dy TYPE i.
DATA dx TYPE i.
DATA value TYPE i.
DATA seq_number TYPE i.
DATA seq_dimention TYPE i.
DATA sign_coef TYPE i VALUE -1.
value = mv_initial_value.
" Fill in the first row (index 0)
DO mv_dimention TIMES.
APPEND VALUE #( dy = dy dx = dx value = value ) TO lt_coordinates.
value = value + 1.
dx = dx + 1.
ENDDO.
seq_dimention = mv_dimention.
" Find the row and column numbers and set the values.
DO ( 2 * mv_dimention - 2 ) / 2 TIMES.
sign_coef = - sign_coef.
seq_dimention = seq_dimention - 1.
DO 2 TIMES.
seq_number = seq_number + 1.
DO seq_dimention TIMES.
IF seq_number MOD 2 <> 0.
dy = dy + 1 * sign_coef.
ELSE.
dx = dx - 1 * sign_coef.
ENDIF.
APPEND VALUE #( dy = dy dx = dx value = value ) TO lt_coordinates.
value = value + 1.
ENDDO.
ENDDO.
ENDDO.
ro_result = me.
ENDMETHOD.
METHOD get_coordinates.
rv_result = lt_coordinates.
ENDMETHOD.
METHOD print.
DATA cnt TYPE i.
DATA line TYPE string.
SORT lt_coordinates BY dy dx ASCENDING.
LOOP AT lt_coordinates ASSIGNING FIELD-SYMBOL(<ls_coordinates>).
cnt = cnt + 1.
line = |{ line } { <ls_coordinates>-value }|.
IF cnt MOD mv_dimention = 0.
WRITE / line.
CLEAR line.
ENDIF.
ENDLOOP.
ENDMETHOD.
ENDCLASS.
START-OF-SELECTION.
DATA(go_spiral_matrix) = NEW lcl_spiral_matrix( iv_dimention = 5
iv_initial_value = 0 ).
go_spiral_matrix->print( ).

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INT empty=0;
PROC spiral = (INT n)[,]INT: (
INT dx:=1, dy:=0; # Starting increments #
INT x:=0, y:=0; # Starting location #
[0:n-1,0:n-1]INT my array;
FOR y FROM LWB my array TO UPB my array DO
FOR x FROM LWB my array TO UPB my array DO
my array[x,y]:=empty
OD
OD;
FOR i TO n**2 DO
my array[x,y] := i;
INT nx:=x+dx, ny:=y+dy;
IF ( 0<=nx AND nx<n AND 0<=ny AND ny<n | my array[nx,ny] = empty | FALSE ) THEN
x:=nx; y:=ny
ELSE
INT swap:=dx; dx:=-dy; dy:=swap;
x+:=dx; y+:=dy
FI
OD;
my array
);
PROC print spiral = ([,]INT my array)VOID:(
FOR y FROM LWB my array TO UPB my array DO
FOR x FROM LWB my array TO UPB my array DO
print(whole(my array[x,y],-3))
OD;
print(new line)
OD
);
print spiral(spiral(5))

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Task/Spiral-matrix/AWK/spiral-matrix.awk Normal file
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# syntax: GAWK -f SPIRAL_MATRIX.AWK [-v offset={0|1}] [size]
# converted from BBC BASIC
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) }
bot_col = bot_row = 0
top_col = top_row = size - 1
direction = col = row = 0
for (i=0; i<=size*size-1; i++) { # build
arr[col,row] = i + offset
if (direction == 0) {
if (col < top_col) { col++ }
else { direction = 1 ; row++ ; bot_row++ }
}
else if (direction == 1) {
if (row < top_row) { row++ }
else { direction = 2 ; col-- ; top_col-- }
}
else if (direction == 2) {
if (col > bot_col) { col-- }
else { direction = 3 ; row-- ; top_row-- }
}
else if (direction == 3) {
if (row > bot_row) { row-- }
else { direction = 0 ; col++ ; bot_col++ }
}
}
width = length(size ^ 2 - 1 + offset) + 1 # column width
for (i=0; i<size; i++) { # print
for (j=0; j<size; j++) {
printf("%*d",width,arr[j,i])
}
printf("\n")
}
exit(0)
}

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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)
INT lev,maxLev,dist,maxDist,v
maxLev=size/2
IF (size&1)=0 THEN
maxLev==-1
FI
maxDist=size-1
v=1
FOR lev=0 TO maxLev
DO
FOR dist=0 TO maxDist
DO
a(Index(size,lev+dist,lev))=v v==+1
OD
FOR dist=0 TO maxDist-1
DO
a(Index(size,size-1-lev,lev+dist+1))=v v==+1
OD
FOR dist=0 TO maxDist-1
DO
a(Index(size,size-2-lev-dist,size-1-lev))=v v==+1
OD
FOR dist=0 TO maxDist-2
DO
a(Index(size,lev,size-2-lev-dist))=v v==+1
OD
maxDist==-2
OD
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/Spiral-matrix/Ada/spiral-matrix-1.ada Normal file
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-- Spiral Square
with Ada.Text_Io; use Ada.Text_Io;
with Ada.Integer_Text_Io; use Ada.Integer_Text_Io;
with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions;
procedure Spiral_Square is
type Array_Type is array(Positive range <>, Positive range <>) of Natural;
function Spiral (N : Positive) return Array_Type is
Result : Array_Type(1..N, 1..N);
Row : Natural := 1;
Col : Natural := 1;
Max_Row : Natural := N;
Max_Col : Natural := N;
Min_Row : Natural := 1;
Min_Col : Natural := 1;
begin
for I in 0..N**2 - 1 loop
Result(Row, Col) := I;
if Row = Min_Row then
Col := Col + 1;
if Col > Max_Col then
Col := Max_Col;
Row := Row + 1;
end if;
elsif Col = Max_Col then
Row := Row + 1;
if Row > Max_Row then
Row := Max_Row;
Col := Col - 1;
end if;
elsif Row = Max_Row then
Col := Col - 1;
if Col < Min_Col then
Col := Min_Col;
Row := Row - 1;
end if;
elsif Col = Min_Col then
Row := Row - 1;
if Row = Min_Row then -- Reduce spiral
Min_Row := Min_Row + 1;
Max_Row := Max_Row - 1;
Row := Min_Row;
Min_Col := Min_Col + 1;
Max_Col := Max_Col - 1;
Col := Min_Col;
end if;
end if;
end loop;
return Result;
end Spiral;
procedure Print(Item : Array_Type) is
Num_Digits : constant Float := Log(X => Float(Item'Length(1)**2), Base => 10.0);
Spacing : constant Positive := Integer(Num_Digits) + 2;
begin
for I in Item'range(1) loop
for J in Item'range(2) loop
Put(Item => Item(I,J), Width => Spacing);
end loop;
New_Line;
end loop;
end Print;
begin
Print(Spiral(5));
end Spiral_Square;

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function Spiral (N : Positive) return Array_Type is
Result : Array_Type (1..N, 1..N);
Left : Positive := 1;
Right : Positive := N;
Top : Positive := 1;
Bottom : Positive := N;
Index : Natural := 0;
begin
while Left < Right loop
for I in Left..Right - 1 loop
Result (Top, I) := Index;
Index := Index + 1;
end loop;
for J in Top..Bottom - 1 loop
Result (J, Right) := Index;
Index := Index + 1;
end loop;
for I in reverse Left + 1..Right loop
Result (Bottom, I) := Index;
Index := Index + 1;
end loop;
for J in reverse Top + 1..Bottom loop
Result (J, Left) := Index;
Index := Index + 1;
end loop;
Left := Left + 1;
Right := Right - 1;
Top := Top + 1;
Bottom := Bottom - 1;
end loop;
Result (Top, Left) := Index;
return Result;
end Spiral;

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Task/Spiral-matrix/AppleScript/spiral-matrix.applescript Normal file
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---------------------- SPIRAL MATRIX ---------------------
-- spiral :: Int -> [[Int]]
on spiral(n)
script go
on |λ|(rows, cols, start)
if 0 < rows then
{enumFromTo(start, start + pred(cols))} & ¬
map(my |reverse|, ¬
transpose(|λ|(cols, pred(rows), start + cols)))
else
{{}}
end if
end |λ|
end script
go's |λ|(n, n, 0)
end spiral
--------------------------- TEST -------------------------
on run
wikiTable(spiral(5), ¬
false, ¬
"text-align:center;width:12em;height:12em;table-layout:fixed;")
end run
-------------------- WIKI TABLE FORMAT -------------------
-- wikiTable :: [Text] -> Bool -> Text -> Text
on wikiTable(lstRows, blnHdr, strStyle)
script fWikiRows
on |λ|(lstRow, iRow)
set strDelim to if_(blnHdr and (iRow = 0), "!", "|")
set strDbl to strDelim & strDelim
linefeed & "|-" & linefeed & strDelim & space & ¬
intercalateS(space & strDbl & space, lstRow)
end |λ|
end script
linefeed & "{| class=\"wikitable\" " & ¬
if_(strStyle ≠ "", "style=\"" & strStyle & "\"", "") & ¬
intercalateS("", ¬
map(fWikiRows, lstRows)) & linefeed & "|}" & linefeed
end wikiTable
------------------------- GENERIC ------------------------
-- comparing :: (a -> b) -> (a -> a -> Ordering)
on comparing(f)
script
on |λ|(a, b)
tell mReturn(f)
set fa to |λ|(a)
set fb to |λ|(b)
if fa < fb then
-1
else if fa > fb then
1
else
0
end if
end tell
end |λ|
end script
end comparing
-- concatMap :: (a -> [b]) -> [a] -> [b]
on concatMap(f, xs)
set lng to length of xs
set acc to {}
tell mReturn(f)
repeat with i from 1 to lng
set acc to acc & (|λ|(item i of xs, i, xs))
end repeat
end tell
if {text, string} contains class of xs then
acc as text
else
acc
end if
end concatMap
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
return lst
else
return {}
end if
end enumFromTo
-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- if_ :: Bool -> a -> a -> a
on if_(bool, x, y)
if bool then
x
else
y
end if
end if_
-- intercalateS :: String -> [String] -> String
on intercalateS(sep, xs)
set {dlm, my text item delimiters} to {my text item delimiters, sep}
set s to xs as text
set my text item delimiters to dlm
return s
end intercalateS
-- length :: [a] -> Int
on |length|(xs)
length of xs
end |length|
-- max :: Ord a => a -> a -> a
on max(x, y)
if x > y then
x
else
y
end if
end max
-- maximumBy :: (a -> a -> Ordering) -> [a] -> a
on maximumBy(f, xs)
set cmp to mReturn(f)
script max
on |λ|(a, b)
if a is missing value or cmp's |λ|(a, b) < 0 then
b
else
a
end if
end |λ|
end script
foldl(max, missing value, xs)
end maximumBy
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- 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
-- pred :: Enum a => a -> a
on pred(x)
x - 1
end pred
-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> a -> [a]
on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}
repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate
-- reverse :: [a] -> [a]
on |reverse|(xs)
if class of xs is text then
(reverse of characters of xs) as text
else
reverse of xs
end if
end |reverse|
-- Simplified version - assuming rows of unvarying length.
-- transpose :: [[a]] -> [[a]]
on transpose(rows)
script cols
on |λ|(_, iCol)
script cell
on |λ|(row)
item iCol of row
end |λ|
end script
concatMap(cell, rows)
end |λ|
end script
map(cols, item 1 of rows)
end transpose
-- unlines :: [String] -> String
on unlines(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines
-- unwords :: [String] -> String
on unwords(xs)
intercalateS(space, xs)
end unwords

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spiralMatrix: function [n][
m: new array.of: @[n,n] null
[dx, dy, x, y]: [1, 0, 0, 0]
loop 0..dec n^2 'i [
m\[y]\[x]: i
[nx,ny]: @[x+dx, y+dy]
if? and? [and? [in? nx 0..n-1][in? ny 0..n-1]][
null? m\[ny]\[nx]
][
[x,y]: @[nx, ny]
]
else [
bdx: dx
[dx, dy]: @[neg dy, bdx]
[x, y]: @[x+dx, y+dy]
]
]
return m
]
loop spiralMatrix 5 'row [
print map row 'x -> pad to :string x 4
]

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Task/Spiral-matrix/AutoHotkey/spiral-matrix.ahk Normal file
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n := 5, dx := x := y := v := 1, dy := 0
Loop % n*n {
a_%x%_%y% := v++
nx := x+dx, ny := y+dy
If (1 > nx || nx > n || 1 > ny || ny > n || a_%nx%_%ny%)
t := dx, dx := -dy, dy := t
x := x+dx, y := y+dy
}
Loop %n% { ; generate printout
y := A_Index ; for each row
Loop %n% ; and for each column
s .= a_%A_Index%_%y% "`t" ; attach stored index
s .= "`n" ; row is complete
}
MsgBox %s% ; show output
/*
---------------------------
1 2 3 4 5
16 17 18 19 6
15 24 25 20 7
14 23 22 21 8
13 12 11 10 9
---------------------------
*/

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Task/Spiral-matrix/BBC-BASIC/spiral-matrix.basic Normal file
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N%=5
@%=LENSTR$(N%*N%-1)+1
BotCol%=0 : TopCol%=N%-1
BotRow%=0 : TopRow%=N%-1
DIM Matrix%(TopCol%,TopRow%)
Dir%=0 : Col%=0 : Row%=0
FOR I%=0 TO N%*N%-1
Matrix%(Col%,Row%)=I%
PRINT TAB(Col%*@%,Row%) I%
CASE Dir% OF
WHEN 0: IF Col% < TopCol% THEN Col%+=1 ELSE Dir%=1 : Row%+=1 : BotRow%+=1
WHEN 1: IF Row% < TopRow% THEN Row%+=1 ELSE Dir%=2 : Col%-=1 : TopCol%-=1
WHEN 2: IF Col% > BotCol% THEN Col%-=1 ELSE Dir%=3 : Row%-=1 : TopRow%-=1
WHEN 3: IF Row% > BotRow% THEN Row%-=1 ELSE Dir%=0 : Col%+=1 : BotCol%+=1
ENDCASE
NEXT
END

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#include <vector>
#include <memory> // for auto_ptr
#include <cmath> // for the ceil and 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 > getSpiralArray( int dimension )
{
auto_ptr< IntTable > spiralArrayPtr( new IntTable(
dimension, IntRow( dimension ) ) );
int numConcentricSquares = static_cast< int >( ceil(
static_cast< double >( dimension ) / 2.0 ) );
int j;
int sideLen = dimension;
int currNum = 0;
for ( int i = 0; i < numConcentricSquares; i++ )
{
// do top side
for ( j = 0; j < sideLen; j++ )
( *spiralArrayPtr )[ i ][ i + j ] = currNum++;
// do right side
for ( j = 1; j < sideLen; j++ )
( *spiralArrayPtr )[ i + j ][ dimension - 1 - i ] = currNum++;
// do bottom side
for ( j = sideLen - 2; j > -1; j-- )
( *spiralArrayPtr )[ dimension - 1 - i ][ i + j ] = currNum++;
// do left side
for ( j = sideLen - 2; j > 0; j-- )
( *spiralArrayPtr )[ i + j ][ i ] = currNum++;
sideLen -= 2;
}
return spiralArrayPtr;
}
void printSpiralArray( const auto_ptr< IntTable >& spiralArrayPtr )
{
size_t dimension = spiralArrayPtr->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 ) << ( *spiralArrayPtr )[ row ][ col ];
cout << endl;
}
}
int main()
{
printSpiralArray( getSpiralArray( 5 ) );
}

17
Task/Spiral-matrix/C++/spiral-matrix-2.cpp Normal file
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#include <vector>
#include <iostream>
using namespace std;
int main() {
const int n = 5;
const int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};
int x = 0, y = -1, c = 0;
vector<vector<int>> m(n, vector<int>(n));
for (int i = 0, im = 0; i < n + n - 1; ++i, im = i % 4)
for (int j = 0, jlen = (n + n - i) / 2; j < jlen; ++j)
m[x += dx[im]][y += dy[im]] = ++c;
for (auto & r : m) {
for (auto & v : r)
cout << v << ' ';
cout << endl;
}
}

37
Task/Spiral-matrix/C-sharp/spiral-matrix-1.cs Normal file
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public int[,] Spiral(int n) {
int[,] result = new int[n, n];
int pos = 0;
int count = n;
int value = -n;
int sum = -1;
do {
value = -1 * value / n;
for (int i = 0; i < count; i++) {
sum += value;
result[sum / n, sum % n] = pos++;
}
value *= n;
count--;
for (int i = 0; i < count; i++) {
sum += value;
result[sum / n, sum % n] = pos++;
}
} while (count > 0);
return result;
}
// Method to print arrays, pads numbers so they line up in columns
public void PrintArray(int[,] array) {
int n = (array.GetLength(0) * array.GetLength(1) - 1).ToString().Length + 1;
for (int i = 0; i < array.GetLength(0); i++) {
for (int j = 0; j < array.GetLength(1); j++) {
Console.Write(array[i, j].ToString().PadLeft(n, ' '));
}
Console.WriteLine();
}
}

21
Task/Spiral-matrix/C-sharp/spiral-matrix-2.cs Normal file
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//generate spiral matrix for given N
int[,] CreateMatrix(int n){
int[] dx = {0, 1, 0, -1}, dy = {1, 0, -1, 0};
int x = 0, y = -1, c = 0;
int[,] m = new int[n,n];
for (int i = 0, im = 0; i < n + n - 1; ++i, im = i % 4)
for (int j = 0, jlen = (n + n - i) / 2; j < jlen; ++j)
m[x += dx[im],y += dy[im]] = ++c;
return n;
}
//print aligned matrix
void Print(int[,] matrix) {
var len = (int)Math.Ceiling(Math.Log10(m.GetLength(0) * m.GetLength(1)))+1;
for(var y = 0; y<m.GetLength(1); y++){
for(var x = 0; x<m.GetLength(0); x++){
Console.Write(m[y, x].ToString().PadRight(len, ' '));
}
Console.WriteLine();
}
}

71
Task/Spiral-matrix/C-sharp/spiral-matrix-3.cs Normal file
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace spiralmat
{
class spiral
{
public static int lev;
int lev_lim, count, bk, cd, low, l, m;
spiral()
{
lev = lev_lim = count = bk = cd = low = l = m = 0;
}
void level(int n1, int r, int c)
{
lev_lim = n1 % 2 == 0 ? n1 / 2 : (n1 + 1) / 2;
if ((r <= lev_lim) && (c <= lev_lim))
lev = Math.Min(r, c);
else
{
bk = r > c ? (n1 + 1) - r : (n1 + 1) - c;
low = Math.Min(r, c);
if (low <= lev_lim)
cd = low;
lev = cd < bk ? cd : bk;
}
}
int func(int n2, int xo, int lo)
{
l = xo;
m = lo;
count = 0;
level(n2, l, m);
for (int ak = 1; ak < lev; ak++)
count += 4 * (n2 - 1 - 2 * (ak - 1));
return count;
}
public static void Main(string[] args)
{
spiral ob = new spiral();
Console.WriteLine("Enter Order..");
int n = int.Parse(Console.ReadLine());
Console.WriteLine("The Matrix of {0} x {1} Order is=>\n", n, n);
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= n; j++)
Console.Write("{0,3:D} ",
ob.func(n, i, j)
+ Convert.ToInt32(
((j >= i) && (i == lev))
? ((j - i) + 1)
: ((j == ((n + 1) - lev) && (i > lev) && (i <= j)))
? (n - 2 * (lev - 1) + (i - 1) - (n - j))
: ((i == ((n + 1) - lev) && (j < i)))
? ((n - 2 * (lev - 1)) + ((n - 2 * (lev - 1)) - 1) + (i - j))
: ((j == lev) && (i > lev) && (i < ((n + 1) - lev)))
? ((n - 2 * (lev - 1)) + ((n - 2 * (lev - 1)) - 1) + ((n - 2 * (lev - 1)) - 1) + (((n + 1) - lev) - i))
: 0));
Console.WriteLine();
}
Console.ReadKey();
}
}
}

30
Task/Spiral-matrix/C-sharp/spiral-matrix-4.cs Normal file
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INPUT:-
Enter order..
5
OUTPUT:-
The Matrix of 5 x 5 Order is=>
1 2 3 4 5
16 17 18 19 6
15 24 25 20 7
14 23 22 21 8
13 12 11 10 9
INPUT:-
Enter order..
6
OUTPUT:-
The Matrix of 6 x 6 Order is=>
1 2 3 4 5 6
20 21 22 23 24 7
19 32 33 34 25 8
18 31 36 35 26 9
17 30 29 28 27 10
16 15 14 13 12 11

35
Task/Spiral-matrix/C/spiral-matrix-1.c Normal file
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#include <stdio.h>
#include <stdlib.h>
#define valid(i, j) 0 <= i && i < m && 0 <= j && j < n && !s[i][j]
int main(int c, char **v)
{
int i, j, m = 0, n = 0;
/* default size: 5 */
if (c >= 2) m = atoi(v[1]);
if (c >= 3) n = atoi(v[2]);
if (m <= 0) m = 5;
if (n <= 0) n = m;
int **s = calloc(1, sizeof(int *) * m + sizeof(int) * m * n);
s[0] = (int*)(s + m);
for (i = 1; i < m; i++) s[i] = s[i - 1] + n;
int dx = 1, dy = 0, val = 0, t;
for (i = j = 0; valid(i, j); i += dy, j += dx ) {
for (; valid(i, j); j += dx, i += dy)
s[i][j] = ++val;
j -= dx; i -= dy;
t = dy; dy = dx; dx = -t;
}
for (t = 2; val /= 10; t++);
for(i = 0; i < m; i++)
for(j = 0; j < n || !putchar('\n'); j++)
printf("%*d", t, s[i][j]);
return 0;
}

18
Task/Spiral-matrix/C/spiral-matrix-2.c Normal file
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#include <stdio.h>
#include <stdlib.h>
int spiral(int w, int h, int x, int y)
{
return y ? w + spiral(h - 1, w, y - 1, w - x - 1) : x;
}
int main(int argc, char **argv)
{
int w = atoi(argv[1]), h = atoi(argv[2]), i, j;
for (i = 0; i < h; i++) {
for (j = 0; j < w; j++)
printf("%4d", spiral(w, h, j, i));
putchar('\n');
}
return 0;
}

16
Task/Spiral-matrix/Clojure/spiral-matrix-1.clj Normal file
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(defn spiral [n]
(let [cyc (cycle [1 n -1 (- n)])]
(->> (range (dec n) 0 -1)
(mapcat #(repeat 2 %))
(cons n)
(mapcat #(repeat %2 %) cyc)
(reductions +)
(map vector (range 0 (* n n)))
(sort-by second)
(map first)))
(let [n 5]
(clojure.pprint/cl-format
true
(str " ~{~<~%~," (* n 3) ":;~2d ~>~}~%")
(spiral n)))

8
Task/Spiral-matrix/Clojure/spiral-matrix-2.clj Normal file
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(defn spiral-matrix [m n & [start]]
(let [row (list (map #(+ start %) (range m)))]
(if (= 1 n) row
(concat row (map reverse
(apply map list
(spiral-matrix (dec n) m (+ start m))))))))
(defn spiral [n m] (spiral-matrix n m 1))

46
Task/Spiral-matrix/CoffeeScript/spiral-matrix-1.coffee Normal file
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# Let's say you want to arrange the first N-squared natural numbers
# in a spiral, where you fill in the numbers clockwise, starting from
# the upper left corner. This code computes the values for each x/y
# coordinate of the square. (Of course, you could precompute the values
# iteratively, but what fun is that?)
spiral_value = (x, y, n) ->
prior_legs =
N: 0
E: 1
S: 2
W: 3
edge_run = (edge_offset) ->
N: -> edge_offset.W - edge_offset.N
E: -> edge_offset.N - edge_offset.E
S: -> edge_offset.E - edge_offset.S
W: -> edge_offset.S - edge_offset.W
edge_offset =
N: y
E: n - 1 - x
S: n - 1 - y
W: x
min_edge_offset = n
for dir of edge_offset
if edge_offset[dir] < min_edge_offset
min_edge_offset = edge_offset[dir]
border = dir
inner_square_edge = n - 2 * min_edge_offset
corner_offset = n * n - inner_square_edge * inner_square_edge
corner_offset += prior_legs[border] * (inner_square_edge - 1)
corner_offset + edge_run(edge_offset)[border]()
spiral_matrix = (n) ->
# return a nested array expression
for y in [0...n]
for x in [0...n]
spiral_value x, y, n
do ->
for n in [6, 7]
console.log "\n----Spiral n=#{n}"
console.log spiral_matrix n

18
Task/Spiral-matrix/CoffeeScript/spiral-matrix-2.coffee Normal file
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> coffee spiral.coffee
----Spiral n=6
[ [ 0, 1, 2, 3, 4, 5 ],
[ 19, 20, 21, 22, 23, 6 ],
[ 18, 31, 32, 33, 24, 7 ],
[ 17, 30, 35, 34, 25, 8 ],
[ 16, 29, 28, 27, 26, 9 ],
[ 15, 14, 13, 12, 11, 10 ] ]
----Spiral n=7
[ [ 0, 1, 2, 3, 4, 5, 6 ],
[ 23, 24, 25, 26, 27, 28, 7 ],
[ 22, 39, 40, 41, 42, 29, 8 ],
[ 21, 38, 47, 48, 43, 30, 9 ],
[ 20, 37, 46, 45, 44, 31, 10 ],
[ 19, 36, 35, 34, 33, 32, 11 ],
[ 18, 17, 16, 15, 14, 13, 12 ] ]

18
Task/Spiral-matrix/Common-Lisp/spiral-matrix-1.lisp Normal file
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(defun spiral (rows columns)
(do ((N (* rows columns))
(spiral (make-array (list rows columns) :initial-element nil))
(dx 1) (dy 0) (x 0) (y 0)
(i 0 (1+ i)))
((= i N) spiral)
(setf (aref spiral y x) i)
(let ((nx (+ x dx)) (ny (+ y dy)))
(cond
((and (< -1 nx columns)
(< -1 ny rows)
(null (aref spiral ny nx)))
(setf x nx
y ny))
(t (psetf dx (- dy)
dy dx)
(setf x (+ x dx)
y (+ y dy)))))))

11
Task/Spiral-matrix/Common-Lisp/spiral-matrix-2.lisp Normal file
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(defun spiral (m n &optional (start 1))
(let ((row (list (loop for x from 0 to (1- m) collect (+ x start)))))
(if (= 1 n) row
;; first row, plus (n-1) x m spiral rotated 90 degrees
(append row (map 'list #'reverse
(apply #'mapcar #'list
(spiral (1- n) m (+ start m))))))))
;; test
(loop for row in (spiral 4 3) do
(format t "~{~4d~^~}~%" row))

20
Task/Spiral-matrix/D/spiral-matrix-1.d Normal file
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void main() {
import std.stdio;
enum n = 5;
int[n][n] M;
int pos, side = n;
foreach (immutable i; 0 .. n / 2 + n % 2) {
foreach (immutable j; 0 .. side)
M[i][i + j] = pos++;
foreach (immutable j; 1 .. side)
M[i + j][n - 1 - i] = pos++;
foreach_reverse (immutable j; 0 .. side - 1)
M[n - 1 - i][i + j] = pos++;
foreach_reverse (immutable j; 1 .. side - 1)
M[i + j][i] = pos++;
side -= 2;
}
writefln("%(%(%2d %)\n%)", M);
}

52
Task/Spiral-matrix/D/spiral-matrix-2.d Normal file
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import std.stdio;
/// 2D spiral generator
const struct Spiral {
int w, h;
int opApply(int delegate(ref int, ref int, ref int) dg) {
int idx, x, y, xy, dx = 1, dy;
int[] subLen = [w, h-1];
void turn() {
auto t = -dy;
dy = dx;
dx = t;
xy = 1 - xy;
}
void forward(int d = 1) {
x += d * dx;
y += d * dy;
idx += d;
}
Bye:
while (true) {
if (subLen[xy] == 0)
break;
foreach (_; 0 .. subLen[xy]--)
if (dg(idx, x, y))
break Bye;
else
forward();
forward(-1);
turn();
forward();
}
return 0;
}
}
int[][] spiralMatrix(int w, int h) {
auto m = new typeof(return)(h, w);
foreach (value, x, y; Spiral(w, h))
m[y][x] = value;
return m;
}
void main() {
foreach (r; spiralMatrix(9, 4))
writefln("%(%2d %)", r);
}

56
Task/Spiral-matrix/DCL/spiral-matrix.dcl Normal file
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$ p1 = f$integer( p1 )
$ max = p1 * p1
$
$ i = 0
$ r = 1
$ rd = 0
$ c = 1
$ cd = 1
$ loop:
$ a'r'_'c' = i
$ nr = r + rd
$ nc = c + cd
$ if nr .eq. 0 .or. nc .eq. 0 .or. nr .gt. p1 .or. nc .gt. p1 .or. f$type( a'nr'_'nc' ) .nes. ""
$ then
$ gosub change_directions
$ endif
$ r = r + rd
$ c = c + cd
$ i = i + 1
$ if i .lt. max then $ goto loop
$ length = f$length( f$string( max - 1 ))
$ r = 1
$ loop2:
$ c = 1
$ output = ""
$ loop3:
$ output = output + f$fao( "!#UL ", length, a'r'_'c' )
$ c = c + 1
$ if c .le. p1 then $ goto loop3
$ write sys$output output
$ r = r + 1
$ if r .le. p1 then $ goto loop2
$ exit
$
$ change_directions:
$ if rd .eq. 0 .and cd .eq. 1
$ then
$ rd = 1
$ cd = 0
$ else
$ if rd .eq. 1 .and. cd .eq. 0
$ then
$ rd = 0
$ cd = -1
$ else
$ if rd .eq. 0 .and. cd .eq. -1
$ then
$ rd = -1
$ cd = 0
$ else
$ rd = 0
$ cd = 1
$ endif
$ endif
$ endif
$ return

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Task/Spiral-matrix/Delphi/spiral-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 MakeSpiralMatrix(var Mat: TMatrix; SizeX,SizeY: integer);
{Create a spiral matrix of specified size}
var Inx: integer;
var R: TRect;
procedure DoRect(R: TRect; var Inx: integer);
{Create on turn of the spiral base on the rectangle}
var X,Y: integer;
begin
{Do top part of rectangle}
for X:=R.Left to R.Right do
begin
Mat[X,R.Top]:=Inx;
Inc(Inx);
end;
{Do Right part of rectangle}
for Y:=R.Top+1 to R.Bottom do
begin
Mat[R.Right,Y]:=Inx;
Inc(Inx);
end;
{Do bottom part of rectangle}
for X:= R.Right-1 downto R.Left do
begin
Mat[X,R.Bottom]:=Inx;
Inc(Inx);
end;
{Do left part of rectangle}
for Y:=R.Bottom-1 downto R.Top+1 do
begin
Mat[R.Left,Y]:=Inx;
Inc(Inx);
end;
end;
begin
{Set matrix size}
SetLength(Mat,SizeX,SizeY);
{create matching rectangle}
R:=Rect(0,0,SizeX-1,SizeY-1);
Inx:=0;
{draw and deflate rectangle until spiral is done}
while (R.Left<=R.Right) and (R.Top<=R.Bottom) do
begin
DoRect(R,Inx);
InflateRect(R,-1,-1);
end;
end;
procedure SpiralMatrix(Memo: TMemo);
{Display spiral matrix}
var Mat: TMatrix;
begin
Memo.Lines.Add('5x5 Matrix');
MakeSpiralMatrix(Mat,5,5);
DisplayMatrix(Memo,Mat);
Memo.Lines.Add('8x8 Matrix');
MakeSpiralMatrix(Mat,8,8);
DisplayMatrix(Memo,Mat);
Memo.Lines.Add('14x8 Matrix');
MakeSpiralMatrix(Mat,14,8);
DisplayMatrix(Memo,Mat);
end;

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Task/Spiral-matrix/E/spiral-matrix-1.e Normal file
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def spiral(size) {
def array := makeFlex2DArray(size, size)
var i := -1 # Counter of numbers to fill
var p := makeVector2(0, 0) # "Position"
var dp := makeVector2(1, 0) # "Velocity"
# If the cell we were to fill next (even after turning) is full, we're done.
while (array[p.y(), p.x()] == null) {
array[p.y(), p.x()] := (i += 1) # Fill cell
def next := p + dp # Look forward
# If the cell we were to fill next is already full, then turn clockwise.
# Gimmick: If we hit the edges of the array, by the modulo we wrap around
# and see the already-filled cell on the opposite edge.
if (array[next.y() %% size, next.x() %% size] != null) {
dp := dp.clockwise()
}
# Move forward
p += dp
}
return array
}

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Task/Spiral-matrix/E/spiral-matrix-2.e Normal file
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? print(spiral(5))
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8

19
Task/Spiral-matrix/Elixir/spiral-matrix-1.elixir Normal file
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defmodule RC do
def spiral_matrix(n) do
wide = length(to_char_list(n*n-1))
fmt = String.duplicate("~#{wide}w ", n) <> "~n"
runs = Enum.flat_map(n..1, &[&1,&1]) |> tl
delta = Stream.cycle([{0,1},{1,0},{0,-1},{-1,0}])
running(Enum.zip(runs,delta),0,-1,[])
|> Enum.with_index |> Enum.sort |> Enum.chunk(n)
|> Enum.each(fn row -> :io.format fmt, (for {_,i} <- row, do: i) end)
end
defp running([{run,{dx,dy}}|rest], x, y, track) do
new_track = Enum.reduce(1..run, track, fn i,acc -> [{x+i*dx, y+i*dy} | acc] end)
running(rest, x+run*dx, y+run*dy, new_track)
end
defp running([],_,_,track), do: track |> Enum.reverse
end
RC.spiral_matrix(5)

30
Task/Spiral-matrix/Elixir/spiral-matrix-2.elixir Normal file
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defmodule RC do
def spiral_matrix(n) do
wide = String.length(to_string(n*n-1))
fmt = String.duplicate("~#{wide}w ", n) <> "~n"
right(n,n-1,0,[]) |> Enum.reverse |> Enum.with_index |> Enum.sort |> Enum.chunk(n) |>
Enum.each(fn row ->
:io.format fmt, (for {_,i} <- row, do: i)
end)
end
def right(n, side, i, coordinates) do
down(n, side, i, Enum.reduce(0..side, coordinates, fn j,acc -> [{i, i+j} | acc] end))
end
def down(_, 0, _, coordinates), do: coordinates
def down(n, side, i, coordinates) do
left(n, side-1, i, Enum.reduce(1..side, coordinates, fn j,acc -> [{i+j, n-1-i} | acc] end))
end
def left(n, side, i, coordinates) do
up(n, side, i, Enum.reduce(side..0, coordinates, fn j,acc -> [{n-1-i, i+j} | acc] end))
end
def up(_, 0, _, coordinates), do: coordinates
def up(n, side, i, coordinates) do
right(n, side-1, i+1, Enum.reduce(side..1, coordinates, fn j,acc -> [{i+j, i} | acc] end))
end
end
RC.spiral_matrix(5)

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Task/Spiral-matrix/Elixir/spiral-matrix-3.elixir Normal file
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defmodule RC do
def spiral_matrix(n) do
fmt = String.duplicate("~#{length(to_char_list(n*n-1))}w ", n) <> "~n"
Enum.flat_map(n..1, &[&1, &1])
|> tl
|> Enum.reduce({{0,-1},{0,1},[]}, fn run,{{x,y},{dx,dy},acc} ->
side = for i <- 1..run, do: {x+i*dx, y+i*dy}
{{x+run*dx, y+run*dy}, {dy, -dx}, acc++side}
end)
|> elem(2)
|> Enum.with_index
|> Enum.sort
|> Enum.map(fn {_,i} -> i end)
|> Enum.chunk(n)
|> Enum.each(fn row -> :io.format fmt, row end)
end
end
RC.spiral_matrix(5)

29
Task/Spiral-matrix/Euphoria/spiral-matrix.euphoria Normal file
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function spiral(integer dimension)
integer side, curr, curr2
sequence s
s = repeat(repeat(0,dimension),dimension)
side = dimension
curr = 0
for i = 0 to floor(dimension/2) do
for j = 1 to side-1 do
s[i+1][i+j] = curr -- top
curr2 = curr + side-1
s[i+j][i+side] = curr2 -- right
curr2 += side-1
s[i+side][i+side-j+1] = curr2 -- bottom
curr2 += side-1
s[i+side-j+1][i+1] = curr2 -- left
curr += 1
end for
curr = curr2 + 1
side -= 2
end for
if remainder(dimension,2) then
s[floor(dimension/2)+1][floor(dimension/2)+1] = curr
end if
return s
end function
? spiral(5)

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Task/Spiral-matrix/F-Sharp/spiral-matrix.fs Normal file
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let Spiral n =
let sq = Array2D.create n n 0 // Set up an output array
let nCur = ref -1 // Current value being inserted
let NextN() = nCur := (!nCur+1) ; !nCur // Inc current value and return new value
let Frame inset = // Create the "frame" at an offset from the outside
let rangeF = [inset..(n - inset - 2)] // Range we use going forward
let rangeR = [(n - inset - 1)..(-1)..(inset + 1)] // Range we use going backward
rangeF |> Seq.iter (fun i -> sq.[inset,i] <- NextN()) // Top of frame
rangeF |> Seq.iter (fun i -> sq.[i,n-inset-1] <- NextN()) // Right side of frame
rangeR |> Seq.iter (fun i -> sq.[n-inset-1,i] <- NextN()) // Bottom of frame
rangeR |> Seq.iter (fun i -> sq.[i,inset] <- NextN()) // Left side of frame
[0..(n/2 - 1)] |> Seq.iter (fun i -> Frame i) // Fill in all frames
if n &&& 1 = 1 then sq.[n/2,n/2] <- n*n - 1 // If n is odd, fill in the last single value
sq // Return our output array

19
Task/Spiral-matrix/Factor/spiral-matrix.factor Normal file
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USING: arrays grouping io kernel math math.combinatorics
math.ranges math.statistics prettyprint sequences
sequences.repeating ;
IN: rosetta-code.spiral-matrix
: counts ( n -- seq ) 1 [a,b] 2 repeat rest ;
: vals ( n -- seq )
[ 1 swap 2dup [ neg ] bi@ 4array ] [ 2 * 1 - cycle ] bi ;
: evJKT2 ( n -- seq )
[ counts ] [ vals ] bi [ <array> ] 2map concat ;
: spiral ( n -- matrix )
[ evJKT2 cum-sum inverse-permutation ] [ group ] bi ;
: spiral-demo ( -- ) 5 9 [ spiral simple-table. nl ] bi@ ;
MAIN: spiral-demo

49
Task/Spiral-matrix/Fortran/spiral-matrix.f Normal file
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PROGRAM SPIRAL
IMPLICIT NONE
INTEGER, PARAMETER :: size = 5
INTEGER :: i, x = 0, y = 1, count = size, n = 0
INTEGER :: array(size,size)
DO i = 1, count
x = x + 1
array(x,y) = n
n = n + 1
END DO
DO
count = count - 1
DO i = 1, count
y = y + 1
array(x,y) = n
n = n + 1
END DO
DO i = 1, count
x = x - 1
array(x,y) = n
n = n + 1
END DO
IF (n > size*size-1) EXIT
count = count - 1
DO i = 1, count
y = y - 1
array(x,y) = n
n = n + 1
END DO
DO i = 1, count
x = x + 1
array(x,y) = n
n = n + 1
END DO
IF (n > size*size-1) EXIT
END DO
DO y = 1, size
DO x = 1, size
WRITE (*, "(I4)", ADVANCE="NO") array (x, y)
END DO
WRITE (*,*)
END DO
END PROGRAM SPIRAL

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Task/Spiral-matrix/FreeBASIC/spiral-matrix.basic Normal file
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' FB 1.05.0 Win64
Enum Direction
across
down
back
up
End Enum
Dim As Integer n
Do
Input "Enter size of matrix "; n
Loop Until n > 0
Dim spiral(1 To n, 1 To n) As Integer '' all zero by default
' enter the numbers 0 to (n^2 - 1) spirally in the matrix
Dim As Integer row = 1, col = 1, lowRow = 1, highRow = n, lowCol = 1, highCol = n
Dim d As Direction = across
For i As Integer = 0 To (n * n - 1)
spiral(row, col) = i
Select Case d
Case across
col += 1
If col > highCol Then
col = highCol
row += 1
d = down
End if
Case down
row += 1
If row > highRow Then
row = highRow
col -= 1
d = back
End if
Case back
col -= 1
If col < lowCol Then
col = lowCol
row -= 1
d = up
lowRow += 1
End If
Case up
row -= 1
If row < lowRow Then
row = lowRow
col += 1
d = across
highRow -= 1
lowCol += 1
highCol -= 1
End If
End Select
Next
' print spiral 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 "####"; spiral(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

47
Task/Spiral-matrix/GAP/spiral-matrix.gap Normal file
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# Spiral matrix with numbers 1 .. n<sup>2</sup>, more natural in GAP
SpiralMatrix := function(n)
local i, j, k, di, dj, p, vi, vj, imin, imax, jmin, jmax;
a := NullMat(n, n);
vi := [ 1, 0, -1, 0 ];
vj := [ 0, 1, 0, -1 ];
imin := 0;
imax := n;
jmin := 1;
jmax := n + 1;
p := 1;
di := vi[p];
dj := vj[p];
i := 1;
j := 1;
for k in [1 .. n*n] do
a[j][i] := k;
i := i + di;
j := j + dj;
if i < imin or i > imax or j < jmin or j > jmax then
i := i - di;
j := j - dj;
p := RemInt(p, 4) + 1;
di := vi[p];
dj := vj[p];
i := i + di;
j := j + dj;
if p = 1 then
imax := imax - 1;
elif p = 2 then
jmax := jmax - 1;
elif p = 3 then
imin := imin + 1;
else
jmin := jmin + 1;
fi;
fi;
od;
return a;
end;
PrintArray(SpiralMatrix(5));
# [ [ 1, 2, 3, 4, 5 ],
# [ 16, 17, 18, 19, 6 ],
# [ 15, 24, 25, 20, 7 ],
# [ 14, 23, 22, 21, 8 ],
# [ 13, 12, 11, 10, 9 ] ]

58
Task/Spiral-matrix/Go/spiral-matrix.go Normal file
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package main
import (
"fmt"
"strconv"
)
var n = 5
func main() {
if n < 1 {
return
}
top, left, bottom, right := 0, 0, n-1, n-1
sz := n * n
a := make([]int, sz)
i := 0
for left < right {
// work right, along top
for c := left; c <= right; c++ {
a[top*n+c] = i
i++
}
top++
// work down right side
for r := top; r <= bottom; r++ {
a[r*n+right] = i
i++
}
right--
if top == bottom {
break
}
// work left, along bottom
for c := right; c >= left; c-- {
a[bottom*n+c] = i
i++
}
bottom--
// work up left side
for r := bottom; r >= top; r-- {
a[r*n+left] = i
i++
}
left++
}
// center (last) element
a[top*n+left] = i
// print
w := len(strconv.Itoa(n*n - 1))
for i, e := range a {
fmt.Printf("%*d ", w, e)
if i%n == n-1 {
fmt.Println("")
}
}
}

54
Task/Spiral-matrix/Groovy/spiral-matrix-1.groovy Normal file
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enum Direction {
East([0,1]), South([1,0]), West([0,-1]), North([-1,0]);
private static _n
private final stepDelta
private bound
private Direction(delta) {
stepDelta = delta
}
public static setN(int n) {
Direction._n = n
North.bound = 0
South.bound = n-1
West.bound = 0
East.bound = n-1
}
public List move(i, j) {
def dir = this
def newIJDir = [[i,j],stepDelta].transpose().collect { it.sum() } + dir
if (((North.bound)..(South.bound)).contains(newIJDir[0])
&& ((West.bound)..(East.bound)).contains(newIJDir[1])) {
newIJDir
} else {
(++dir).move(i, j)
}
}
public Object next() {
switch (this) {
case North: West.bound++; return East;
case East: North.bound++; return South;
case South: East.bound--; return West;
case West: South.bound--; return North;
}
}
}
def spiralMatrix = { n ->
if (n < 1) return []
def M = (0..<n).collect { [0]*n }
def i = 0
def j = 0
Direction.n = n
def dir = Direction.East
(0..<(n**2)).each { k ->
M[i][j] = k
(i,j,dir) = (k < (n**2 - 1)) \
? dir.move(i,j) \
: [i,j,dir]
}
M
}

7
Task/Spiral-matrix/Groovy/spiral-matrix-2.groovy Normal file
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(1..10).each { n ->
spiralMatrix(n).each { row ->
row.each { printf "%5d", it }
println()
}
println ()
}

9
Task/Spiral-matrix/Haskell/spiral-matrix-1.hs Normal file
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import Data.List
import Control.Monad
grade xs = map snd. sort $ zip xs [0..]
values n = cycle [1,n,-1,-n]
counts n = (n:).concatMap (ap (:) return) $ [n-1,n-2..1]
reshape n = unfoldr (\xs -> if null xs then Nothing else Just (splitAt n xs))
spiral n = reshape n . grade. scanl1 (+). concat $ zipWith replicate (counts n) (values n)
displayRow = putStrLn . intercalate " " . map show
main = mapM displayRow $ spiral 5

9
Task/Spiral-matrix/Haskell/spiral-matrix-2.hs Normal file
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import Data.List
import Control.Applicative
counts = tail . reverse . concat . map (replicate 2) . enumFromTo 1
values = cycle . ((++) <$> map id <*> map negate) . (1 :) . (: [])
grade = map snd . sort . flip zip [0..]
copies = grade . scanl1 (+) . concat . map (uncurry replicate) . (zip <$> counts <*> values)
parts = (<*>) take $ (.) <$> (map . take) <*> (iterate . drop) <*> copies
disp = (>> return ()) . mapM (putStrLn . intercalate " " . map show) . parts
main = disp 5

10
Task/Spiral-matrix/Haskell/spiral-matrix-3.hs Normal file
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import Data.List (transpose)
import Text.Printf (printf)
-- spiral is the first row plus a smaller spiral rotated 90 deg
spiral 0 _ _ = [[]]
spiral h w s = [s .. s+w-1] : rot90 (spiral w (h-1) (s+w))
where rot90 = (map reverse).transpose
-- this is sort of hideous, someone may want to fix it
main = mapM_ (\row->mapM_ ((printf "%4d").toInteger) row >> putStrLn "") (spiral 10 9 1)

30
Task/Spiral-matrix/Haskell/spiral-matrix-4.hs Normal file
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import Data.List (intercalate, transpose)
---------------------- SPIRAL MATRIX ---------------------
spiral :: Int -> [[Int]]
spiral n = go n n 0
where
go rows cols x
| 0 < rows =
[x .. pred cols + x] :
fmap
reverse
(transpose $ go cols (pred rows) (x + cols))
| otherwise = [[]]
--------------------------- TEST -------------------------
main :: IO ()
main = putStrLn $ wikiTable $ spiral 5
--------------------- TABLE FORMATTING -------------------
wikiTable :: Show a => [[a]] -> String
wikiTable =
concat
. ("{| class=\"wikitable\" style=\"text-align: right;" :)
. ("width:12em;height:12em;table-layout:fixed;\"\n|-\n" :)
. return
. (<> "\n|}")
. intercalate "\n|-\n"
. fmap (('|' :) . (' ' :) . intercalate " || " . fmap show)

46
Task/Spiral-matrix/IS-BASIC/spiral-matrix.basic Normal file
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100 PROGRAM "SpiralMa.bas"
110 TEXT 80
120 INPUT PROMPT "Enter size of matrix (max. 10): ":N
130 NUMERIC A(1 TO N,1 TO N)
140 CALL INIT(A)
150 CALL WRITE(A)
160 DEF INIT(REF T)
170 LET BCOL,BROW,COL,ROW=1:LET TCOL,TROW=N:LET DIR=0
180 FOR I=0 TO N^2-1
190 LET T(COL,ROW)=I
200 SELECT CASE DIR
210 CASE 0
220 IF ROW<TROW THEN
230 LET ROW=ROW+1
240 ELSE
250 LET DIR=1:LET COL=COL+1:LET BCOL=BCOL+1
260 END IF
270 CASE 1
280 IF COL<TCOL THEN
290 LET COL=COL+1
300 ELSE
310 LET DIR=2:LET ROW=ROW-1:LET TROW=TROW-1
320 END IF
330 CASE 2
340 IF ROW>BROW THEN
350 LET ROW=ROW-1
360 ELSE
370 LET DIR=3:LET COL=COL-1:LET TCOL=TCOL-1
380 END IF
390 CASE 3
400 IF COL>BCOL THEN
410 LET COL=COL-1
420 ELSE
430 LET DIR=0:LET ROW=ROW+1:LET BROW=BROW+1
440 END IF
450 END SELECT
460 NEXT
470 END DEF
480 DEF WRITE(REF T)
490 FOR I=LBOUND(T,1) TO UBOUND(T,1)
500 FOR J=LBOUND(T,2) TO UBOUND(T,2)
510 PRINT USING " ##":T(I,J);
520 NEXT
530 PRINT
540 NEXT
550 END DEF

28
Task/Spiral-matrix/Icon/spiral-matrix.icon Normal file
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procedure main(A) # spiral matrix
N := 0 < integer(\A[1]|5) # N=1... (dfeault 5)
WriteMatrix(SpiralMatrix(N))
end
procedure WriteMatrix(M) #: write the matrix
every x := M[r := 1 to *M, c := 1 to *M[r]] do
writes(right(\x|"-", 3), if c = *M[r] then "\n" else "")
return
end
procedure SpiralMatrix(N) #: create spiral matrix
every (!(M := list(N))):= list(N) # build empty matrix NxN
# setup before starting first turn
corner := 0 # . corner we're at
i := -1 # . cell contents
r:= 1 ; c :=0 # . row & col
cincr := integer(sin(0)) # . column incr
until i > N^2 do {
rincr := cincr # row incr follows col
cincr := integer(sin(&pi/2*(corner+:=1))) # col incr at each corner
if (run := N-corner/2) = 0 then break # shorten run to 0 at U/R & L/L
every run to 1 by -1 do
M[r +:= rincr,c +:= cincr] := i +:= 1 # move, count, and fill
}
return M
end

8
Task/Spiral-matrix/J/spiral-matrix.j Normal file
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spiral =: ,~ $ [: /: }.@(2 # >:@i.@-) +/\@# <:@+: $ (, -)@(1&,)
spiral 5
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8

51
Task/Spiral-matrix/Java/spiral-matrix.java Normal file
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public class Blah {
public static void main(String[] args) {
print2dArray(getSpiralArray(5));
}
public static int[][] getSpiralArray(int dimension) {
int[][] spiralArray = new int[dimension][dimension];
int numConcentricSquares = (int) Math.ceil((dimension) / 2.0);
int j;
int sideLen = dimension;
int currNum = 0;
for (int i = 0; i < numConcentricSquares; i++) {
// do top side
for (j = 0; j < sideLen; j++) {
spiralArray[i][i + j] = currNum++;
}
// do right side
for (j = 1; j < sideLen; j++) {
spiralArray[i + j][dimension - 1 - i] = currNum++;
}
// do bottom side
for (j = sideLen - 2; j > -1; j--) {
spiralArray[dimension - 1 - i][i + j] = currNum++;
}
// do left side
for (j = sideLen - 2; j > 0; j--) {
spiralArray[i + j][i] = currNum++;
}
sideLen -= 2;
}
return spiralArray;
}
public static void print2dArray(int[][] array) {
for (int[] row : array) {
for (int elem : row) {
System.out.printf("%3d", elem);
}
System.out.println();
}
}
}

21
Task/Spiral-matrix/JavaScript/spiral-matrix-1.js Normal file
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spiralArray = function (edge) {
var arr = Array(edge),
x = 0, y = edge,
total = edge * edge--,
dx = 1, dy = 0,
i = 0, j = 0;
while (y) arr[--y] = [];
while (i < total) {
arr[y][x] = i++;
x += dx; y += dy;
if (++j == edge) {
if (dy < 0) {x++; y++; edge -= 2}
j = dx; dx = -dy; dy = j; j = 0;
}
}
return arr;
}
// T E S T:
arr = spiralArray(edge = 5);
for (y= 0; y < edge; y++) console.log(arr[y].join(" "));

67
Task/Spiral-matrix/JavaScript/spiral-matrix-2.js Normal file
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(function (n) {
// Spiral: the first row plus a smaller spiral rotated 90 degrees clockwise
function spiral(lngRows, lngCols, nStart) {
return lngRows ? [range(nStart, (nStart + lngCols) - 1)].concat(
transpose(
spiral(lngCols, lngRows - 1, nStart + lngCols)
).map(reverse)
) : [
[]
];
}
// rows and columns transposed (for 90 degree rotation)
function transpose(lst) {
return lst.length > 1 ? lst[0].map(function (_, col) {
return lst.map(function (row) {
return row[col];
});
}) : lst;
}
// elements in reverse order (for 90 degree rotation)
function reverse(lst) {
return lst.length > 1 ? lst.reduceRight(function (acc, x) {
return acc.concat(x);
}, []) : lst;
}
// [m..n]
function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
return m + i;
});
}
// TESTING
var lstSpiral = spiral(n, n, 0);
// OUTPUT FORMATTING - JSON and wikiTable
function wikiTable(lstRows, blnHeaderRow, strStyle) {
return '{| class="wikitable" ' + (
strStyle ? 'style="' + strStyle + '"' : ''
) + lstRows.map(function (lstRow, iRow) {
var strDelim = ((blnHeaderRow && !iRow) ? '!' : '|');
return '\n|-\n' + strDelim + ' ' + lstRow.map(function (v) {
return typeof v === 'undefined' ? ' ' : v;
}).join(' ' + strDelim + strDelim + ' ');
}).join('') + '\n|}';
}
return [
wikiTable(
lstSpiral,
false,
'text-align:center;width:12em;height:12em;table-layout:fixed;'
),
JSON.stringify(lstSpiral)
].join('\n\n');
})(5);

1
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[[0,1,2,3,4],[15,16,17,18,5],[14,23,24,19,6],[13,22,21,20,7],[12,11,10,9,8]]

88
Task/Spiral-matrix/JavaScript/spiral-matrix-4.js Normal file
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(() => {
"use strict";
// ------------------ SPIRAL MATRIX ------------------
// spiral :: Int -> [[Int]]
const spiral = n => {
const go = (rows, cols, start) =>
Boolean(rows) ? [
enumFromTo(start)(start + pred(cols)),
...transpose(
go(
cols,
pred(rows),
start + cols
)
).map(reverse)
] : [
[]
];
return go(n, n, 0);
};
// ---------------------- TEST -----------------------
// main :: () -> String
const main = () => {
const
n = 5,
cellWidth = 1 + `${pred(n ** 2)}`.length;
return unlines(
spiral(n).map(
row => (
row.map(x => `${x}`
.padStart(cellWidth, " "))
)
.join("")
)
);
};
// --------------------- GENERIC ---------------------
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m =>
n => Array.from({
length: 1 + n - m
}, (_, i) => m + i);
// pred :: Enum a => a -> a
const pred = x => x - 1;
// reverse :: [a] -> [a]
const reverse = xs =>
"string" === typeof xs ? (
xs.split("").reverse()
.join("")
) : xs.slice(0).reverse();
// transpose :: [[a]] -> [[a]]
const transpose = rows =>
// The columns of the input transposed
// into new rows.
// Simpler version of transpose, assuming input
// rows of even length.
Boolean(rows.length) ? rows[0].map(
(_, i) => rows.flatMap(
v => v[i]
)
) : [];
// unlines :: [String] -> String
const unlines = xs =>
// A single string formed by the intercalation
// of a list of strings with the newline character.
xs.join("\n");
// MAIN ---
return main();
})();

26
Task/Spiral-matrix/Jq/spiral-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" ) ;
def right:
if . == [1, 0] then [ 0, -1]
elif . == [0, -1] then [-1, 0]
elif . == [-1, 0] then [ 0, 1]
elif . == [0, 1] then [ 1, 0]
else error("invalid direction: \(.)")
end;

14
Task/Spiral-matrix/Jq/spiral-matrix-2.jq Normal file
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def spiral(n):
# we just placed m at i,j, and we are moving in the direction d
def _next(i; j; m; d):
if m == (n*n) - 1 then .
elif .[i+d[0]][j+d[1]] == false
then .[i+d[0]][j+d[1]] = m+1 | _next(i+d[0]; j+d[1]; m+1; d)
else (d|right) as $d
| .[i+$d[0]][j+$d[1]] = m+1 | _next(i+$d[0]; j+$d[1]; m+1; $d)
end;
matrix(n;n;false) | .[0][0] = 0 | _next(0;0;0; [0,1]) ;
# Example
spiral(5) | neatly(3)

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Task/Spiral-matrix/Julia/spiral-matrix-1.julia Normal file
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immutable Spiral
m::Int
n::Int
cmax::Int
dir::Array{Array{Int,1},1}
bdelta::Array{Array{Int,1},1}
end
function Spiral(m::Int, n::Int)
cmax = m*n
dir = Array{Int,1}[[0,1], [1,0], [0,-1], [-1,0]]
bdelta = Array{Int,1}[[0,0,0,1], [-1,0,0,0],
[0,-1,0,0], [0,0,1,0]]
Spiral(m, n, cmax, dir, bdelta)
end
function spiral(m::Int, n::Int)
0<m&&0<n || error("The matrix dimensions must be positive.")
Spiral(m, n)
end
spiral(n::Int) = spiral(n, n)
type SpState
cnt::Int
dirdex::Int
cell::Array{Int,1}
bounds::Array{Int,1}
end
Base.length(sp::Spiral) = sp.cmax
Base.start(sp::Spiral) = SpState(1, 1, [1,1], [sp.n,sp.m,1,1])
Base.done(sp::Spiral, sps::SpState) = sps.cnt > sp.cmax
function Base.next(sp::Spiral, sps::SpState)
s = sub2ind((sp.m, sp.n), sps.cell[1], sps.cell[2])
if sps.cell[rem1(sps.dirdex+1, 2)] == sps.bounds[sps.dirdex]
sps.bounds += sp.bdelta[sps.dirdex]
sps.dirdex = rem1(sps.dirdex+1, 4)
end
sps.cell += sp.dir[sps.dirdex]
sps.cnt += 1
return (s, sps)
end

24
Task/Spiral-matrix/Julia/spiral-matrix-2.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/Spiral-matrix/Julia/spiral-matrix-3.julia Normal file
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n = 5
println("The n = ", n, " spiral matrix:")
a = zeros(Int, (n, n))
for (i, s) in enumerate(spiral(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(spiral(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(spiral(n))
a[s] = p[i]
end
println(pretty(a))

40
Task/Spiral-matrix/Kotlin/spiral-matrix.kotlin Normal file
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// version 1.1.3
typealias Vector = IntArray
typealias Matrix = Array<Vector>
fun spiralMatrix(n: Int): Matrix {
val result = Matrix(n) { Vector(n) }
var pos = 0
var count = n
var value = -n
var sum = -1
do {
value = -value / n
for (i in 0 until count) {
sum += value
result[sum / n][sum % n] = pos++
}
value *= n
count--
for (i in 0 until count) {
sum += value
result[sum / n][sum % n] = pos++
}
}
while (count > 0)
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(spiralMatrix(5))
printMatrix(spiralMatrix(10))
}

76
Task/Spiral-matrix/Liberty-BASIC/spiral-matrix.basic Normal file
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nomainwin
UpperLeftX = 50
UpperLeftY = 50
WindowWidth =900
WindowHeight =930
statictext #w.st, "", 10, 850, 870, 40
open "Spiral matrix" for graphics_nsb_nf as #w
#w "trapclose [quit]"
#w "backcolor darkblue; color cyan; fill darkblue"
for N =2 to 50
#w.st "!font courier_new "; int( 60 /N); " bold"
#w "down; font arial "; int( 240 /N); " bold"
g$ ="ruld" ' direction sequence
if N/2 =int( N/2) then pg =2 else pg =0 ' pointer to current direction
' last move is left or right depending on N even/odd
d$ =""
for i =1 to N -1 ' calculate direction to move
d$ =nChar$( i, mid$( g$, pg +1, 1)) +d$
pg =( pg +1) mod 4
d$ =nChar$( i, mid$( g$, pg +1, 1)) +d$
pg =( pg +1) mod 4
next i
d$ =nChar$( N -1, "r") +d$ ' first row
#w.st " N ="; N; " "; d$
xp =60 +250 /N
yp =80 +250 /N
stp =int( 750 /N)
for i =0 to N^2 -1
dir$ =mid$( d$, i, 1)
select case dir$
case "r"
xp =xp +stp
case "d"
yp =yp +stp
case "l"
xp =xp -stp
case "u"
yp =yp -stp
end select
#w "place "; xp; " "; yp
#w "\"; i
next i
timer 3000, [on]
wait
[on]
timer 0
#w "cls"
scan
next N
wait
function nChar$( n, i$)
for i =1 to n
nChar$ =nChar$ +i$
next i
end function
[quit]
close #w
end

19
Task/Spiral-matrix/Lua/spiral-matrix-1.lua Normal file
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av, sn = math.abs, function(s) return s~=0 and s/av(s) or 0 end
function sindex(y, x) -- returns the value at (x, y) in a spiral that starts at 1 and goes outwards
if y == -x and y >= x then return (2*y+1)^2 end
local l = math.max(av(y), av(x))
return (2*l-1)^2+4*l+2*l*sn(x+y)+sn(y^2-x^2)*(l-(av(y)==l and sn(y)*x or sn(x)*y)) -- OH GOD WHAT
end
function spiralt(side)
local ret, start, stop = {}, math.floor((-side+1)/2), math.floor((side-1)/2)
for i = 1, side do
ret[i] = {}
for j = 1, side do
ret[i][j] = side^2 - sindex(stop - i + 1,start + j - 1) --moves the coordinates so (0,0) is at the center of the spiral
end
end
return ret
end
for i,v in ipairs(spiralt(8)) do for j, u in ipairs(v) do io.write(u .. " ") end print() end

13
Task/Spiral-matrix/Lua/spiral-matrix-2.lua Normal file
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local function printspiral(n)
local function z(x,y)
local m = math.min(x, y, n-1-x, n-1-y)
return x<y and (n-2*m-2)^2+(x-m)+(y-m) or (n-2*m)^2-(x-m)-(y-m)
end
for y = 1, n do
for x = 1, n do
io.write(string.format("%2d ", n^2-z(x-1,y-1)))
end
print()
end
end
printspiral(9)

19
Task/Spiral-matrix/Lua/spiral-matrix-3.lua Normal file
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local function makespiral(n)
local t, z = {}, function(x,y)
local m = math.min(x, y, n-1-x, n-1-y)
return x<y and (n-2*m-2)^2+(x-m)+(y-m) or (n-2*m)^2-(x-m)-(y-m)
end
for y = 1, n do t[y] = {}
for x = 1, n do t[y][x] = n^2-z(x-1,y-1) end
end
return t
end
local function printspiral(t)
for y = 1, #t do
for x = 1, #t[y] do
io.write(string.format("%2d ", t[y][x]))
end
print()
end
end
printspiral(makespiral(9))

11
Task/Spiral-matrix/MATLAB/spiral-matrix-1.m Normal file
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function matrix = reverseSpiral(n)
matrix = (-spiral(n))+n^2;
if mod(n,2)==0
matrix = flipud(matrix);
else
matrix = fliplr(matrix);
end
end %reverseSpiral

9
Task/Spiral-matrix/MATLAB/spiral-matrix-2.m Normal file
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>> reverseSpiral(5)
ans =
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8

26
Task/Spiral-matrix/Maple/spiral-matrix.maple Normal file
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with(ArrayTools):
spiralArray := proc(size::integer)
local M, sideLength, count, i, j:
M := Matrix(size):
count := 0:
sideLength := size:
for i from 1 to ceil(sideLength / 2) do
for j from 1 to sideLength do
M[i,i + j - 1] := count++:
end:
for j from 1 to sideLength - 1 do
M[i + j, sideLength + i - 1] := count++:
end:
for j from 1 to sideLength - 1 do
M[i + sideLength - 1, sideLength - j + i - 1] := count++:
end:
for j from 1 to sideLength - 2 do
M[sideLength + i - j - 1, i] := count++
end:
sideLength -= 2:
end:
return M;
end proc:
spiralArray(5);

16
Task/Spiral-matrix/Mathematica/spiral-matrix-1.math Normal file
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AddSquareRing[x_List/;Equal@@Dimensions[x] && Length[Dimensions[x]]==2]:=Module[{new=x,size,smallest},
size=Length[x];
smallest=x[[1,1]];
Do[
new[[i]]=Prepend[new[[i]],smallest-i];
new[[i]]=Append[new[[i]],smallest-3 size+i-3]
,{i,size}];
PrependTo[new,Range[smallest-3size-3-size-1,smallest-3size-3]];
AppendTo[new,Range[smallest-size-1,smallest-size-size-2,-1]];
new
]
MakeSquareSpiral[size_Integer/;size>0]:=Module[{largest,start,times},
start=size^2+If[Mod[size,2]==0,{{-4,-3},{-1,-2}},{{-1}}];
times=If[Mod[size,2]==0,size/2-1,(size-1)/2];
Nest[AddSquareRing,start,times]
]

2
Task/Spiral-matrix/Mathematica/spiral-matrix-2.math Normal file
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MakeSquareSpiral[2] // MatrixForm
MakeSquareSpiral[7] // MatrixForm

40
Task/Spiral-matrix/Maxima/spiral-matrix.maxima Normal file
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spiral(n) := block([a, i, j, k, p, di, dj, vi, vj, imin, imax, jmin, jmax],
a: zeromatrix(n, n),
vi: [1, 0, -1, 0],
vj: [0, 1, 0, -1],
imin: 0,
imax: n,
jmin: 1,
jmax: n + 1,
p: 1,
di: vi[p],
dj: vj[p],
i: 1,
j: 1,
for k from 1 thru n*n do (
a[j, i]: k,
i: i + di,
j: j + dj,
if i < imin or i > imax or j < jmin or j > jmax then (
i: i - di,
j: j - dj,
p: mod(p, 4) + 1,
di: vi[p],
dj: vj[p],
i: i + di,
j: j + dj,
if p = 1 then imax: imax - 1
elseif p = 2 then jmax: jmax - 1
elseif p = 3 then imin: imin + 1
else jmin: jmin + 1
)
),
a
)$
spiral(5);
/* matrix([ 1, 2, 3, 4, 5],
[16, 17, 18, 19, 6],
[15, 24, 25, 20, 7],
[14, 23, 22, 21, 8],
[13, 12, 11, 10, 9]) */

8
Task/Spiral-matrix/MiniZinc/spiral-matrix.minizinc Normal file
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%Spiral Matrix. Nigel Galloway, February 3rd., 2020
int: Size;
array [1..Size,1..Size] of var 1..Size*Size: spiral;
constraint spiral[1,1..]=1..Size;
constraint forall(n in 2..(Size+1) div 2)(forall(g in n..Size+1-n)(spiral[n,g]=spiral[n,g-1]+1));
constraint forall(n in 1..(Size+1) div 2)(forall(g in n+1..Size+1-n)(spiral[g,Size-n+1]=spiral[g-1,Size-n+1]+1));
constraint forall(n in 1..Size div 2)(forall(g in n..Size-n)(spiral[Size-n+1,g]=spiral[Size-n+1,g+1]+1)) /\ forall(n in 1..Size div 2)(forall(g in n+1..Size-n)(spiral[g,n]=spiral[g+1,n]+1));
output [show2d(spiral)];

91
Task/Spiral-matrix/NetRexx/spiral-matrix.netrexx Normal file
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/* NetRexx */
options replace format comments java crossref symbols binary
parse arg size .
if \size.datatype('W') then do
printArray(generateArray(3))
say
printArray(generateArray(4))
say
printArray(generateArray(5))
say
end
else do
printArray(generateArray(size))
say
end
return
-- -----------------------------------------------------------------------------
method generateArray(dimension = int) private static returns int[,]
-- the output array
array = int[dimension, dimension]
-- get the number of squares, including the center one if
-- the dimension is odd
squares = dimension % 2 + dimension // 2
-- length of a side for the current square
sidelength = dimension
current = 0
loop i_ = 0 to squares - 1
-- do each side of the current square
-- top side
loop j_ = 0 to sidelength - 1
array[i_, i_ + j_] = current
current = current + 1
end j_
-- down the right side
loop j_ = 1 to sidelength - 1
array[i_ + j_, dimension - 1 - i_] = current
current = current + 1
end j_
-- across the bottom
loop j_ = sidelength - 2 to 0 by -1
array[dimension - 1 - i_, i_ + j_] = current
current = current + 1
end j_
-- and up the left side
loop j_ = sidelength - 2 to 1 by -1
array[i_ + j_, i_] = current
current = current + 1
end j_
-- reduce the length of the side by two rows
sidelength = sidelength - 2
end i_
return array
-- -----------------------------------------------------------------------------
method printArray(array = int[,]) private static
dimension = array[1].length
rl = formatSize(array)
loop i_ = 0 to dimension - 1
line = Rexx("|")
loop j_ = 0 to dimension - 1
line = line Rexx(array[i_, j_]).right(rl)
end j_
line = line "|"
say line
end i_
return
-- -----------------------------------------------------------------------------
method formatSize(array = int[,]) private static returns Rexx
dim = array[1].length
maxNum = Rexx(dim * dim - 1).length()
return maxNum

27
Task/Spiral-matrix/Nim/spiral-matrix.nim Normal file
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import sequtils, strutils
proc `$`(m: seq[seq[int]]): string =
for r in m:
let lg = result.len
for c in r:
result.addSep(" ", lg)
result.add align($c, 2)
result.add '\n'
proc spiral(n: Positive): seq[seq[int]] =
result = newSeqWith(n, repeat(-1, n))
var dx = 1
var dy, x, y = 0
for i in 0 ..< (n * n):
result[y][x] = i
let (nx, ny) = (x+dx, y+dy)
if nx in 0 ..< n and ny in 0 ..< n and result[ny][nx] == -1:
x = nx
y = ny
else:
swap dx, dy
dx = -dx
x += dx
y += dy
echo spiral(5)

39
Task/Spiral-matrix/OCaml/spiral-matrix-1.ocaml Normal file
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let next_dir = function
| 1, 0 -> 0, -1
| 0, 1 -> 1, 0
| -1, 0 -> 0, 1
| 0, -1 -> -1, 0
| _ -> assert false
let next_pos ~pos:(x,y) ~dir:(nx,ny) = (x+nx, y+ny)
let next_cell ar ~pos:(x,y) ~dir:(nx,ny) =
try ar.(x+nx).(y+ny)
with _ -> -2
let for_loop n init fn =
let rec aux i v =
if i < n then aux (i+1) (fn i v)
in
aux 0 init
let spiral ~n =
let ar = Array.make_matrix n n (-1) in
let pos = 0, 0 in
let dir = 0, 1 in
let set (x, y) i = ar.(x).(y) <- i in
let step (pos, dir) =
match next_cell ar pos dir with
| -1 -> (next_pos pos dir, dir)
| _ -> let dir = next_dir dir in (next_pos pos dir, dir)
in
for_loop (n*n) (pos, dir)
(fun i (pos, dir) -> set pos i; step (pos, dir));
(ar)
let print =
Array.iter (fun line ->
Array.iter (Printf.printf " %2d") line;
print_newline())
let () = print(spiral 5)

17
Task/Spiral-matrix/OCaml/spiral-matrix-2.ocaml Normal file
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let spiral n =
let ar = Array.make_matrix n n (-1) in
let out i = i < 0 || i >= n in
let too_far (x,y) = out x || out y || ar.(x).(y) >= 0 in
let step x y (dx,dy) = (x+dx,y+dy) in
let turn (i,j) = (j,-i) in
let rec iter (x,y) d i =
ar.(x).(y) <- i;
if i < n*n-1 then
let d' = if too_far (step x y d) then turn d else d in
iter (step x y d') d' (i+1) in
(iter (0,0) (0,1) 0; ar)
let show =
Array.iter (fun v -> Array.iter (Printf.printf " %2d") v; print_newline())
let _ = show (spiral 5)

21
Task/Spiral-matrix/Octave/spiral-matrix.octave Normal file
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function a = spiral(n)
a = ones(n*n, 1);
u = -(i = n) * (v = ones(n, 1));
for k = n-1:-1:1
j = 1:k;
a(j+i) = u(j) = -u(j);
a(j+(i+k)) = v(j) = -v(j);
i += 2*k;
endfor
a(cumsum(a)) = 1:n*n;
a = reshape(a, n, n)'-1;
endfunction
>> spiral(5)
ans =
0 1 2 3 4
15 16 17 18 5
14 23 24 19 6
13 22 21 20 7
12 11 10 9 8

55
Task/Spiral-matrix/OoRexx/spiral-matrix.rexx Normal file
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call printArray generateArray(3)
say
call printArray generateArray(4)
say
call printArray generateArray(5)
::routine generateArray
use arg dimension
-- the output array
array = .array~new(dimension, dimension)
-- get the number of squares, including the center one if
-- the dimension is odd
squares = dimension % 2 + dimension // 2
-- length of a side for the current square
sidelength = dimension
current = 0
loop i = 1 to squares
-- do each side of the current square
-- top side
loop j = 0 to sidelength - 1
array[i, i + j] = current
current += 1
end
-- down the right side
loop j = 1 to sidelength - 1
array[i + j, dimension - i + 1] = current
current += 1
end
-- across the bottom
loop j = sidelength - 2 to 0 by -1
array[dimension - i + 1, i + j] = current
current += 1
end
-- and up the left side
loop j = sidelength - 2 to 1 by -1
array[i + j, i] = current
current += 1
end
-- reduce the length of the side by two rows
sidelength -= 2
end
return array
::routine printArray
use arg array
dimension = array~dimension(1)
loop i = 1 to dimension
line = "|"
loop j = 1 to dimension
line = line array[i, j]~right(2)
end
line = line "|"
say line
end

42
Task/Spiral-matrix/Oz/spiral-matrix.oz Normal file
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declare
fun {Spiral N}
%% create nested array
Arr = {Array.new 1 N unit}
for Y in 1..N do Arr.Y := {Array.new 1 N 0} end
%% fill it recursively with increasing numbers
C = {Counter 0}
in
{Fill Arr 1 N C}
Arr
end
proc {Fill Arr S E C}
%% go right
for X in S..E do
Arr.S.X := {C}
end
%% go down
for Y in S+1..E do
Arr.Y.E := {C}
end
%% go left
for X in E-1..S;~1 do
Arr.E.X := {C}
end
%% go up
for Y in E-1..S+1;~1 do
Arr.Y.S := {C}
end
%% fill the inner rectangle
if E - S > 1 then {Fill Arr S+1 E-1 C} end
end
fun {Counter N}
C = {NewCell N}
in
fun {$}
C := @C + 1
end
end
in
{Inspect {Spiral 5}}

9
Task/Spiral-matrix/PARI-GP/spiral-matrix.parigp Normal file
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spiral(dim) = {
my (M = matrix(dim, dim), p = s = 1, q = i = 0);
for (n=1, dim,
for (b=1, dim-n+1, M[p,q+=s] = i; i++);
for (b=1, dim-n, M[p+=s,q] = i; i++);
s = -s;
);
M
}

55
Task/Spiral-matrix/PL-I/spiral-matrix.pli Normal file
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/* Generates a square matrix containing the integers from 0 to N**2-1, */
/* where N is the length of one side of the square. */
/* Written 22 February 2010. */
declare n fixed binary;
put skip list ('Please type the size of the square:');
get list (n);
begin;
declare A(n,n) fixed binary;
declare (i, j, iinc, jinc, q) fixed binary;
A = -1;
i, j = 1; iinc = 0; jinc = 1;
do q = 0 to n**2-1;
if a(i,j) < 0 then
a(i,j) = q;
else
do;
/* back up */
j = j -jinc; i = i - iinc;
/* change direction */
if iinc = 0 & jinc = 1 then do; iinc = 1; jinc = 0; end;
else if iinc = 1 & jinc = 0 then do; iinc = 0; jinc = -1; end;
else if iinc = 0 & jinc = -1 then do; iinc = -1; jinc = 0; end;
else if iinc = -1 & jinc = 0 then do; iinc = 0; jinc = 1; end;
/* Take one step in the new direction */
i = i + iinc; j = j + jinc;
a(i,j) = q;
end;
if i+iinc > n | i+iinc < 1 then
do;
iinc = 0; jinc = 1;
if j+1 > n then jinc = -1; else if j-1 < 1 then jinc = 1;
if a(i+iinc,j+jinc) >= 0 then jinc = -jinc;
/* j = j + jinc; /* to move on from the present (filled) position */
end;
else i = i + iinc;
if j+jinc > n | j+jinc < 1 then
do;
jinc = 0; iinc = 1;
if i+1 > n then iinc = -1; else if i-1 < 1 then iinc = 1;
if a(i+iinc,j+jinc) >= 0 then iinc = -iinc;
i = i + iinc; /* to move on from the present (filled) position */
end;
else j = j + jinc;
end;
/* Display the square. */
do i = 1 to n;
put skip edit (A(i,*)) (F(4));
end;
end;

70
Task/Spiral-matrix/Pascal/spiral-matrix.pas Normal file
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program Spiralmat;
type
tDir = (left,down,right,up);
tdxy = record
dx,dy: longint;
end;
tdeltaDir = array[tDir] of tdxy;
const
Nextdir : array[tDir] of tDir = (down,right,up,left);
cDir : tDeltaDir = ((dx:1;dy:0),(dx:0;dy:1),(dx:-1;dy:0),(dx:0;dy:-1));
cMaxN = 32;
type
tSpiral = array[0..cMaxN,0..cMaxN] of LongInt;
function FillSpiral(n:longint):tSpiral;
var
b,i,k, dn,x,y : longInt;
dir : tDir;
tmpSp : tSpiral;
BEGIN
b := 0;
x := 0;
y := 0;
//only for the first line
k := -1;
dn := n-1;
tmpSp[x,y] := b;
dir := left;
repeat
i := 0;
while i < dn do
begin
inc(b);
tmpSp[x,y] := b;
inc(x,cDir[dir].dx);
inc(y,cDir[dir].dy);
inc(i);
end;
Dir:= NextDir[dir];
inc(k);
IF k > 1 then
begin
k := 0;
//shorten the line every second direction change
dn := dn-1;
if dn <= 0 then
BREAK;
end;
until false;
//the last
tmpSp[x,y] := b+1;
FillSpiral := tmpSp;
end;
var
a : tSpiral;
x,y,n : LongInt;
BEGIN
For n := 1 to 5{cMaxN} do
begin
A:=FillSpiral(n);
For y := 0 to n-1 do
begin
For x := 0 to n-1 do
write(A[x,y]:4);
writeln;
end;
writeln;
end;
END.

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Task/Spiral-matrix/Perl/spiral-matrix.pl Normal file
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sub spiral
{my ($n, $x, $y, $dx, $dy, @a) = (shift, 0, 0, 1, 0);
foreach (0 .. $n**2 - 1)
{$a[$y][$x] = $_;
my ($nx, $ny) = ($x + $dx, $y + $dy);
($dx, $dy) =
$dx == 1 && ($nx == $n || defined $a[$ny][$nx])
? ( 0, 1)
: $dy == 1 && ($ny == $n || defined $a[$ny][$nx])
? (-1, 0)
: $dx == -1 && ($nx < 0 || defined $a[$ny][$nx])
? ( 0, -1)
: $dy == -1 && ($ny < 0 || defined $a[$ny][$nx])
? ( 1, 0)
: ($dx, $dy);
($x, $y) = ($x + $dx, $y + $dy);}
return @a;}
foreach (spiral 5)
{printf "%3d", $_ foreach @$_;
print "\n";}

19
Task/Spiral-matrix/Phix/spiral-matrix.phix Normal file
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(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">counter</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">len</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dy</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%%%dd"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)))</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"??"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span><span style="color: #000000;">n</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: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">n</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- 2n runs..</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">len</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- of a length...</span>
<span style="color: #000000;">x</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">dx</span>
<span style="color: #000000;">y</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">dy</span>
<span style="color: #000000;">m</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">y</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">counter</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">counter</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">len</span> <span style="color: #0000FF;">-=</span> <span style="color: #7060A8;">odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- ..-1 every other </span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dy</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">dy</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">}</span> <span style="color: #000080;font-style:italic;">-- in new direction</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)})</span>
<!--

19
Task/Spiral-matrix/PicoLisp/spiral-matrix.l Normal file
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(load "@lib/simul.l")
(de spiral (N)
(prog1 (grid N N)
(let (Dir '(north east south west .) This 'a1)
(for Val (* N N)
(=: val Val)
(setq This
(or
(with ((car Dir) This)
(unless (: val) This) )
(with ((car (setq Dir (cdr Dir))) This)
(unless (: val) This) ) ) ) ) ) ) )
(mapc
'((L)
(for This L (prin (align 3 (: val))))
(prinl) )
(spiral 5) )

36
Task/Spiral-matrix/PowerShell/spiral-matrix.psh Normal file
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function Spiral-Matrix ( [int]$N )
{
# Initialize variables
$X = 0
$Y = -1
$i = 0
$Sign = 1
# Intialize array
$A = New-Object 'int[,]' $N, $N
# Set top row
1..$N | ForEach { $Y += $Sign; $A[$X,$Y] = ++$i }
# For each remaining half spiral...
ForEach ( $M in ($N-1)..1 )
{
# Set the vertical quarter spiral
1..$M | ForEach { $X += $Sign; $A[$X,$Y] = ++$i }
# Curve the spiral
$Sign = -$Sign
# Set the horizontal quarter spiral
1..$M | ForEach { $Y += $Sign; $A[$X,$Y] = ++$i }
}
# Convert the array to text output
$Spiral = ForEach ( $X in 1..$N ) { ( 1..$N | ForEach { $A[($X-1),($_-1)] } ) -join "`t" }
return $Spiral
}
Spiral-Matrix 5
""
Spiral-Matrix 7

51
Task/Spiral-matrix/Prolog/spiral-matrix.pro Normal file
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% Prolog implementation: SWI-Prolog 7.2.3
replace([_|T], 0, E, [E|T]) :- !.
replace([H|T], N, E, Xs) :-
succ(N1, N), replace(T, N1, E, Xs1), Xs = [H|Xs1].
% True if Xs is the Original grid with the element at (X, Y) replaces by E.
replace_in([H|T], (0, Y), E, Xs) :- replace(H, Y, E, NH), Xs = [NH|T], !.
replace_in([H|T], (X, Y), E, Xs) :-
succ(X1, X), replace_in(T, (X1, Y), E, Xs1), Xs = [H|Xs1].
% True, if E is the value at (X, Y) in Xs
get_in(Xs, (X, Y), E) :- nth0(X, Xs, L), nth0(Y, L, E).
create(N, Mx) :- % NxN grid full of nils
numlist(1, N, Ns),
findall(X, (member(_, Ns), X = nil), Ls),
findall(X, (member(_, Ns), X = Ls), Mx).
% Depending of the direction, returns two possible coordinates and directions
% (C,D) that will be used in case of a turn, and (A,B) otherwise.
ops(right, (X,Y), (A,B), (C,D), D1, D2) :-
A is X, B is Y+1, D1 = right, C is X+1, D is Y, D2 = down.
ops(left, (X,Y), (A,B), (C,D), D1, D2) :-
A is X, B is Y-1, D1 = left, C is X-1, D is Y, D2 = up.
ops(up, (X,Y), (A,B), (C,D), D1, D2) :-
A is X-1, B is Y, D1 = up, C is X, D is Y+1, D2 = right.
ops(down, (X,Y), (A,B), (C,D), D1, D2) :-
A is X+1, B is Y, D1 = down, C is X, D is Y-1, D2 = left.
% True if NCoor is the right coor in spiral shape. Returns a new direction also.
next(Dir, Mx, Coor, NCoor, NDir) :-
ops(Dir, Coor, C1, C2, D1, D2),
(get_in(Mx, C1, nil) -> NCoor = C1, NDir = D1
; NCoor = C2, NDir = D2).
% Returns an spiral with [H|Vs] elements called R, only work if the length of
% [H|Vs], is the square of the size of the grid.
spiralH(Dir, Mx, Coor, [H|Vs], R) :-
replace_in(Mx, Coor, H, NMx),
(Vs = [] -> R = NMx
; next(Dir, Mx, Coor, NCoor, NDir),
spiralH(NDir, NMx, NCoor, Vs, R)).
% True if Mx is the grid in spiral shape of the numbers from 0 to N*N-1.
spiral(N, Mx) :-
Sq is N*N-1, numlist(0, Sq, Ns),
create(N, EMx), spiralH(right, EMx, (0,0), Ns, Mx).

57
Task/Spiral-matrix/PureBasic/spiral-matrix.basic Normal file
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Procedure spiralMatrix(size = 1)
Protected i, x = -1, y, count = size, n
Dim a(size - 1,size - 1)
For i = 1 To count
x + 1
a(x,y) = n
n + 1
Next
Repeat
count - 1
For i = 1 To count
y + 1
a(x,y) = n
n + 1
Next
For i = 1 To count
x - 1
a(x,y) = n
n + 1
Next
count - 1
For i = 1 To count
y - 1
a(x,y) = n
n + 1
Next
For i = 1 To count
x + 1
a(x,y) = n
n + 1
Next
Until count < 1
PrintN("Spiral: " + Str(Size) + #CRLF$)
Protected colWidth = Len(Str(size * size - 1)) + 1
For y = 0 To size - 1
For x = 0 To size - 1
Print("" + LSet(Str(a(x, y)), colWidth, " ") + "")
Next
PrintN("")
Next
PrintN("")
EndProcedure
If OpenConsole()
spiralMatrix(2)
PrintN("")
spiralMatrix(5)
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
Input()
CloseConsole()
EndIf

22
Task/Spiral-matrix/Python/spiral-matrix-1.py Normal file
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def spiral(n):
dx,dy = 1,0 # Starting increments
x,y = 0,0 # Starting location
myarray = [[None]* n for j in range(n)]
for i in xrange(n**2):
myarray[x][y] = i
nx,ny = x+dx, y+dy
if 0<=nx<n and 0<=ny<n and myarray[nx][ny] == None:
x,y = nx,ny
else:
dx,dy = -dy,dx
x,y = x+dx, y+dy
return myarray
def printspiral(myarray):
n = range(len(myarray))
for y in n:
for x in n:
print "%2i" % myarray[x][y],
print
printspiral(spiral(5))

23
Task/Spiral-matrix/Python/spiral-matrix-2.py Normal file
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def spiral(n):
def spiral_part(x, y, n):
if x == -1 and y == 0:
return -1
if y == (x+1) and x < (n // 2):
return spiral_part(x-1, y-1, n-1) + 4*(n-y)
if x < (n-y) and y <= x:
return spiral_part(y-1, y, n) + (x-y) + 1
if x >= (n-y) and y <= x:
return spiral_part(x, y-1, n) + 1
if x >= (n-y) and y > x:
return spiral_part(x+1, y, n) + 1
if x < (n-y) and y > x:
return spiral_part(x, y-1, n) - 1
array = [[0] * n for j in xrange(n)]
for x in xrange(n):
for y in xrange(n):
array[x][y] = spiral_part(y, x, n)
return array
for row in spiral(5):
print " ".join("%2s" % x for x in row)

18
Task/Spiral-matrix/Python/spiral-matrix-3.py Normal file
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def rot_right(a):
return zip(*a[::-1])
def sp(m, n, start = 0):
""" Generate number range spiral of dimensions m x n
"""
if n == 0:
yield ()
else:
yield tuple(range(start, m + start))
for row in rot_right(list(sp(n - 1, m, m + start))):
yield row
def spiral(m):
return sp(m, m)
for row in spiral(5):
print(''.join('%3i' % i for i in row))

16
Task/Spiral-matrix/Python/spiral-matrix-4.py Normal file
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def spiral(n):
dat = [[None] * n for i in range(n)]
le = [[i + 1, i + 1] for i in reversed(range(n))]
le = sum(le, [])[1:] # for n = 5 le will be [5, 4, 4, 3, 3, 2, 2, 1, 1]
dxdy = [[1, 0], [0, 1], [-1, 0], [0, -1]] * ((len(le) + 4) / 4) # long enough
x, y, val = -1, 0, -1
for steps, (dx, dy) in zip(le, dxdy):
x, y, val = x + dx, y + dy, val + 1
for j in range(steps):
dat[y][x] = val
if j != steps-1:
x, y, val = x + dx, y + dy, val + 1
return dat
for row in spiral(5): # calc spiral and print it
print ' '.join('%3s' % x for x in row)

19
Task/Spiral-matrix/Python/spiral-matrix-5.py Normal file
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import itertools
concat = itertools.chain.from_iterable
def partial_sums(items):
s = 0
for x in items:
s += x
yield s
grade = lambda xs: sorted(range(len(xs)), key=xs.__getitem__)
values = lambda n: itertools.cycle([1,n,-1,-n])
counts = lambda n: concat([i,i-1] for i in range(n,0,-1))
reshape = lambda n, xs: zip(*([iter(xs)] * n))
spiral = lambda n: reshape(n, grade(list(partial_sums(concat(
[v]*c for c,v in zip(counts(n), values(n)))))))
for row in spiral(5):
print(' '.join('%3s' % x for x in row))

43
Task/Spiral-matrix/Python/spiral-matrix-6.py Normal file
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'''Spiral Matrix'''
# spiral :: Int -> [[Int]]
def spiral(n):
'''The rows of a spiral matrix of order N.
'''
def go(rows, cols, x):
return [range(x, x + cols)] + [
reversed(x) for x
in zip(*go(cols, rows - 1, x + cols))
] if 0 < rows else [[]]
return go(n, n, 0)
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Spiral matrix of order 5, in wiki table markup.
'''
print(
wikiTable(spiral(5))
)
# ---------------------- FORMATTING ----------------------
# wikiTable :: [[a]] -> String
def wikiTable(rows):
'''Wiki markup for a no-frills tabulation of rows.'''
return '{| class="wikitable" style="' + (
'width:12em;height:12em;table-layout:fixed;"|-\n'
) + '\n|-\n'.join(
'| ' + ' || '.join(
str(cell) for cell in row
)
for row in rows
) + '\n|}'
# MAIN ---
if __name__ == '__main__':
main()

12
Task/Spiral-matrix/Python/spiral-matrix-7.py Normal file
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def spiral_matrix(n):
m = [[0] * n for i in range(n)]
dx, dy = [0, 1, 0, -1], [1, 0, -1, 0]
x, y, c = 0, -1, 1
for i in range(n + n - 1):
for j in range((n + n - i) // 2):
x += dx[i % 4]
y += dy[i % 4]
m[x][y] = c
c += 1
return m
for i in spiral_matrix(5): print(*i)

5
Task/Spiral-matrix/Python/spiral-matrix-8.py Normal file
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1 2 3 4 5
16 17 18 19 6
15 24 25 20 7
14 23 22 21 8
13 12 11 10 9

47
Task/Spiral-matrix/Quackery/spiral-matrix.quackery Normal file
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[ stack ] is stepcount ( --> s )
[ stack ] is position ( --> s )
[ stack ] is heading ( --> s )
[ heading take
behead join
heading put ] is right ( --> )
[ heading share 0 peek
unrot times
[ position share
stepcount share
unrot poke
over position tally
1 stepcount tally ]
nip ] is walk ( [ n --> [ )
[ dip [ temp put [] ]
temp share times
[ temp share split
dip
[ nested join ] ]
drop temp release ] is matrixify ( n [ --> [ )
[ 0 stepcount put ( set up... )
0 position put
' [ 1 ] over join
-1 join over negate join
heading put
0 over dup * of
over 1 - walk right ( turtle draws spiral )
over 1 - times
[ i 1+ walk right
i 1+ walk right ]
1 walk
matrixify ( ...tidy up )
heading release
position release
stepcount release ] is spiral ( n --> [ )
9 spiral
witheach
[ witheach
[ dup 10 < if sp echo sp ]
cr ]

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