# Print NxN spiral of ascending numbers [closed]

The numbers should be printed with leading zeroes in a field with length = (number of digits of N^2).

Input (N):

4


Output:

01 12 11 10
02 13 16 09
03 14 15 08
04 05 06 07


I am interested in the algorithm and the cleanliness of the implementation. So, the white space does not count and the upper limit for N is 42.

• yes according to me. Commented Feb 9, 2011 at 16:15
• According to my calculations, the length of field is L = floor(log10(N^2)) + 1 Is this correct? Commented Feb 9, 2011 at 16:17
• What's the upper limit on N?
– user475
Commented Feb 10, 2011 at 8:26
• I am interested in the algorithm and the cleanliness of the implementation. So, let's don't bother with very big numbers and set the upper limit of N to 42 :) Commented Feb 10, 2011 at 9:00
• Was this motivated by the Ulam Spiral? (although your spiral is descending if viewed as starting on the inside)
– smci
Commented Jan 21, 2012 at 11:58

## Python

n=input()

matrix=[[j+1]*n for j in range(n)]

x=y=0
for i in range(n)[::-2]:
x+=i*4;y+=1

for j in range(i):
matrix[j+y-1][y]=x+j

matrix[y-1][y:y+i]=range(x,x-i,-1)

R=matrix[n-y][y-1]+1
matrix[n-y][y:n-y+1]=range(R,R+i)

for j in range(y,y+i-1):
matrix[j][n-y]=matrix[j-1][n-y]-1

for row in matrix:
print ' '.join(r.zfill(len(n*n)) for r in row)

• An approach that precalculate corner numbers. Eg, for 9x box, 32 56 72 80, which is (n-1)*4 where n is box sizes (9,7,5,3) in this case.
• Right side of those numbers are 1-, and top to bottom is 1+, so basically generate from left to right, top to bottom, bottom to right, right to top side.

$echo 9 | python codegolf-769-me.py 01 32 31 30 29 28 27 26 25 02 33 56 55 54 53 52 51 24 03 34 57 72 71 70 69 50 23 04 35 58 73 80 79 68 49 22 05 36 59 74 81 78 67 48 21 06 37 60 75 76 77 66 47 20 07 38 61 62 63 64 65 46 19 08 39 40 41 42 43 44 45 18 09 10 11 12 13 14 15 16 17  Other tests $ echo 2 | python codegolf-769-me.py
1 4
2 3

$echo 5 | python codegolf-769-me.py 01 16 15 14 13 02 17 24 23 12 03 18 25 22 11 04 19 20 21 10 05 06 07 08 09$ echo 10 | python codegolf-769-me.py
001 036 035 034 033 032 031 030 029 028
002 037 064 063 062 061 060 059 058 027
003 038 065 084 083 082 081 080 057 026
004 039 066 085 096 095 094 079 056 025
005 040 067 086 097 100 093 078 055 024
006 041 068 087 098 099 092 077 054 023
007 042 069 088 089 090 091 076 053 022
008 043 070 071 072 073 074 075 052 021
009 044 045 046 047 048 049 050 051 020
010 011 012 013 014 015 016 017 018 019


In Ruby:

N=gets.to_i

index = -N
width = N
result = []
n = 0
dir=-1

while n < N*N
dir = (dir + 1) % 4
dir_x, dir_y = [[0,1],[1,0],[0,-1],[-1,0]][dir]
width -= 1 if [1,3].include?(dir)

1.upto(width) { |m|
n += 1
index += dir_y * N + dir_x
result[index] = n
}
end

width = (N*N).to_s.size
result.each_slice(N) { |l|
print l.map {|n| "%0#{width}d" % n }.join(" "), "\n"
}


Test:

$ruby1.9 769.rb <<< 9 01 32 31 30 29 28 27 26 25 02 33 56 55 54 53 52 51 24 03 34 57 72 71 70 69 50 23 04 35 58 73 80 79 68 49 22 05 36 59 74 81 78 67 48 21 06 37 60 75 76 77 66 47 20 07 38 61 62 63 64 65 46 19 08 39 40 41 42 43 44 45 18 09 10 11 12 13 14 15 16 17  An other solution using calculations from here : N=gets.to_i r=[] tr=->x,y{ x+(N-1)/2 + (y+(N-1)/2+(N-1)%2)*N } r[tr[0,0]] = N*N 1.upto(N*N-1) { |n| shell = ((Math.sqrt(n)+1)/2).to_i leg = (n-(2*shell-1)**2)/(2*shell) element = (n-(2*shell-1)**2)-2*shell*leg-shell+1 x,y = [[element,-shell],[shell,element],[-element,shell],[-shell,-element]][leg] r[tr[x,y]] = N*N-n } r.each_slice(N) {|l| puts l.map { |n| "%0#{(N*N).to_s.size}d" % (n or 0) }.join(" ") }  Test: $ ruby1.9 769-2.rb <<< 5
01 16 15 14 13
02 17 24 23 12
03 18 25 22 11
04 19 20 21 10
05 06 07 08 09


In Python3:

n=int(input())
results = {}
val = 1
location = (0,0)
direction = (0,1)

def nxt():
return (location[0]+direction[0], location[1]+direction[1])

while val<=n*n:
if set([-1,n]).intersection(nxt()) or nxt() in results:
direction = (direction[1],direction[0]*-1)

results[location], location, val = str(val), nxt(), val+1

slen = len(str(n*n))
for y in range(n):
print( *[results[(x,y)].rjust(slen,'0') for x in range(n)] )


Sample Output for 7:

01 24 23 22 21 20 19
02 25 40 39 38 37 18
03 26 41 48 47 36 17
04 27 42 49 46 35 16
05 28 43 44 45 34 15
06 29 30 31 32 33 14
07 08 09 10 11 12 13


edit: A recursive solution - 263 Bytes

def a(m,s):
b,r,t=m-s*s+1,s-1,range
return[[[]],[[m]]][s]if s<2 else[[b]+list(t(b+4*r-1,b+3*r-1,-1))]+[[b+y+1]+a(m,s-2)[y]+[b+3*r-y-1]for y in t(s-2)]+[list(t(b+r,b+2*r+1))]
n=int(input())
for r in a(n*n,n):
print(*[str(x).zfill(len(str(n*n)))for x in r])

• Nice solution, I've checked it out at ideone.com/u43VJ , it works with Python3 (can you please note this). Thanks! Commented Feb 10, 2011 at 6:52

Java Solution

public static void main(String[] args) {
int INPUT = 5;
String[][] grid = new String[INPUT][INPUT];
int xDirection = 0;
int yDirection = 0;
int flag = 1;
for (int i = 0; i < INPUT * INPUT; i++) {
String temp = "";
for (int k = 0; k < (""+INPUT*INPUT).length() - ("" + (i + 1)).length(); k++) {
temp += "" + 0;
}
temp += (i + 1);

if (xDirection > INPUT-1)
{flag=2; yDirection++; xDirection--; i--; continue;}
else if (yDirection > INPUT -1)
{flag=3; yDirection--; xDirection--; i--; continue;}
else if (xDirection < 0)
{flag=4; xDirection++; yDirection--; i--; continue;}

if ( grid[xDirection][yDirection]==null ){
grid[xDirection][yDirection] = ""+temp;
}
else{
if (flag ==1 ) {
flag=2;
xDirection--;
}
else if (flag ==2){
flag=3;
yDirection--;
}
else if (flag==3){
flag=4;
xDirection++;
}
else{
flag=1;
yDirection++;
}
i--;
}
switch(flag){
case 1: xDirection++;break;
case 2: yDirection++;break;
case 3: xDirection--;break;
case 4: yDirection--; break;
}
}
for (int i = 0; i < INPUT; i++) {
for (int k = 0; k < INPUT; k++)
System.out.print(grid[i][k] + " ");
System.out.println();
}
}


sample output for input 10

001 036 035 034 033 032 031 030 029 028
002 037 064 063 062 061 060 059 058 027
003 038 065 084 083 082 081 080 057 026
004 039 066 085 096 095 094 079 056 025
005 040 067 086 097 100 093 078 055 024
006 041 068 087 098 099 092 077 054 023
007 042 069 088 089 090 091 076 053 022
008 043 070 071 072 073 074 075 052 021
009 044 045 046 047 048 049 050 051 020
010 011 012 013 014 015 016 017 018 019

• Cool, I have checked it out and it works: ideone.com/mLoJX Commented Feb 9, 2011 at 18:52
• But, it prints extra information, only the desired output is needed. And, it will be super-cool if it can be made less verbose. Commented Feb 9, 2011 at 18:54
• Also, the main function should be put in a class. Commented Feb 9, 2011 at 19:01
• Ah!..forgot to comment debugging sysouts :( Commented Feb 9, 2011 at 21:07
• maybe you can fix it in your code? Commented Feb 10, 2011 at 6:43

# Perl, 178 chars

Uses Math::Complex and maintains the current direction in a complex variable (1/i/-1/.i). Run with:

$perl -MMath::Complex spiral.pl  Put N in $l.

# $l = shift;$d=i;
$x=0; until($s{$x}){$s{$x}=++$n;
$x+=$d;
$d*=-i if Re($x)==Im($x)+(Re($x)<$l/2) ||Re($x)==$l-1-Im($x)
}
for$y(0..$l-1){
printf'%0'.length($l**2).'d ',$s{$_+i*$y}for 0..$l-1; print"\n" }  C #include<stdio.h> #include<math.h> int main() { int A[42][42],i,j,N,c=1,k; scanf("%d",&N); for (i = 0, j = N - 1 ; j >= 0 ; i++, j--) { for(k = i ; k < j; k++)A[i][k]=c++; for(k = i ; k < j; k++)A[k][j]=c++; for(k = j ; k > i; k--)A[j][k]=c++; for(k = j ; k > i; k--)A[k][i]=c++; } if (N%2) A[N/2][N/2]=c; for (i=0;i<N;i++) { for (j=0;j<N;j++) printf("%0*d ",((int)log10(N*N)+1),A[j][i]); printf("\n"); } }  ## Python 2.7: def spiral(n): rows = [[n * n]] current = n * n - 1 while current: rows = zip(*([range(current, current - len(rows[0]), -1)] + rows))[::-1] current -= len(rows) digits = len(str(n * n)) for row in rows: print" ".join(str(cell).zfill(digits) for cell in row) spiral(5)  ## PHP, 272 chars including comment Func-based, recursive version - more interesting for me as it better expresses intention. It works for distinct width and height too. <?php$n = $argv[1]; for($y = 0; $y<$n; $y++){ for($x = 0; $x<$n; $x++) printf("%02d ", f($n, $n,$x, $y)); echo "\n"; } function f($w, $h,$x, $y){ return ($y)
?$w + f($h - 1, $w,$y - 1, $w -$x - 1) //strip-off first row and "rotate"
:$x; }  Output: C:\www>php -f golfed_spiral.php 8 00 01 02 03 04 05 06 07 27 28 29 30 31 32 33 08 26 47 48 49 50 51 34 09 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  ## C#, 380-ish golfed I didn't bother pasting in the golfed version as I was pretty confident this wasn't going to break any records. But I wanted to give it a shot thinking about it a bit differently. Rather than write out each line or position as I come to it, I'm moving the cursor into position, writing out the starting center number, and spiraling out from there (which illustrated an interesting pattern of positions-to-move per direction change). There's a fair amount of character space wasted getting the console buffer to accept the larger values as well calculating the position for the upper left corner (which I'm sure can be improved). At any rate, it was an interesting exercise.  static void Main(string[] p) { int squareSize = 4; Console.BufferHeight = 300; Console.BufferWidth = 300; int maxTravel = 0; int currentTravel = 0; int travelCounter = 0; var a = squareSize % 2 == 0; int direction = a ? 2 : 0; int pad = squareSize * squareSize; int padLength = (pad + "").Length; int y = a ? (squareSize / 2) - 1 : (squareSize - 1) / 2; int x = a ? y + 1 : y; x = x + (x * padLength); for (int i = pad; i > 0; i--) { Console.SetCursorPosition(x, y); Console.Write((i + "").PadLeft(padLength, '0') + " "); switch (direction) { case 0: y--; break; case 1: x += padLength + 1; break; case 2: y++; break; case 3: x -= padLength + 1; break; } if (++currentTravel > maxTravel) { currentTravel = 0; direction = ++direction % 4; if (++travelCounter == 2) { travelCounter = 0; maxTravel++; } } } }  ### Ruby This isn't a particularly good golfable solution, but it might be of algorithmic interest. I've always been fascinated by a similar problem, namely, finding the clockwise spiral path through an NxM matrix. One really intuitive way of solving that problem is to keep rotating the matrix counterclockwise and peel it like an orange. I use a similar — albeit not as elegant — method to do the reverse: def spiral_matrix(n) matrix = Array.new(n) { Array.new(n) } path = [*1..n*n] padding = (n*n).to_s.size layer = 0 until path.empty? matrix[layer].map! { |l| l || path.shift } matrix = matrix.transpose.reverse layer += 1 unless matrix[layer].include?(nil) end matrix = matrix.transpose.reverse until matrix[0][0] == 1 matrix.transpose.each do |row| row.each do |l| print "%0#{padding}d" % l, ' ' end puts end end  ## Racket Just wanted to try it with a solution using close to 0 memory. No array, no nothing. The value can be generated for any position anytime. We could ask a spiral of any size (if what receives the output stream can handle it). In hope that someone ever needs gigantic spirals. Here's the code ; number of chars required to write x in base 10 ; defined for x > 0 (define log10 (λ (x) (inexact->exact (+ 1 (floor (/ (log x) (log 10))))))) ; tells the square number ; works for squares of both even and odd sizes ; outer square # = 0 (define square# (λ (x y size) ; x and y begin at 0 (min x y (- size 1 x) (- size 1 y)))) ; tells the number of values in a square (define square-val-qty (λ (sqr# size) ; size is the whole spiral size (let ((res (* 4 (- size (* 2 sqr#) 1)))) (cond ((zero? res) 1) (else res))))) ; at which value a square starts ; works for odd/even spirals (define square-1st-val (λ (sqr# size) (+ (* 4 sqr# (- size sqr#)) 1))) ; square size from spiral size (define square-side (λ (sqr# size) (- size (* 2 sqr#)))) (define 1+ (λ (n) (+ n 1))) (define 1- (λ (n) (- n 1))) ; calculates the position on the square (from 0) (define position-on-square (λ (x y size) (let* ((sqr# (square# x y size)) (sqr-x (- x sqr#)) (sqr-y (- y sqr#)) (sqr-side (square-side sqr# size))) (cond ((and (zero? sqr-x) (< sqr-y (1- sqr-side))) ; left part sqr-y) ((and (eq? sqr-y (1- sqr-side)) (< sqr-x (1- sqr-side))) ; bottom (+ (1- sqr-side) sqr-x)) ((and (not (eq? sqr-y 0)) (eq? sqr-x (1- sqr-side))) ; right (+ (* 2 (1- sqr-side)) (- sqr-side sqr-y 1))) (else ; top (+ (* 3 (1- sqr-side)) (- sqr-side sqr-x 1))))))) ; returns the spiral value at the given position (define spiral-value (λ (x y size) (+ (square-1st-val (square# x y size) size) (position-on-square x y size)))) ; pads a string with char (define left-pad (λ (str char width) (cond ((< (string-length str) width) (left-pad (string-append (string char) str) char width)) (else str)))) ; draws a spiral! (define draw-spiral (λ (size) (let ((x 0) (y 0) (width (log10 (* size size)))) (letrec ((draw (λ () (printf "~a " (left-pad (number->string (spiral-value x y size)) #\0 width)) (cond ((and (eq? x (1- size)) (eq? y (1- size))) (printf "~n~n")) ((eq? x (1- size)) (set! x 0) (set! y (1+ y)) (printf "~n") (draw)) (else (set! x (1+ x)) (draw)))))) (draw)))))  Testing with this (draw-spiral 1) (draw-spiral 2) (draw-spiral 3) (draw-spiral 4) (draw-spiral 5) (draw-spiral 15) (draw-spiral 16)  Results in output 1 1 4 2 3 1 8 7 2 9 6 3 4 5 01 12 11 10 02 13 16 09 03 14 15 08 04 05 06 07 01 16 15 14 13 02 17 24 23 12 03 18 25 22 11 04 19 20 21 10 05 06 07 08 09 001 056 055 054 053 052 051 050 049 048 047 046 045 044 043 002 057 104 103 102 101 100 099 098 097 096 095 094 093 042 003 058 105 144 143 142 141 140 139 138 137 136 135 092 041 004 059 106 145 176 175 174 173 172 171 170 169 134 091 040 005 060 107 146 177 200 199 198 197 196 195 168 133 090 039 006 061 108 147 178 201 216 215 214 213 194 167 132 089 038 007 062 109 148 179 202 217 224 223 212 193 166 131 088 037 008 063 110 149 180 203 218 225 222 211 192 165 130 087 036 009 064 111 150 181 204 219 220 221 210 191 164 129 086 035 010 065 112 151 182 205 206 207 208 209 190 163 128 085 034 011 066 113 152 183 184 185 186 187 188 189 162 127 084 033 012 067 114 153 154 155 156 157 158 159 160 161 126 083 032 013 068 115 116 117 118 119 120 121 122 123 124 125 082 031 014 069 070 071 072 073 074 075 076 077 078 079 080 081 030 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 001 060 059 058 057 056 055 054 053 052 051 050 049 048 047 046 002 061 112 111 110 109 108 107 106 105 104 103 102 101 100 045 003 062 113 156 155 154 153 152 151 150 149 148 147 146 099 044 004 063 114 157 192 191 190 189 188 187 186 185 184 145 098 043 005 064 115 158 193 220 219 218 217 216 215 214 183 144 097 042 006 065 116 159 194 221 240 239 238 237 236 213 182 143 096 041 007 066 117 160 195 222 241 252 251 250 235 212 181 142 095 040 008 067 118 161 196 223 242 253 256 249 234 211 180 141 094 039 009 068 119 162 197 224 243 254 255 248 233 210 179 140 093 038 010 069 120 163 198 225 244 245 246 247 232 209 178 139 092 037 011 070 121 164 199 226 227 228 229 230 231 208 177 138 091 036 012 071 122 165 200 201 202 203 204 205 206 207 176 137 090 035 013 072 123 166 167 168 169 170 171 172 173 174 175 136 089 034 014 073 124 125 126 127 128 129 130 131 132 133 134 135 088 033 015 074 075 076 077 078 079 080 081 082 083 084 085 086 087 032 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031  Quite CPU intensive compared to precalculated matrices if you need the whole spiral, but might be useful. Who knows! E.g.: (spiral-value 1234567 7654321 234567890) -> 1152262488724319  Didn't golf it... It's quite small despite the appearance. I used long names and comments. # Python 2, 800 bytes from collections import namedtuple Crd = namedtuple('Crd',['row','col','val']) C1 = Crd(1,1,1) def add(c1, c2): return Crd(c1.row + c2.row, c1.col + c2.col, c1.val + c2.val) def deltas(l): for i in xrange(1,l): yield Crd(0,1,1) for i in xrange(1,l): yield Crd(1,0,1) for i in xrange(1,l): yield Crd(0,-1,1) for i in xrange(1,l-1): yield Crd(-1,0,1) def ring(c, l): yield c for d in deltas(l): c = add(c, d) yield c def spiral(n): cur = C1 while n > 0: for c in ring(cur, n): yield c cur = c cur = add(cur, Crd(0,1,1)) n -= 2 n = input() fmt = '%' + str(len(str(long(n*n)))) + 'd' crds = sorted(list(spiral(n))) for r in xrange(1,n+1): print ' '.join([fmt % c.val for c in crds if c.row == r])  Try it online! A few years back a friend of mine was asked this question in an interview. They told me about it at our family's Thanksgiving dinner so I think of this as the "Thanksgiving problem". # PHP, 172 171+1 bytes, 24 operations creates an array walking the indexes through a spiral; then prints the result. // 1) input squared -> 2) string length -> 3)$e = length of maximum number
for($e=strlen($argn**2);
// 4) decrement input (line length) every second iteration; 5) loop while input>0
$argn-=$i%2;
// 24) post-increment iteration counter $i$i++)
// 6,7,8) loop through current line
for($p=$argn;$p--;)$r
// 9) $i=$i modulo 4; 10,11) (1-$i)%2 == [1,0,-1,0][$i] -> 12) increment/decrement $y coordinate3 [$y+=(1-$i%=4)%2] // 13,14) (2-$i)%2 == [0,1,0,-1][$i] -> 15) increment/decrement$x coordinate
[$x+=(2-$i)%2]
// 16) print formatted to string; 17) assign to field [$y,$x] in $r =sprintf("%0{$e}d ",++$n); // 18) pre-increment row counter$z; 19) loop while row exists
for(;$r[++$z];
// 21) join row; 22) append newline; 23) print
print join($r[$z])."\n")
// 20) sort row by indexes
ksort($r[$z]);


Run as pipe with -nR or try it online.

Add one assignment to save five bytes: replace the final loop with

for(;$s=$r[++$z];print join($s)."\n")ksort(\$s);


Sample code : This works for 4x5 but failing 3x5

while (k < m && l < n) { /* Print the first row from the remaining rows */ for (i = l; i < n; ++i) { printf("%d ", a[k][i]); } k++;

    /* Print the last column from the remaining columns */
for (i = k; i < m; ++i)
{
printf("%d ", a[i][n-1]);
}
n--;

/* Print the last row from the remaining rows */
if ( k < m)
{
for (i = n-1; i >= l; --i)
{
printf("%d ", a[m-1][i]);
}
m--;
}

/* Print the first column from the remaining columns */
if (l < n)
{
for (i = m-1; i >= k; --i)
{
printf("%d ", a[i][l]);
}
l++;
}
}

• Welcome to PPCG! This is code golf. Please show some effort to solve the problem in as few characters as possible. In particular, you can use single-character variable names, remove unnecessary whitespace and comments. Please also include the byte count of your submission after you've reduced it. You can always keep the readable version in addition to the golfed one. Commented Feb 18, 2015 at 22:04