Spiral matrix
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Produce a spiral array.
A spiral array is a square arrangement of the first N2 natural numbers, where the
numbers increase sequentially as you go around the edges of the array spiraling inwards.
For example, given 5, produce this array:
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
- Related tasks
11l
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))- Output:
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
360 Assembly
For maximum compatibility, this program uses only the basic instruction set.
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- Output:
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
ABAP
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( ).
- Output:
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
Action!
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- Output:
Screenshot from Atari 8-bit computer
Matrix size: 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 Matrix size: 6 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
Ada
-- 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;
The following is a variant using a different algorithm (which can also be used recursively):
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;
ALGOL 68
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))- 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
AppleScript
(ES6)
---------------------- 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
- Output:
| 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 |
Arturo
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
]
- Output:
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
AutoHotkey
ahk forum: discussion
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
---------------------------
*/
AWK
# 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)
}
- Output:
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
BBC BASIC
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
C
Note: program produces a matrix starting from 1 instead of 0, because task says "natural numbers".
#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;
}
Recursive method, width and height given on command line:
#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;
}
C#
Solution based on the J hints:
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();
}
}
Translated proper C++ solution:
//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();
}
}
Spiral Matrix without using an Array
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();
}
}
}
- Output:
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
C++
#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 ) );
}
C++ solution done properly:
#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;
}
}
Clojure
Based on the J hints (almost as incomprehensible, maybe)
(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)))
Recursive generation:
(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))
CoffeeScript
# 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
- Output:
> 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 ] ]
Common Lisp
(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)))))))
> (pprint (spiral 6 6))
#2A((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))
> (pprint (spiral 5 3))
#2A((0 1 2)
(11 12 3)
(10 13 4)
(9 14 5)
(8 7 6))
Recursive generation:
(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))
D
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);
}
- Output:
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
Using a generator for any rectangular array:
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);
}
- Output:
0 1 2 3 4 5 6 7 8 21 22 23 24 25 26 27 28 9 20 35 34 33 32 31 30 29 10 19 18 17 16 15 14 13 12 11
DCL
$ 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
- Output:
$ @spiral_matrix 3 0 1 2 7 8 3 6 5 4 $ @spiral_matrix 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 ...
Delphi
This code actually creates a matrix in memory and stores values in the matrix, instead of just simulating one by drawing the pattern. It can also create matrices of any size and the matrices don't have to be square. It works by creating a rectangle of the same size as the matrix. It enters the values in the matrix along circumference of the matrix. It then uses the Windows library routine "InflateRect" to decrease the size of the rectangle until the whole matrix is filled with spiraling values. Since a rectangle can be any size and doesn't have to be square, it works with any size matrix, including non-square matrices.
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;
- Output:
5x5 Matrix [ 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] 8x8 Matrix [ 0 1 2 3 4 5 6 7] [ 27 28 29 30 31 32 33 8] [ 26 47 48 49 50 51 34 9] [ 25 46 59 60 61 52 35 10] [ 24 45 58 63 62 53 36 11] [ 23 44 57 56 55 54 37 12] [ 22 43 42 41 40 39 38 13] [ 21 20 19 18 17 16 15 14] 14x8 Matrix [ 0 1 2 3 4 5 6 7 8 9 10 11 12 13] [ 39 40 41 42 43 44 45 46 47 48 49 50 51 14] [ 38 71 72 73 74 75 76 77 78 79 80 81 52 15] [ 37 70 95 96 97 98 99 100 101 102 103 82 53 16] [ 36 69 94 111 110 109 108 107 106 105 104 83 54 17] [ 35 68 93 92 91 90 89 88 87 86 85 84 55 18] [ 34 67 66 65 64 63 62 61 60 59 58 57 56 19] [ 33 32 31 30 29 28 27 26 25 24 23 22 21 20] Elapsed Time: 11.242 ms.
E
First, some quick data types to unclutter the actual algorithm.
/** Missing scalar multiplication, but we don't need it. */
def makeVector2(x, y) {
return def vector {
to x() { return x }
to y() { return y }
to add(other) { return makeVector2(x + other.x(), y + other.y()) }
to clockwise() { return makeVector2(-y, x) }
}
}
/** Bugs: (1) The printing is specialized. (2) No bounds check on the column. */
def makeFlex2DArray(rows, cols) {
def storage := ([null] * (rows * cols)).diverge()
return def flex2DArray {
to __printOn(out) {
for y in 0..!rows {
for x in 0..!cols {
out.print(<import:java.lang.makeString>.format("%3d", [flex2DArray[y, x]]))
}
out.println()
}
}
to get(r, c) { return storage[r * cols + c] }
to put(r, c, v) { storage[r * cols + c] := v }
}
}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
}Example:
? 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 8EasyLang
proc mkspiral n . t[] .
subr side
for i to l
ind += d
t[ind] = cnt
cnt += 1
.
.
len t[] n * n
l = n
while cnt < len t[]
d = 1
side
l -= 1
d = n
side
d = -1
side
l -= 1
d = -n
side
.
.
n = 5
mkspiral n t[]
numfmt 0 3
for i to n * n
write t[i]
if i mod n = 0
print ""
.
.
- Output:
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
Elixir
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)
The other way
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)
Another way
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)
- Output:
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
Euphoria
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)- Output:
{
{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}
}
F#
No fancy schmancy elegance here, just putting the numbers in the right place (though I commend the elegance)...
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
Factor
This is an implementation of Joey Tuttle's method for computing a spiral directly as a list and then reshaping it into a matrix, as described in the J entry. To summarize, we construct a list with n*n elements by following some simple rules, then take its cumulative sum, and finally its inverse permutation (or grade in J parlance). This gives us a list which can be reshaped to the final matrix.
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
- Output:
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 0 1 2 3 4 5 6 7 8 31 32 33 34 35 36 37 38 9 30 55 56 57 58 59 60 39 10 29 54 71 72 73 74 61 40 11 28 53 70 79 80 75 62 41 12 27 52 69 78 77 76 63 42 13 26 51 68 67 66 65 64 43 14 25 50 49 48 47 46 45 44 15 24 23 22 21 20 19 18 17 16
Fortran
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
FreeBASIC
' 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
- Output:
Enter size of matrix ? 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
FutureBasic
void local fn SpiralMatrix( size as int )
int t = 0, b = size - 1, l = 0, r = size - 1
int value = 0, i, j
while ( t <= b && l <= r) {
for i = l to r
mda(t,i) = value++
next
t++
for i = t to b
mda(i,r) = value++
next
r--
if ( t <= b )
for i = r to l step -1
mda(b,i) = value++
next
b--
end if
if ( l <= r )
for i = b to t step -1
mda(i,l) = value++
next
l++
end if
wend
for i = 0 to size -1
for j = 0 to size - 1
printf @"%2d \b",mda_integer(i,j)
next
print
next
end fn
fn SpiralMatrix( 5 )
HandleEvents- Output:
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
GAP
# 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 ] ]
Go
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("")
}
}
}
Groovy
Naive "path-walking" solution:
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
}
Test:
(1..10).each { n ->
spiralMatrix(n).each { row ->
row.each { printf "%5d", it }
println()
}
println ()
}
- Output:
0
0 1
3 2
0 1 2
7 8 3
6 5 4
0 1 2 3
11 12 13 4
10 15 14 5
9 8 7 6
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
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
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
0 1 2 3 4 5 6 7
27 28 29 30 31 32 33 8
26 47 48 49 50 51 34 9
25 46 59 60 61 52 35 10
24 45 58 63 62 53 36 11
23 44 57 56 55 54 37 12
22 43 42 41 40 39 38 13
21 20 19 18 17 16 15 14
0 1 2 3 4 5 6 7 8
31 32 33 34 35 36 37 38 9
30 55 56 57 58 59 60 39 10
29 54 71 72 73 74 61 40 11
28 53 70 79 80 75 62 41 12
27 52 69 78 77 76 63 42 13
26 51 68 67 66 65 64 43 14
25 50 49 48 47 46 45 44 15
24 23 22 21 20 19 18 17 16
0 1 2 3 4 5 6 7 8 9
35 36 37 38 39 40 41 42 43 10
34 63 64 65 66 67 68 69 44 11
33 62 83 84 85 86 87 70 45 12
32 61 82 95 96 97 88 71 46 13
31 60 81 94 99 98 89 72 47 14
30 59 80 93 92 91 90 73 48 15
29 58 79 78 77 76 75 74 49 16
28 57 56 55 54 53 52 51 50 17
27 26 25 24 23 22 21 20 19 18
Haskell
Solution based on the J hints:
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
An alternative, point-free solution based on the same J source.
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
Another alternative:
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)
Or less ambitiously,
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)
- Output:
| 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 |
Icon and Unicon
At first I looked at keeping the filling of the matrix on track using /M[r,c] which fails when out of bounds or if the cell is null, but then I noticed the progression of the row and column increments from corner to corner reminded me of sines and cosines. I'm not sure if the use of a trigonometric function counts as elegance, perversity, or both. The generator could be easily modified to start at an arbitrary corner. Or count down to produce and evolute.
- Output:
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
IS-BASIC
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 DEFJ
This function is the result of some beautiful insights:
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
Would you like some hints that will allow you to reimplement it in another language?
These inward spiralling arrays are known as "involutes"; we can also generate outward-spiraling "evolutes", and we can start or end the spiral at any corner, and go in either direction (clockwise or counterclockwise). See the first link (to JSoftware.com).
Java
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();
}
}
}
- Output:
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
JavaScript
Imperative
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(" "));
- Output:
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
Functional
ES5
Translating one of the Haskell versions:
(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);
Output:
| 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 |
[[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]]
ES6
(() => {
"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();
})();
- Output:
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
jq
The strategy employed here is to start at [0,0] and move to the right ([0,1] == same row, next column) until we reach a boundary or a populated cell; then turn right, and proceed as before.
Initially fill the matrix with "false" so we can easily distinguish between unvisited cells (false) and non-existent cells (null).
Infrastructure:
# 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;Create a spiral n by n matrix
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)- Output:
$ jq -n -r -f spiral.jq 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
Julia
Define an iterator that marches through matrix indices in the spiral pattern, which makes it easy to generate spiral matrices and related objects. Note that Julia uses column major ordering of matrices and that Julia allows multi-dimensional arrays to be addressed by scalar index as well as by subscripts.
Spiral Matrix Iterator
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
Helper Functions
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
Main
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))
- Output:
The n = 5 spiral matrix:
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
Generalize to a non-square matrix (3x5):
0 1 2 3 4
11 12 13 14 5
10 9 8 7 6
An n = 7 prime spiral matrix:
2 3 5 7 11 13 17
89 97 101 103 107 109 19
83 173 179 181 191 113 23
79 167 223 227 193 127 29
73 163 211 199 197 131 31
71 157 151 149 139 137 37
67 61 59 53 47 43 41
Kotlin
// 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))
}
- Output:
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 0 1 2 3 4 5 6 7 8 9 35 36 37 38 39 40 41 42 43 10 34 63 64 65 66 67 68 69 44 11 33 62 83 84 85 86 87 70 45 12 32 61 82 95 96 97 88 71 46 13 31 60 81 94 99 98 89 72 47 14 30 59 80 93 92 91 90 73 48 15 29 58 79 78 77 76 75 74 49 16 28 57 56 55 54 53 52 51 50 17 27 26 25 24 23 22 21 20 19 18
Liberty BASIC
Extended to include automatic scaling of the display scale and font. See spiralM5
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
endLua
Original
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
Alternate
If only the printed output is required, without intermediate array storage, then:
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)
If the intermediate array storage is required, then:
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))
- Output:
(same for both)
0 1 2 3 4 5 6 7 8 31 32 33 34 35 36 37 38 9 30 55 56 57 58 59 60 39 10 29 54 71 72 73 74 61 40 11 28 53 70 79 80 75 62 41 12 27 52 69 78 77 76 63 42 13 26 51 68 67 66 65 64 43 14 25 50 49 48 47 46 45 44 15 24 23 22 21 20 19 18 17 16
Maple
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);- Output:
[ 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]
Mathematica / Wolfram Language
We split the task up in 2 functions, one that adds a 'ring' around a present matrix. And a function that adds rings to a 'core':
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]
]
Examples:
MakeSquareSpiral[2] // MatrixForm
MakeSquareSpiral[7] // MatrixForm
gives back:
MATLAB
There already exists a command to generate a spiral matrix in MATLAB. But, it creates a matrix that spirals outward, not inward like the task specification requires. It turns out that these matrices can be transformed into each other using some pretty simple transformations.
We start with a simple linear transformation: Then depending on if n is odd or even we use either an up/down or left/right mirror transformation.
function matrix = reverseSpiral(n)
matrix = (-spiral(n))+n^2;
if mod(n,2)==0
matrix = flipud(matrix);
else
matrix = fliplr(matrix);
end
end %reverseSpiral
Sample Usage:
>> 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
Maxima
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]) */
MiniZinc
%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)];- Output:
minizinc -DSize= spiral.mzn [| 1, 2, 3, 4 | 12, 13, 14, 5 | 11, 16, 15, 6 | 10, 9, 8, 7 |] ---------- minizinc -DSize=5 zigzag.mzn [| 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 |] ---------- minizinc -DSize=6 zigzag.mzn [| 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 |] ----------
NetRexx
/* 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
- Output:
| 0 1 2 | | 7 8 3 | | 6 5 4 | | 0 1 2 3 | | 11 12 13 4 | | 10 15 14 5 | | 9 8 7 6 | | 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 |
Nim
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)
- Output:
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
OCaml
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)
Another implementation:
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)
Octave
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
ooRexx
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
- Output:
| 0 1 2 | | 7 8 3 | | 6 5 4 | | 0 1 2 3 | | 11 12 13 4 | | 10 15 14 5 | | 9 8 7 6 | | 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 |
Oz
Simple, recursive solution:
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 {$}
C := @C + 1
end
end
in
{Inspect {Spiral 5}}PARI/GP
spiral(dim) = {
my (M = matrix(dim, dim), p = s = 1, q = i = 0);
for (n=1, dim,
for (b=1, dim-n+1, M[p,q+=s] = i; i++);
for (b=1, dim-n, M[p+=s,q] = i; i++);
s = -s;
);
M
}Output:
spiral(7) [ 0 1 2 3 4 5 6] [23 24 25 26 27 28 7] [22 39 40 41 42 29 8] [21 38 47 48 43 30 9] [20 37 46 45 44 31 10] [19 36 35 34 33 32 11] [18 17 16 15 14 13 12]
Pascal
program Spiralmat;
type
tDir = (left,down,right,up);
tdxy = record
dx,dy: longint;
end;
tdeltaDir = array[tDir] of tdxy;
const
Nextdir : array[tDir] of tDir = (down,right,up,left);
cDir : tDeltaDir = ((dx:1;dy:0),(dx:0;dy:1),(dx:-1;dy:0),(dx:0;dy:-1));
cMaxN = 32;
type
tSpiral = array[0..cMaxN,0..cMaxN] of LongInt;
function FillSpiral(n:longint):tSpiral;
var
b,i,k, dn,x,y : longInt;
dir : tDir;
tmpSp : tSpiral;
BEGIN
b := 0;
x := 0;
y := 0;
//only for the first line
k := -1;
dn := n-1;
tmpSp[x,y] := b;
dir := left;
repeat
i := 0;
while i < dn do
begin
inc(b);
tmpSp[x,y] := b;
inc(x,cDir[dir].dx);
inc(y,cDir[dir].dy);
inc(i);
end;
Dir:= NextDir[dir];
inc(k);
IF k > 1 then
begin
k := 0;
//shorten the line every second direction change
dn := dn-1;
if dn <= 0 then
BREAK;
end;
until false;
//the last
tmpSp[x,y] := b+1;
FillSpiral := tmpSp;
end;
var
a : tSpiral;
x,y,n : LongInt;
BEGIN
For n := 1 to 5{cMaxN} do
begin
A:=FillSpiral(n);
For y := 0 to n-1 do
begin
For x := 0 to n-1 do
write(A[x,y]:4);
writeln;
end;
writeln;
end;
END.
- Output:
1 1 2 4 3 .... 1 2 3 4 5 16 17 18 19 6 15 24 25 20 7 14 23 22 21 8 13 12 11 10 9
Perl
sub spiral
{my ($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";}
Phix
Simple is better.
with javascript_semantics integer n = 6, x = 1, y = 0, counter = 0, len = n, dx = 0, dy = 1 string fmt = sprintf("%%%dd",length(sprintf("%d",n*n))) sequence m = repeat(repeat("??",n),n) for i=1 to 2*n do -- 2n runs.. for j=1 to len do -- of a length... x += dx y += dy m[x][y] = sprintf(fmt,counter) counter += 1 end for len -= odd(i) -- ..-1 every other {dx,dy} = {dy,-dx} -- in new direction end for printf(1,"%s\n",{join(apply(m,join),"\n")})
- Output:
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
PicoLisp
This example uses 'grid' from "lib/simul.l", which maintains a two-dimensional structure and is normally used for simulations and board games.
(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) )- 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
PL/I
/* 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;PowerShell
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
- 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 1 2 3 4 5 6 7 24 25 26 27 28 29 8 23 40 41 42 43 30 9 22 39 48 49 44 31 10 21 38 47 46 45 32 11 20 37 36 35 34 33 12 19 18 17 16 15 14 13
Prolog
% 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).
- Output:
?- spiral(6,Mx), forall(member(X,Mx), writeln(X)). [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]
PureBasic
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
- Output:
Spiral: 2 0 1 3 2 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
Python
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))
- Output:
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
Recursive Solution
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)
Adding a cache for the spiral_part function it could be quite efficient.
Recursion by rotating the solution for rest of the square except the first row,
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))
Another way, based on preparing lists ahead
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)
Functional Solutions
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))
Or, as an alternative to generative mutation:
'''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()
| 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 |
Simple solution
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)
- 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
Quackery
This task really lends itself to a turtle graphics metaphor.
[ 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 ]- Output:
0 1 2 3 4 5 6 7 8 31 32 33 34 35 36 37 38 9 30 55 56 57 58 59 60 39 10 29 54 71 72 73 74 61 40 11 28 53 70 79 80 75 62 41 12 27 52 69 78 77 76 63 42 13 26 51 68 67 66 65 64 43 14 25 50 49 48 47 46 45 44 15 24 23 22 21 20 19 18 17 16
R
Sequence Solution
spiral <- function(n) matrix(order(cumsum(rep(rep_len(c(1, n, -1, -n), 2 * n - 1), n - seq(2 * n - 1) %/% 2))), n, byrow = T) - 1
spiral(5)
- Output:
[,1] [,2] [,3] [,4] [,5] [1,] 0 1 2 3 4 [2,] 15 16 17 18 5 [3,] 14 23 24 19 6 [4,] 13 22 21 20 7 [5,] 12 11 10 9 8
Recursive Solution
spiral_matrix <- function(n) {
spiralv <- function(v) {
n <- sqrt(length(v))
if (n != floor(n))
stop("length of v should be a square of an integer")
if (n == 0)
stop("v should be of positive length")
if (n == 1)
m <- matrix(v, 1, 1)
else
m <- rbind(v[1:n], cbind(spiralv(v[(2 * n):(n^2)])[(n - 1):1, (n - 1):1], v[(n + 1):(2 * n - 1)]))
m
}
spiralv(1:(n^2))
}
Iterative Solution
Not the most elegant, but certainly distinct from the other R solutions. The key is the observation that we need to produce n elements from left to right, then n-1 elements down, then n-1 left, then n-2 right, then n-2 down, ... . This gives us two patterns. One in the direction that we need to write and another in the number of elements to write. After this, all that is left is battling R's indexing system.
spiralMatrix <- function(n)
{
spiral <- matrix(0, nrow = n, ncol = n)
firstNumToWrite <- 0
neededLength <- n
startPt <- cbind(1, 0)#(1, 0) is needed for the first call to writeRight to work. We need to start in row 1.
writingDirectionIndex <- 0
#These two functions select a collection of adjacent elements and replaces them with the needed sequence.
#This heavily uses R's vector recycling rules.
writeDown <- function(seq) spiral[startPt[1] + seq, startPt[2]] <<- seq_len(neededLength) - 1 + firstNumToWrite
writeRight <- function(seq) spiral[startPt[1], startPt[2] + seq] <<- seq_len(neededLength) - 1 + firstNumToWrite
while(firstNumToWrite != n^2)
{
writingDirectionIndex <- writingDirectionIndex %% 4 + 1
seq <- seq_len(neededLength)
switch(writingDirectionIndex,
writeRight(seq),
writeDown(seq),
writeRight(-seq),
writeDown(-seq))
if(writingDirectionIndex %% 2) neededLength <- neededLength - 1
max <- max(spiral)
firstNumToWrite <- max + 1
startPt <- which(max == spiral, arr.ind = TRUE)
}
spiral
}
Racket
#lang racket
(require math)
(define (spiral rows columns)
(define (index x y) (+ (* x columns) y))
(do ((N (* rows columns))
(spiral (make-vector (* rows columns) #f))
(dx 1) (dy 0) (x 0) (y 0)
(i 0 (+ i 1)))
((= i N) spiral)
(vector-set! spiral (index y x) i)
(let ((nx (+ x dx)) (ny (+ y dy)))
(cond
((and (< -1 nx columns)
(< -1 ny rows)
(not (vector-ref spiral (index ny nx))))
(set! x nx)
(set! y ny))
(else
(set!-values (dx dy) (values (- dy) dx))
(set! x (+ x dx))
(set! y (+ y dy)))))))
(vector->matrix 4 4 (spiral 4 4))
- Output:
(mutable-array #[#[0 1 2 3] #[11 12 13 4] #[10 15 14 5] #[9 8 7 6]])
Raku
(formerly Perl 6)
Object-oriented Solution
Suppose we set up a Turtle class like this:
class Turtle {
my @dv = [0,-1], [1,-1], [1,0], [1,1], [0,1], [-1,1], [-1,0], [-1,-1];
my $points = 8; # 'compass' points of neighbors on grid: north=0, northeast=1, east=2, etc.
has @.loc = 0,0;
has $.dir = 0;
has %.world;
has $.maxegg;
has $.range-x;
has $.range-y;
method turn-left ($angle = 90) { $!dir -= $angle / 45; $!dir %= $points; }
method turn-right($angle = 90) { $!dir += $angle / 45; $!dir %= $points; }
method lay-egg($egg) {
%!world{~@!loc} = $egg;
$!maxegg max= $egg;
$!range-x minmax= @!loc[0];
$!range-y minmax= @!loc[1];
}
method look($ahead = 1) {
my $there = @!loc »+« @dv[$!dir] »*» $ahead;
%!world{~$there};
}
method forward($ahead = 1) {
my $there = @!loc »+« @dv[$!dir] »*» $ahead;
@!loc = @($there);
}
method showmap() {
my $form = "%{$!maxegg.chars}s";
my $endx = $!range-x.max;
for $!range-y.list X $!range-x.list -> ($y, $x) {
print (%!world{"$x $y"} // '').fmt($form);
print $x == $endx ?? "\n" !! ' ';
}
}
}
# Now we can build the spiral in the normal way from outside-in like this:
sub MAIN(Int $size = 5) {
my $t = Turtle.new(dir => 2);
my $counter = 0;
$t.forward(-1);
for 0..^ $size -> $ {
$t.forward;
$t.lay-egg($counter++);
}
for $size-1 ... 1 -> $run {
$t.turn-right;
$t.forward, $t.lay-egg($counter++) for 0..^$run;
$t.turn-right;
$t.forward, $t.lay-egg($counter++) for 0..^$run;
}
$t.showmap;
}
Or we can build the spiral from inside-out like this:
sub MAIN(Int $size = 5) {
my $t = Turtle.new(dir => ($size %% 2 ?? 4 !! 0));
my $counter = $size * $size;
while $counter {
$t.lay-egg(--$counter);
$t.turn-left;
$t.turn-right if $t.look;
$t.forward;
}
$t.showmap;
}
Note that with these "turtle graphics" we don't actually have to care about the coordinate system, since the showmap method can show whatever rectangle was modified by the turtle. So unlike the standard inside-out algorithm, we don't have to find the center of the matrix first.
Procedural Solution
sub spiral_matrix ( $n ) {
my @sm;
my $len = $n;
my $pos = 0;
for ^($n/2).ceiling -> $i {
my $j = $i + 1;
my $e = $n - $j;
@sm[$i ][$i + $_] = $pos++ for ^( $len); # Top
@sm[$j + $_][$e ] = $pos++ for ^(--$len); # Right
@sm[$e ][$i + $_] = $pos++ for reverse ^( $len); # Bottom
@sm[$j + $_][$i ] = $pos++ for reverse ^(--$len); # Left
}
return @sm;
}
say .fmt('%3d') for spiral_matrix(5);
- Output:
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
REXX
Original logic borrowed (mostly) from the Fortran example.
static column width
/*REXX program displays a spiral in a square array (of any size) starting at START. */
parse arg size start . /*obtain optional arguments from the CL*/
if size =='' | size =="," then size =5 /*Not specified? Then use the default.*/
if start=='' | start=="," then start=0 /*Not specified? Then use the default.*/
tot=size**2; L=length(tot + start) /*total number of elements in spiral. */
k=size /*K: is the counter for the spiral. */
row=1; col=0 /*start spiral at row 1, column 0. */
/* [↓] construct the numbered spiral. */
do n=0 for k; col=col + 1; @.col.row=n + start; end; if k==0 then exit
/* [↑] build the first row of spiral. */
do until n>=tot /*spiral matrix.*/
do one=1 to -1 by -2 until n>=tot; k=k-1 /*perform twice.*/
do n=n for k; row=row + one; @.col.row=n + start; end /*for the row···*/
do n=n for k; col=col - one; @.col.row=n + start; end /* " " col···*/
end /*one*/ /* ↑↓ direction.*/
end /*until n≥tot*/ /* [↑] done with the matrix spiral. */
/* [↓] display spiral to the screen. */
do r=1 for size; _= right(@.1.r, L) /*construct display row by row. */
do c=2 for size -1; _=_ right(@.c.r, L) /*construct a line for the display. */
end /*col*/ /* [↑] line has an extra leading blank*/
say _ /*display a line (row) of the spiral. */
end /*row*/ /*stick a fork in it, we're all done. */
- output using the default array size of: 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
- output using an array size and start value of: 10 -70000
-70000 -69999 -69998 -69997 -69996 -69995 -69994 -69993 -69992 -69991 -69965 -69964 -69963 -69962 -69961 -69960 -69959 -69958 -69957 -69990 -69966 -69937 -69936 -69935 -69934 -69933 -69932 -69931 -69956 -69989 -69967 -69938 -69917 -69916 -69915 -69914 -69913 -69930 -69955 -69988 -69968 -69939 -69918 -69905 -69904 -69903 -69912 -69929 -69954 -69987 -69969 -69940 -69919 -69906 -69901 -69902 -69911 -69928 -69953 -69986 -69970 -69941 -69920 -69907 -69908 -69909 -69910 -69927 -69952 -69985 -69971 -69942 -69921 -69922 -69923 -69924 -69925 -69926 -69951 -69984 -69972 -69943 -69944 -69945 -69946 -69947 -69948 -69949 -69950 -69983 -69973 -69974 -69975 -69976 -69977 -69978 -69979 -69980 -69981 -69982
{{out|output|text= (shown at 3/4 size) using an array size of: 36
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 25 26 27 28 29 30 31 32 33 34 35 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 36 138 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 174 37 137 270 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 304 175 38 136 269 394 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 426 305 176 39 135 268 393 510 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 540 427 306 177 40 134 267 392 509 618 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 646 541 428 307 178 41 133 266 391 508 617 718 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 744 647 542 429 308 179 42 132 265 390 507 616 717 810 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 834 745 648 543 430 309 180 43 131 264 389 506 615 716 809 894 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 916 835 746 649 544 431 310 181 44 130 263 388 505 614 715 808 893 970 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 990 917 836 747 650 545 432 311 182 45 129 262 387 504 613 714 807 892 969 1038 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1056 991 918 837 748 651 546 433 312 183 46 128 261 386 503 612 713 806 891 968 1037 1098 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1114 1057 992 919 838 749 652 547 434 313 184 47 127 260 385 502 611 712 805 890 967 1036 1097 1150 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1164 1115 1058 993 920 839 750 653 548 435 314 185 48 126 259 384 501 610 711 804 889 966 1035 1096 1149 1194 1231 1232 1233 1234 1235 1236 1237 1238 1239 1206 1165 1116 1059 994 921 840 751 654 549 436 315 186 49 125 258 383 500 609 710 803 888 965 1034 1095 1148 1193 1230 1259 1260 1261 1262 1263 1264 1265 1240 1207 1166 1117 1060 995 922 841 752 655 550 437 316 187 50 124 257 382 499 608 709 802 887 964 1033 1094 1147 1192 1229 1258 1279 1280 1281 1282 1283 1266 1241 1208 1167 1118 1061 996 923 842 753 656 551 438 317 188 51 123 256 381 498 607 708 801 886 963 1032 1093 1146 1191 1228 1257 1278 1291 1292 1293 1284 1267 1242 1209 1168 1119 1062 997 924 843 754 657 552 439 318 189 52 122 255 380 497 606 707 800 885 962 1031 1092 1145 1190 1227 1256 1277 1290 1295 1294 1285 1268 1243 1210 1169 1120 1063 998 925 844 755 658 553 440 319 190 53 121 254 379 496 605 706 799 884 961 1030 1091 1144 1189 1226 1255 1276 1289 1288 1287 1286 1269 1244 1211 1170 1121 1064 999 926 845 756 659 554 441 320 191 54 120 253 378 495 604 705 798 883 960 1029 1090 1143 1188 1225 1254 1275 1274 1273 1272 1271 1270 1245 1212 1171 1122 1065 1000 927 846 757 660 555 442 321 192 55 119 252 377 494 603 704 797 882 959 1028 1089 1142 1187 1224 1253 1252 1251 1250 1249 1248 1247 1246 1213 1172 1123 1066 1001 928 847 758 661 556 443 322 193 56 118 251 376 493 602 703 796 881 958 1027 1088 1141 1186 1223 1222 1221 1220 1219 1218 1217 1216 1215 1214 1173 1124 1067 1002 929 848 759 662 557 444 323 194 57 117 250 375 492 601 702 795 880 957 1026 1087 1140 1185 1184 1183 1182 1181 1180 1179 1178 1177 1176 1175 1174 1125 1068 1003 930 849 760 663 558 445 324 195 58 116 249 374 491 600 701 794 879 956 1025 1086 1139 1138 1137 1136 1135 1134 1133 1132 1131 1130 1129 1128 1127 1126 1069 1004 931 850 761 664 559 446 325 196 59 115 248 373 490 599 700 793 878 955 1024 1085 1084 1083 1082 1081 1080 1079 1078 1077 1076 1075 1074 1073 1072 1071 1070 1005 932 851 762 665 560 447 326 197 60 114 247 372 489 598 699 792 877 954 1023 1022 1021 1020 1019 1018 1017 1016 1015 1014 1013 1012 1011 1010 1009 1008 1007 1006 933 852 763 666 561 448 327 198 61 113 246 371 488 597 698 791 876 953 952 951 950 949 948 947 946 945 944 943 942 941 940 939 938 937 936 935 934 853 764 667 562 449 328 199 62 112 245 370 487 596 697 790 875 874 873 872 871 870 869 868 867 866 865 864 863 862 861 860 859 858 857 856 855 854 765 668 563 450 329 200 63 111 244 369 486 595 696 789 788 787 786 785 784 783 782 781 780 779 778 777 776 775 774 773 772 771 770 769 768 767 766 669 564 451 330 201 64 110 243 368 485 594 695 694 693 692 691 690 689 688 687 686 685 684 683 682 681 680 679 678 677 676 675 674 673 672 671 670 565 452 331 202 65 109 242 367 484 593 592 591 590 589 588 587 586 585 584 583 582 581 580 579 578 577 576 575 574 573 572 571 570 569 568 567 566 453 332 203 66 108 241 366 483 482 481 480 479 478 477 476 475 474 473 472 471 470 469 468 467 466 465 464 463 462 461 460 459 458 457 456 455 454 333 204 67 107 240 365 364 363 362 361 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minimum column width
This REXX version automatically adjusts the width of the spiral matrix columns to minimize the area of the matrix display (so more elements may be shown on a display screen).
/*REXX program displays a spiral in a square array (of any size) starting at START. */
parse arg size start . /*obtain optional arguments from the CL*/
if size =='' | size =="," then size =5 /*Not specified? Then use the default.*/
if start=='' | start=="," then start=0 /*Not specified? Then use the default.*/
tot=size**2; L=length(tot + start) /*total number of elements in spiral. */
k=size /*K: is the counter for the spiral. */
row=1; col=0 /*start spiral at row 1, column 0. */
/* [↓] construct the numbered spiral. */
do n=0 for k; col=col + 1; @.col.row=n + start; end; if k==0 then exit
/* [↑] build the first row of spiral. */
do until n>=tot /*spiral matrix.*/
do one=1 to -1 by -2 until n>=tot; k=k - 1 /*perform twice.*/
do n=n for k; row=row + one; @.col.row=n + start; end /*for the row···*/
do n=n for k; col=col - one; @.col.row=n + start; end /* " " col···*/
end /*one*/ /* ↑↓ direction.*/
end /*until n≥tot*/ /* [↑] done with the matrix spiral. */
!.=0 /* [↓] display spiral to the screen. */
do two=0 for 2 /*1st time? Find max column and width.*/
do r=1 for size; _= /*construct display row by row. */
do c=1 for size; x=@.c.r /*construct a line column by column. */
if two then _=_ right(x, !.c) /*construct a line for the display. */
else !.c=max(!.c, length(x)) /*find the maximum width of the column.*/
end /*c*/ /* [↓] line has an extra leading blank*/
if two then say substr(_, 2) /*this SUBSTR ignores the first blank. */
end /*r*/
end /*two*/ /*stick a fork in it, we're all done. */
{{out|output|text= (shown at 3/4 size) using an array size of: 36
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 25 26 27 28 29 30 31 32 33 34 35 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 36 138 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 174 37 137 270 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 304 175 38 136 269 394 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 426 305 176 39 135 268 393 510 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 540 427 306 177 40 134 267 392 509 618 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 646 541 428 307 178 41 133 266 391 508 617 718 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 744 647 542 429 308 179 42 132 265 390 507 616 717 810 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 834 745 648 543 430 309 180 43 131 264 389 506 615 716 809 894 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 916 835 746 649 544 431 310 181 44 130 263 388 505 614 715 808 893 970 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 990 917 836 747 650 545 432 311 182 45 129 262 387 504 613 714 807 892 969 1038 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1056 991 918 837 748 651 546 433 312 183 46 128 261 386 503 612 713 806 891 968 1037 1098 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1114 1057 992 919 838 749 652 547 434 313 184 47 127 260 385 502 611 712 805 890 967 1036 1097 1150 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1164 1115 1058 993 920 839 750 653 548 435 314 185 48 126 259 384 501 610 711 804 889 966 1035 1096 1149 1194 1231 1232 1233 1234 1235 1236 1237 1238 1239 1206 1165 1116 1059 994 921 840 751 654 549 436 315 186 49 125 258 383 500 609 710 803 888 965 1034 1095 1148 1193 1230 1259 1260 1261 1262 1263 1264 1265 1240 1207 1166 1117 1060 995 922 841 752 655 550 437 316 187 50 124 257 382 499 608 709 802 887 964 1033 1094 1147 1192 1229 1258 1279 1280 1281 1282 1283 1266 1241 1208 1167 1118 1061 996 923 842 753 656 551 438 317 188 51 123 256 381 498 607 708 801 886 963 1032 1093 1146 1191 1228 1257 1278 1291 1292 1293 1284 1267 1242 1209 1168 1119 1062 997 924 843 754 657 552 439 318 189 52 122 255 380 497 606 707 800 885 962 1031 1092 1145 1190 1227 1256 1277 1290 1295 1294 1285 1268 1243 1210 1169 1120 1063 998 925 844 755 658 553 440 319 190 53 121 254 379 496 605 706 799 884 961 1030 1091 1144 1189 1226 1255 1276 1289 1288 1287 1286 1269 1244 1211 1170 1121 1064 999 926 845 756 659 554 441 320 191 54 120 253 378 495 604 705 798 883 960 1029 1090 1143 1188 1225 1254 1275 1274 1273 1272 1271 1270 1245 1212 1171 1122 1065 1000 927 846 757 660 555 442 321 192 55 119 252 377 494 603 704 797 882 959 1028 1089 1142 1187 1224 1253 1252 1251 1250 1249 1248 1247 1246 1213 1172 1123 1066 1001 928 847 758 661 556 443 322 193 56 118 251 376 493 602 703 796 881 958 1027 1088 1141 1186 1223 1222 1221 1220 1219 1218 1217 1216 1215 1214 1173 1124 1067 1002 929 848 759 662 557 444 323 194 57 117 250 375 492 601 702 795 880 957 1026 1087 1140 1185 1184 1183 1182 1181 1180 1179 1178 1177 1176 1175 1174 1125 1068 1003 930 849 760 663 558 445 324 195 58 116 249 374 491 600 701 794 879 956 1025 1086 1139 1138 1137 1136 1135 1134 1133 1132 1131 1130 1129 1128 1127 1126 1069 1004 931 850 761 664 559 446 325 196 59 115 248 373 490 599 700 793 878 955 1024 1085 1084 1083 1082 1081 1080 1079 1078 1077 1076 1075 1074 1073 1072 1071 1070 1005 932 851 762 665 560 447 326 197 60 114 247 372 489 598 699 792 877 954 1023 1022 1021 1020 1019 1018 1017 1016 1015 1014 1013 1012 1011 1010 1009 1008 1007 1006 933 852 763 666 561 448 327 198 61 113 246 371 488 597 698 791 876 953 952 951 950 949 948 947 946 945 944 943 942 941 940 939 938 937 936 935 934 853 764 667 562 449 328 199 62 112 245 370 487 596 697 790 875 874 873 872 871 870 869 868 867 866 865 864 863 862 861 860 859 858 857 856 855 854 765 668 563 450 329 200 63 111 244 369 486 595 696 789 788 787 786 785 784 783 782 781 780 779 778 777 776 775 774 773 772 771 770 769 768 767 766 669 564 451 330 201 64 110 243 368 485 594 695 694 693 692 691 690 689 688 687 686 685 684 683 682 681 680 679 678 677 676 675 674 673 672 671 670 565 452 331 202 65 109 242 367 484 593 592 591 590 589 588 587 586 585 584 583 582 581 580 579 578 577 576 575 574 573 572 571 570 569 568 567 566 453 332 203 66 108 241 366 483 482 481 480 479 478 477 476 475 474 473 472 471 470 469 468 467 466 465 464 463 462 461 460 459 458 457 456 455 454 333 204 67 107 240 365 364 363 362 361 360 359 358 357 356 355 354 353 352 351 350 349 348 347 346 345 344 343 342 341 340 339 338 337 336 335 334 205 68 106 239 238 237 236 235 234 233 232 231 230 229 228 227 226 225 224 223 222 221 220 219 218 217 216 215 214 213 212 211 210 209 208 207 206 69 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70
Ring
# Project : Spiral matrix
load "guilib.ring"
load "stdlib.ring"
new qapp
{
win1 = new qwidget() {
setwindowtitle("Spiral matrix")
setgeometry(100,100,600,400)
n = 5
result = newlist(n,n)
spiral = newlist(n,n)
k = 1
top = 1
bottom = n
left = 1
right = n
while (k <= n*n)
for i= left to right
result[top][i] = k
k = k + 1
next
top = top + 1
for i = top to bottom
result[i][right] = k
k = k + 1
next
right = right - 1
for i = right to left step -1
result[bottom][i] = k
k = k + 1
next
bottom = bottom - 1
for i = bottom to top step -1
result[i][left] = k
k = k + 1
next
left = left + 1
end
for m = 1 to n
for p = 1 to n
spiral[p][m] = new qpushbutton(win1) {
x = 150+m*40
y = 30 + p*40
setgeometry(x,y,40,40)
settext(string(result[m][p]))
}
next
next
show()
}
exec()
}Output:
RPL
« { 0 1 } → n step
« { 1 1 } n DUP 2 →LIST -1 CON @ empty cell = -1
1 n SQ FOR j
OVER j PUT
DUP2 SWAP step ADD
IF IFERR GET THEN DROP2 1 ELSE -1 ≠ END @ if next step is out of border or an already written cell
THEN step REVLIST { 1 -1 } * 'step' STO END @ then turn right
SWAP step ADD SWAP
NEXT
» » 'SPIRAL' STO
5 SPIRAL
- Output:
1: [[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]]
Ruby
def spiral(n)
spiral = Array.new(n) {Array.new(n, nil)} # n x n array of nils
runs = n.downto(0).each_cons(2).to_a.flatten # n==5; [5,4,4,3,3,2,2,1,1,0]
delta = [[1,0], [0,1], [-1,0], [0,-1]].cycle
x, y, value = -1, 0, -1
for run in runs
dx, dy = delta.next
run.times { spiral[y+=dy][x+=dx] = (value+=1) }
end
spiral
end
def print_matrix(m)
width = m.flatten.map{|x| x.to_s.size}.max
m.each {|row| puts row.map {|x| "%#{width}s " % x}.join}
end
print_matrix spiral(5)
- Output:
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
The other way
n = 5
m = Array.new(n){Array.new(n)}
pos, side = -1, n
for i in 0 .. (n-1)/2
(0...side).each{|j| m[i][i+j] = (pos+=1) }
(1...side).each{|j| m[i+j][n-1-i] = (pos+=1) }
side -= 2
side.downto(0) {|j| m[n-1-i][i+j] = (pos+=1) }
side.downto(1) {|j| m[i+j][i] = (pos+=1) }
end
fmt = "%#{(n*n-1).to_s.size}d " * n
puts m.map{|row| fmt % row}
Output as above.
It processes the Array which is for work without creating it.
def spiral_matrix(n)
x, y, dx, dy = -1, 0, 0, -1
fmt = "%#{(n*n-1).to_s.size}d " * n
n.downto(1).flat_map{|x| [x, x-1]}.flat_map{|run|
dx, dy = -dy, dx # turn 90
run.times.map { [y+=dy, x+=dx] }
}.each_with_index.sort.map(&:last).each_slice(n){|row| puts fmt % row}
end
spiral_matrix(5)
Rust
const VECTORS: [(isize, isize); 4] = [(1, 0), (0, 1), (-1, 0), (0, -1)];
pub fn spiral_matrix(size: usize) -> Vec<Vec<u32>> {
let mut matrix = vec![vec![0; size]; size];
let mut movement = VECTORS.iter().cycle();
let (mut x, mut y, mut n) = (-1, 0, 1..);
for (move_x, move_y) in std::iter::once(size)
.chain((1..size).rev().flat_map(|n| std::iter::repeat(n).take(2)))
.flat_map(|steps| std::iter::repeat(movement.next().unwrap()).take(steps))
{
x += move_x;
y += move_y;
matrix[y as usize][x as usize] = n.next().unwrap();
}
matrix
}
fn main() {
for i in spiral_matrix(4).iter() {
for j in i.iter() {
print!("{:>2} ", j);
}
println!();
}
}
- Output:
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
Scala
class Folder(){
var dir = (1,0)
var pos = (-1,0)
def apply(l:List[Int], a:Array[Array[Int]]) = {
var (x,y) = pos //start position
var (dx,dy) = dir //direction
l.foreach {e => x = x + dx; y = y + dy; a(y)(x) = e } //copy l elements to array using current direction
pos = (x,y)
dir = (-dy, dx) //turn
}
}
def spiral(n:Int) = {
def dup(n:Int) = (1 to n).flatMap(i=>List(i,i)).toList
val folds = n :: dup(n-1).reverse //define fold part lengths
var array = new Array[Array[Int]](n,n)
val fold = new Folder()
var seq = (0 until n*n).toList //sequence to fold
folds.foreach {len => fold(seq.take(len),array); seq = seq.drop(len)}
array
}
Explanation: if you see the sequence of numbers to spiral around as a tape to fold around, you can see this pattern on the lenght of tape segment to fold in each step:
Using this the solution becomes very simple,
- make the list of lengths to fold
- create the sequence to fold
- for each segment call a fold function that keeps track of where it is and knows how to turn around.
It's simple to make this generic, changing start position, initial direction, etc. The code could be more compact, but I'm leaving it like this for clarity.
Scilab
function a = spiral(n)
a = ones(n*n, 1)
v = ones(n, 1)
u = -n*v;
i = n
for k = n-1:-1:1
j = 1:k
u(j) = -u(j)
a(j+i) = u(j)
v(j) = -v(j)
a(j+(i+k)) = v(j)
i = i+2*k
end
a(cumsum(a)) = (1:n*n)'
a = matrix(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.
Seed7
$ include "seed7_05.s7i";
const type: matrix is array array integer;
const func matrix: spiral (in integer: n) is func
result
var matrix: myArray is matrix.value;
local
var integer: i is 0;
var integer: dx is 1;
var integer: dy is 0;
var integer: x is 1;
var integer: y is 1;
var integer: nx is 0;
var integer: ny is 0;
var integer: swap is 0;
begin
myArray := n times n times 0;
for i range 1 to n**2 do
myArray[x][y] := i;
nx := x + dx;
ny := y + dy;
if nx >= 1 and nx <= n and ny >= 1 and ny <= n and myArray[nx][ny] = 0 then
x := nx;
y := ny;
else
swap := dx;
dx := -dy;
dy := swap;
x +:= dx;
y +:= dy;
end if;
end for;
end func;
const proc: writeMatrix (in matrix: myArray) is func
local
var integer: x is 0;
var integer: y is 0;
begin
for key y range myArray do
for key x range myArray[y] do
write(myArray[x][y] lpad 4);
end for;
writeln;
end for;
end func;
const proc: main is func
begin
writeMatrix(spiral(5));
end func;- 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
Sidef
func spiral(n) {
var (x, y, dx, dy, a) = (0, 0, 1, 0, [])
{ |i|
a[y][x] = i
var (nx, ny) = (x+dx, y+dy)
( if (dx == 1 && (nx == n || a[ny][nx]!=nil)) { [ 0, 1] }
elsif (dy == 1 && (ny == n || a[ny][nx]!=nil)) { [-1, 0] }
elsif (dx == -1 && (nx < 0 || a[ny][nx]!=nil)) { [ 0, -1] }
elsif (dy == -1 && (ny < 0 || a[ny][nx]!=nil)) { [ 1, 0] }
else { [dx, dy] }
) » (\dx, \dy)
x = x+dx
y = y+dy
} << (1 .. n**2)
return a
}
spiral(5).each { |row|
row.map {"%3d" % _}.join(' ').say
}
- 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
Stata
function spiral_mat(n) {
a = J(n*n, 1, 1)
u = J(n, 1, -n)
v = J(n, 1, 1)
for (k=(i=n)-1; k>=1; i=i+2*k--) {
j = 1..k
a[j:+i] = u[j] = -u[j]
a[j:+(i+k)] = v[j] = -v[j]
}
return(rowshape(invorder(runningsum(a)),n):-1)
}
spiral_mat(5)
1 2 3 4 5
+--------------------------+
1 | 0 1 2 3 4 |
2 | 15 16 17 18 5 |
3 | 14 23 24 19 6 |
4 | 13 22 21 20 7 |
5 | 12 11 10 9 8 |
+--------------------------+
Tcl
Using print_matrix from Matrix Transpose#Tcl
package require Tcl 8.5
namespace path {::tcl::mathop}
proc spiral size {
set m [lrepeat $size [lrepeat $size .]]
set x 0; set dx 0
set y -1; set dy 1
set i -1
while {$i < $size ** 2 - 1} {
if {$dy == 0} {
incr x $dx
if {0 <= $x && $x < $size && [lindex $m $x $y] eq "."} {
lset m $x $y [incr i]
} else {
# back up and change direction
incr x [- $dx]
set dy [- $dx]
set dx 0
}
} else {
incr y $dy
if {0 <= $y && $y < $size && [lindex $m $x $y] eq "."} {
lset m $x $y [incr i]
} else {
# back up and change direction
incr y [- $dy]
set dx $dy
set dy 0
}
}
}
return $m
}
print_matrix [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
TI-83 BASIC
5->N
DelVar [F]
{N,N}→dim([F])
1→A: N→B
1→C: N→D
0→E: E→G
1→I: 1→J
For(K,1,N*N)
K-1→[F](I,J)
If E=0: Then
If J<D: Then
J+1→J
Else: 1→G
I+1→I: A+1→A
End
End
If E=1: Then
If I<B: Then
I+1→I
Else: 2→G
J-1→J: D-1→D
End
End
If E=2: Then
If J>C: Then
J-1→J
Else: 3→G
I-1→I: B-1→B
End
End
If E=3: Then
If I>A: Then
I-1→I
Else: 0→G
J+1→J: C+1→C
End
End
G→E
End
[F]- Output:
[[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]]
TSE SAL
// library: math: create: array: spiral: inwards <description></description> <version control></version control> <version>1.0.0.0.15</version> (filenamemacro=creamasi.s) [<Program>] [<Research>] [kn, ri, mo, 31-12-2012 01:15:43]
PROC PROCMathCreateArraySpiralInwards( INTEGER nI )
// e.g. PROC Main()
// e.g. STRING s1[255] = "5"
// e.g. IF ( NOT ( Ask( "math: create: array: spiral: inwards: nI = ", s1, _EDIT_HISTORY_ ) ) AND ( Length( s1 ) > 0 ) ) RETURN() ENDIF
// e.g. PROCMathCreateArraySpiralInwards( Val( s1 ) )
// e.g. END
// e.g.
// e.g. <F12> Main()
//
INTEGER columnEndI = 0
//
INTEGER columnBeginI = nI - 1
//
INTEGER rowEndI = 0
//
INTEGER rowBeginI = nI - 1
//
INTEGER columnI = 0
//
INTEGER rowI = 0
//
INTEGER minI = 0
INTEGER maxI = nI * nI - 1
INTEGER I = 0
//
INTEGER columnWidthI = Length( Str( nI * nI - 1 ) ) + 1
//
INTEGER directionRightI = 0
INTEGER directionLeftI = 1
INTEGER directionDownI = 2
INTEGER directionUpI = 3
//
INTEGER directionI = directionRightI
//
FOR I = minI TO maxI
//
SetGlobalInt( Format( "MatrixS", columnI, ",", rowI ), I )
// SetGlobalInt( Format( "MatrixS", columnI, ",", rowI ), I )
//
PutStrXY( ( Query( ScreenCols ) / 8 ) + columnI * columnWidthI, ( Query( ScreenRows ) / 8 ) + rowI, Str( I ), Color( BRIGHT RED ON WHITE ) )
// PutStrXY( ( Query( ScreenCols ) / 8 ) + columnI * columnWidthI, ( Query( ScreenRows ) / 8 ) + rowI, Str( I + 1 ), Color( BRIGHT RED ON WHITE ) )
//
CASE directionI
//
WHEN directionRightI
//
IF ( columnI < columnBeginI )
//
columnI = columnI + 1
//
ELSE
//
directionI = directionDownI
//
rowI = rowI + 1
//
rowEndI = rowEndI + 1
//
ENDIF
//
WHEN directionDownI
//
IF ( rowI < rowBeginI )
//
rowI = rowI + 1
//
ELSE
//
directionI = directionLeftI
//
columnI = columnI - 1
//
columnBeginI = columnBeginI - 1
//
ENDIF
//
WHEN directionLeftI
//
IF ( columnI > columnEndI )
//
columnI = columnI - 1
//
ELSE
//
directionI = directionUpI
//
rowI = rowI - 1
//
rowBeginI = rowBeginI - 1
//
ENDIF
//
WHEN directionUpI
//
IF ( rowI > rowEndI )
//
rowI = rowI - 1
//
ELSE
//
directionI = directionRightI
//
columnI = columnI + 1
//
columnEndI = columnEndI + 1
//
ENDIF
//
OTHERWISE
//
Warn( Format( "PROCMathCreateArraySpiralInwards(", " ", "case", " ", ":", " ", Str( directionI ), ": not known" ) )
//
RETURN()
//
ENDCASE
//
ENDFOR
//
END
PROC Main()
STRING s1[255] = "5"
IF ( NOT ( Ask( "math: create: array: spiral: inwards: nI = ", s1, _EDIT_HISTORY_ ) ) AND ( Length( s1 ) > 0 ) ) RETURN() ENDIF
PROCMathCreateArraySpiralInwards( Val( s1 ) )
ENDuBasic/4tH
This recursive version is quite compact.
Input "Width: ";w
Input "Height: ";h
Print
For i = 0 To h-1
For j = 0 To w-1
Print Using "__#"; FUNC(_Spiral(w,h,j,i));
Next
Print
Next
End
_Spiral Param(4)
If d@ Then
Return (a@ + FUNC(_Spiral(b@-1, a@, d@ - 1, a@ - c@ - 1)))
Else
Return (c@)
EndIfUnison
spiralMatrix.spiralMatrix : Nat -> [[Nat]]
spiralMatrix.spiralMatrix = cases
0 -> []
n ->
go h w s = match h with
0 -> []
h' -> Nat.range s (s + w) +: (List.reverse >> List.transpose) (go w (h' - 1) (w + s))
go n n 1Ursala
Helpful hints from the J example are gratefully acknowledged. The spiral function works for any n, and results are shown for n equal to 5, 6, and 7. The results are represented as lists of lists rather than arrays.
#import std
#import nat
#import int
spiral =
^H/block nleq-<lS&r+ -+
num@NiC+ sum:-0*yK33x+ (|\LL negation**)+ rlc ~&lh==1,
~&rNNXNXSPlrDlSPK32^lrtxiiNCCSLhiC5D/~& iota*+ iota+-
#cast %nLLL
examples = spiral* <5,6,7>- Output:
<
<
<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>>,
<
<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>>,
<
<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>>>
VBScript
Function build_spiral(n)
botcol = 0 : topcol = n - 1
botrow = 0 : toprow = n - 1
'declare a two dimensional array
Dim matrix()
ReDim matrix(topcol,toprow)
dir = 0 : col = 0 : row = 0
'populate the array
For i = 0 To n*n-1
matrix(col,row) = i
Select Case dir
Case 0
If col < topcol Then
col = col + 1
Else
dir = 1 : row = row + 1 : botrow = botrow + 1
End If
Case 1
If row < toprow Then
row = row + 1
Else
dir = 2 : col = col - 1 : topcol = topcol - 1
End If
Case 2
If col > botcol Then
col = col - 1
Else
dir = 3 : row = row - 1 : toprow = toprow - 1
End If
Case 3
If row > botrow Then
row = row - 1
Else
dir = 0 : col = col + 1 : botcol = botcol + 1
End If
End Select
Next
'print the array
For y = 0 To n-1
For x = 0 To n-1
WScript.StdOut.Write matrix(x,y) & vbTab
Next
WScript.StdOut.WriteLine
Next
End Function
build_spiral(CInt(WScript.Arguments(0)))- Output:
F:\>cscript /nologo build_spiral.vbs 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 F:\>cscript /nologo build_spiral.vbs 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
Visual Basic
VB6
This requires VB6.
Option Explicit
Sub Main()
print2dArray getSpiralArray(5)
End Sub
Function getSpiralArray(dimension As Integer) As Integer()
ReDim spiralArray(dimension - 1, dimension - 1) As Integer
Dim numConcentricSquares As Integer
numConcentricSquares = dimension \ 2
If (dimension Mod 2) Then numConcentricSquares = numConcentricSquares + 1
Dim j As Integer, sideLen As Integer, currNum As Integer
sideLen = dimension
Dim i As Integer
For i = 0 To numConcentricSquares - 1
' do top side
For j = 0 To sideLen - 1
spiralArray(i, i + j) = currNum
currNum = currNum + 1
Next
' do right side
For j = 1 To sideLen - 1
spiralArray(i + j, dimension - 1 - i) = currNum
currNum = currNum + 1
Next
' do bottom side
For j = sideLen - 2 To 0 Step -1
spiralArray(dimension - 1 - i, i + j) = currNum
currNum = currNum + 1
Next
' do left side
For j = sideLen - 2 To 1 Step -1
spiralArray(i + j, i) = currNum
currNum = currNum + 1
Next
sideLen = sideLen - 2
Next
getSpiralArray = spiralArray()
End Function
Sub print2dArray(arr() As Integer)
Dim row As Integer, col As Integer
For row = 0 To UBound(arr, 1)
For col = 0 To UBound(arr, 2) - 1
Debug.Print arr(row, col),
Next
Debug.Print arr(row, UBound(arr, 2))
Next
End SubVBA
Solution 1
Sub spiral()
Dim n As Integer, a As Integer, b As Integer
Dim numCsquares As Integer, sideLen As Integer, currNum As Integer
Dim j As Integer, i As Integer
Dim j1 As Integer, j2 As Integer, j3 As Integer
n = 5
Dim spiralArr(9, 9) As Integer
numCsquares = CInt(Application.WorksheetFunction.Ceiling(n / 2, 1))
sideLen = n
currNum = 0
For i = 0 To numCsquares - 1
'do top side
For j = 0 To sideLen - 1
currNum = currNum + 1
spiralArr(i, i + j) = currNum
Next j
'do right side
For j1 = 1 To sideLen - 1
currNum = currNum + 1
spiralArr(i + j1, n - 1 - i) = currNum
Next j1
'do bottom side
j2 = sideLen - 2
Do While j2 > -1
currNum = currNum + 1
spiralArr(n - 1 - i, i + j2) = currNum
j2 = j2 - 1
Loop
'do left side
j3 = sideLen - 2
Do While j3 > 0
currNum = currNum + 1
spiralArr(i + j3, i) = currNum
j3 = j3 - 1
Loop
sideLen = sideLen - 2
Next i
For a = 0 To n - 1
For b = 0 To n - 1
Cells(a + 1, b + 1).Select
ActiveCell.Value = spiralArr(a, b)
Next b
Next a
End SubSolution 2
Sub spiral(n As Integer)
Const FREE = -9 'negative number indicates unoccupied cell
Dim A() As Integer
Dim rowdelta(3) As Integer
Dim coldelta(3) As Integer
'initialize A to a matrix with an extra "border" of occupied cells
'this avoids having to test if we've reached the edge of the matrix
ReDim A(0 To n + 1, 0 To n + 1)
'Since A is initialized with zeros, setting A(1 to n,1 to n) to "FREE"
'leaves a "border" around it occupied with zeroes
For i = 1 To n: For j = 1 To n: A(i, j) = FREE: Next: Next
'set amount to move in directions "right", "down", "left", "up"
rowdelta(0) = 0: coldelta(0) = 1
rowdelta(1) = 1: coldelta(1) = 0
rowdelta(2) = 0: coldelta(2) = -1
rowdelta(3) = -1: coldelta(3) = 0
curnum = 0
'set current cell position
col = 1
row = 1
'set current direction
theDir = 0 'theDir = 1 will fill the matrix counterclockwise
'ok will be true as long as there is a free cell left
ok = True
Do While ok
'occupy current FREE cell and increase curnum
A(row, col) = curnum
curnum = curnum + 1
'check if next cell in current direction is free
'if not, try another direction in clockwise fashion
'if all directions lead to occupied cells then we are finished!
ok = False
For i = 0 To 3
newdir = (theDir + i) Mod 4
If A(row + rowdelta(newdir), col + coldelta(newdir)) = FREE Then
'yes, move to it and change direction if necessary
theDir = newdir
row = row + rowdelta(theDir)
col = col + coldelta(theDir)
ok = True
Exit For
End If
Next i
Loop
'print result
For i = 1 To n
For j = 1 To n
Debug.Print A(i, j),
Next
Debug.Print
Next
End Sub- Output:
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 spiral 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
Visual Basic .NET
Platform: .NET
From VB6. This requires Visual Basic .Net.
Module modSpiralArray
Sub Main()
print2dArray(getSpiralArray(5))
End Sub
Function getSpiralArray(dimension As Integer) As Object
Dim spiralArray(,) As Integer
Dim numConcentricSquares As Integer
ReDim spiralArray(dimension - 1, dimension - 1)
numConcentricSquares = dimension \ 2
If (dimension Mod 2) Then numConcentricSquares = numConcentricSquares + 1
Dim j As Integer, sideLen As Integer, currNum As Integer
sideLen = dimension
Dim i As Integer
For i = 0 To numConcentricSquares - 1
' do top side
For j = 0 To sideLen - 1
spiralArray(i, i + j) = currNum
currNum = currNum + 1
Next
' do right side
For j = 1 To sideLen - 1
spiralArray(i + j, dimension - 1 - i) = currNum
currNum = currNum + 1
Next
' do bottom side
For j = sideLen - 2 To 0 Step -1
spiralArray(dimension - 1 - i, i + j) = currNum
currNum = currNum + 1
Next
' do left side
For j = sideLen - 2 To 1 Step -1
spiralArray(i + j, i) = currNum
currNum = currNum + 1
Next
sideLen = sideLen - 2
Next
getSpiralArray = spiralArray
End Function
Sub print2dArray(arr)
Dim row As Integer, col As Integer, s As String
For row = 0 To UBound(arr, 1)
s = ""
For col = 0 To UBound(arr, 2)
s = s & " " & Right(" " & arr(row, col), 3)
Next
Debug.Print(s)
Next
End Sub
End ModuleWren
import "./fmt" for Conv, Fmt
var n = 5
var top = 0
var left = 0
var bottom = n - 1
var right = n - 1
var sz = n * n
var a = List.filled(sz, 0)
var i = 0
while (left < right) {
// work right, along top
var c = left
while (c <= right) {
a[top*n+c] = i
i = i + 1
c = c + 1
}
top = top + 1
// work down right side
var r = top
while (r <= bottom) {
a[r*n+right] = i
i = i + 1
r = r + 1
}
right = right - 1
if (top == bottom) break
// work left, along bottom
c = right
while (c >= left) {
a[bottom*n+c] = i
i = i + 1
c = c - 1
}
bottom = bottom - 1
r = bottom
// work up left side
while (r >= top) {
a[r*n+left] = i
i = i + 1
r = r - 1
}
left = left + 1
}
// center (last) element
a[top*n+left] = i
// print
var w = Conv.itoa(n*n - 1).count
i = 0
for (e in a) {
Fmt.write("$*d ", w, e)
if (i%n == n - 1) System.print()
i = i + 1
}- Output:
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
XPL0
def N=5;
int A(N,N);
int I, J, X, Y, Steps, Dir;
include c:\cxpl\codes;
[Clear;
I:= 0; X:= -1; Y:= 0; Steps:= N; Dir:= 0;
repeat for J:= 1 to Steps do
[case Dir&3 of
0: X:= X+1;
1: Y:= Y+1;
2: X:= X-1;
3: Y:= Y-1
other [];
A(X,Y):= I;
Cursor(X*3,Y); IntOut(0,I);
I:= I+1;
];
Dir:= Dir+1;
if Dir&1 then Steps:= Steps-1;
until Steps = 0;
Cursor(0,N);
]- Output:
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
Z80 Assembly
N is set at beginning of code (valid range 1..150-ish, then you soon run out of memory), sjasmplus syntax, CP/M executable:
; Spiral matrix in Z80 assembly (for CP/M OS - you can use `tnylpo` or `z88dk-ticks` on PC)
OPT --syntax=abf : OUTPUT "spiralmt.com" ; asm syntax for z00m's variant of sjasmplus
ORG $100
spiral_matrix:
ld a,5 ; N matrix size (argument for the code) (valid range: 1..150)
; setup phase
push af
ld l,a
ld h,0
add hl,hl
ld (delta_d),hl ; down-direction address delta = +N*2
neg
ld l,a
ld h,$FF
add hl,hl
ld (delta_u),hl ; up-direction address delta = -N*2
neg
ld hl,matrix
ld de,2 ; delta_r value to move right in matrix
ld bc,0 ; starting value
dec a ; first sequences will be N-1 long
jr z,.finish ; 1x1 doesn't need any sequence, just set last element
call set_sequence ; initial entry sequence has N-1 elements (same as two more)
; main loop - do twice same length sequence, then decrement length, until zero
.loop:
call set_sequence_twice
dec a
jr nz,.loop
.finish: ; whole spiral is set except last element, set it now
ld (hl),c
inc hl
ld (hl),b
; print matrix - reading it by POP HL (destructive, plus some memory ahead of matrix too)
pop de ; d = N
ld (.oldsp+1),sp
ld sp,matrix ; set stack to beginning of matrix (call/push does damage memory ahead)
ld c,d ; c = N (lines counter)
.print_rows:
ld b,d ; b = N (value per row counter)
.print_row:
pop hl
push de
push bc
call print_hl
pop bc
pop de
djnz .print_row
push de
call print_crlf
pop de
dec c
jr nz,.print_rows
.oldsp:
ld sp,0
rst 0 ; return to CP/M
print_crlf:
ld e,10
call print_char
ld e,13
jr print_char
print_hl:
ld b,' '
ld e,b
call print_char
ld de,-10000
call extract_digit
ld de,-1000
call extract_digit
ld de,-100
call extract_digit
ld de,-10
call extract_digit
ld a,l
print_digit:
ld b,'0'
add a,b
ld e,a
print_char:
push bc
push hl
ld c,2
call 5
pop hl
pop bc
ret
extract_digit:
ld a,-1
.digit_loop:
inc a
add hl,de
jr c,.digit_loop
sbc hl,de
or a
jr nz,print_digit
ld e,b
jr print_char
set_sequence_twice:
call set_sequence
set_sequence:
; A = length, HL = next_to_matrix, DE = delta to advance hl, BC = next_value
push af
.set_loop:
ld (hl),c
inc hl
ld (hl),b
dec hl ; [HL] = BC
add hl,de ; HL += DE
inc bc ; ++BC
dec a
jr nz,.set_loop
push hl ; change DE for next direction (right->down->left->up->right->...)
.d: ld hl,delta_d ; self-modify-code: pointer to next delta
ld e,(hl)
inc hl
ld d,(hl) ; de = address delta for next sequence
inc hl
ld a,low delta_u+2 ; if hl == delta_u+2 => reset it back to delta_r
cp l
jr nz,.next_delta
ld hl,delta_r
.next_delta:
ld (.d+1),hl ; self modify code pointer for next delta value
pop hl
pop af
ret
delta_r: dw +2 ; value to add to move right in matrix
delta_d: dw 0 ; value to add to move down in matrix (set to +N*2)
delta_l: dw -2 ; value to add to move left in matrix
delta_u: dw 0 ; value to add to move up in matrix (set to -N*2)
matrix:
; following memory is used for NxN matrix of uint16_t values (150x150 needs 45000 bytes)- Output:
$ tnylpo spiralmt.com
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
zkl
which turns out to be the same as Ruby
fcn spiralMatrix(n){
sm:=(0).pump(n,List,(0).pump(n,List,False).copy); //L(L(False,False..), L(F,F,..) ...)
drc:=Walker.cycle(T(0,1,0), T(1,0,1), T(0,-1,0), T(-1,0,1)); // deltas
len:=n; r:=0; c:=-1; z:=-1; while(len>0){ //or do(2*n-1){
dr,dc,dl:=drc.next();
do(len-=dl){ sm[r+=dr][c+=dc]=(z+=1); }
}
sm
}foreach n in (T(5,-1,0,1,2)){
spiralMatrix(n).pump(Console.println,fcn(r){ r.apply("%4d".fmt).concat() });
println("---");
}- Output:
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 --- --- --- 0 --- 0 1 3 2 ---
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