Zig-zag matrix

From Rosetta Code
Task
Zig-zag matrix
You are encouraged to solve this task according to the task description, using any language you may know.

Produce a zig-zag array. A zig-zag array is a square arrangement of the first N2 integers, where the numbers increase sequentially as you zig-zag along the anti-diagonals of the array.
For a graphical representation, see JPG zigzag (JPG uses such arrays to encode images).

For example, given 5, produce this array:

 0  1  5  6 14
 2  4  7 13 15
 3  8 12 16 21
 9 11 17 20 22
10 18 19 23 24
See also Spiral matrix

360 Assembly

<lang 360asm>* Zig-zag matrix 15/08/2015 ZIGZAGMA CSECT

        USING  ZIGZAGMA,R12       set base register
        LR     R12,R15            establish addressability 
        LA     R9,N               n : matrix size
        LA     R6,1               i=1
        LA     R7,1               j=1
        LR     R11,R9             n
        MR     R10,R9             *n
        BCTR   R11,0              R11=n**2-1
        SR     R8,R8              k=0

LOOPK CR R8,R11 do k=0 to n**2-1

        BH     ELOOPK             k>limit
        LR     R1,R6              i
        BCTR   R1,0               -1
        MR     R0,R9              *n
        LR     R2,R7              j
        BCTR   R2,0               -1
        AR     R1,R2              (i-1)*n+(j-1)
        SLA    R1,1               index=((i-1)*n+j-1)*2
        STH    R8,T(R1)           t(i,j)=k
        LR     R2,R6              i
        AR     R2,R7              i+j
        LA     R1,2               2
        SRDA   R2,32              shift right r1 to r2
        DR     R2,R1              (i+j)/2
        LTR    R2,R2              if mod(i+j,2)=0
        BNZ    ELSEMOD
        CR     R7,R9              if j<n
        BNL    ELSE1
        LA     R7,1(R7)           j=j+1
        B      EIF1

ELSE1 LA R6,2(R6) i=i+2 EIF1 CH R6,=H'1' if i>1

        BNH    NOT1
        BCTR   R6,0               i=i-1

NOT1 B NOT2 ELSEMOD CR R6,R9 if i<n

        BNL    ELSE2
        LA     R6,1(R6)           i=i+1
        B      EIF2

ELSE2 LA R7,2(R7) j=j+2 EIF2 CH R7,=H'1' if j>1

        BNH    NOT2
        BCTR   R7,0               j=j-1

NOT2 LA R8,1(R8) k=k+1

        B      LOOPK

ELOOPK LA R6,1 end k; i=1 LOOPI CR R6,R9 do i=1 to n

        BH     ELOOPI             i>n
        LA     R10,0              ibuf=0  buffer index
        MVC    BUFFER,=CL80' '
        LA     R7,1               j=1

LOOPJ CR R7,R9 do j=1 to n

        BH     ELOOPJ             j>n
        LR     R1,R6              i
        BCTR   R1,0               -1
        MR     R0,R9              *n
        LR     R2,R7              j
        BCTR   R2,0               -1
        AR     R1,R2              (i-1)*n+(j-1)
        SLA    R1,1               index=((i-1)*n+j-1)*2
        LH     R2,T(R1)           t(i,j)
        LA     R3,BUFFER
        AR     R3,R10
        XDECO  R2,XDEC            edit t(i,j) length=12
        MVC    0(4,R3),XDEC+8     move in buffer length=4
        LA     R10,4(R10)         ibuf=ibuf+1
        LA     R7,1(R7)           j=j+1
        B      LOOPJ

ELOOPJ XPRNT BUFFER,80 end j

        LA     R6,1(R6)           i=i+1
        B      LOOPI

ELOOPI XR R15,R15 end i; return_code=0

        BR     R14                return to caller

N EQU 5 matrix size BUFFER DS CL80 XDEC DS CL12 T DS (N*N)H t(n,n) matrix

        YREGS
        END    ZIGZAGMA</lang>
Output:
   0   1   5   6  14
   2   4   7  13  15
   3   8  12  16  21
   9  11  17  20  22
  10  18  19  23  24

ActionScript

<lang as> package {

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

} </lang>

Ada

<lang ada>with Ada.Text_IO; use Ada.Text_IO;

procedure Test_Zig_Zag is

  type Matrix is array (Positive range <>, Positive range <>) of Natural;
  function Zig_Zag (Size : Positive) return Matrix is
     Data : Matrix (1..Size, 1..Size);
     I, J : Integer := 1;
  begin
     Data (1, 1) := 0;
     for Element in 1..Size**2 - 1 loop
        if (I + J) mod 2 = 0 then
           -- Even stripes
           if J < Size then
              J := J + 1;
           else
              I := I + 2;
           end if;
           if I > 1 then
              I := I - 1;
           end if;
        else
           -- Odd stripes
           if I < Size then
              I := I + 1;
           else
              J := J + 2;
           end if;
           if J > 1 then
              J := J - 1;
           end if;
        end if;
        Data (I, J) := Element;
     end loop;
     return Data;
  end Zig_Zag;
  
  procedure Put (Data : Matrix) is
  begin
     for I in Data'Range (1) loop
        for J in Data'Range (2) loop
           Put (Integer'Image (Data (I, J)));
        end loop;
        New_Line;
     end loop;
  end Put;

begin

  Put (Zig_Zag (5));

end Test_Zig_Zag;</lang> The function Zig_Zag generates a square matrix filled as requested by the task.

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

ALGOL 68

Translation of: D
Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386

<lang algol68>PROC zig zag = (INT n)[,]INT: (

   PROC move = (REF INT i, j)VOID: (
       IF j < n THEN
           i := ( i <= 1 | 1 | i-1 );
           j +:= 1
       ELSE
           i +:= 1
       FI
   );

   [n, n]INT a;
   INT x:=LWB a, y:=LWB a;

   FOR v FROM 0 TO n**2-1 DO
       a[y, x] := v;
       IF ODD (x + y) THEN
           move(x, y)
       ELSE
           move(y, x)
       FI
   OD;
   a

);

INT dim = 5;

  1. IF formatted transput possible THEN
 FORMAT d = $z-d$;
 FORMAT row = $"("n(dim-1)(f(d)",")f(d)")"$;
 FORMAT block = $"("n(dim-1)(f(row)","lx)f(row)")"l$;
 printf((block, zig zag(dim)))

ELSE#

 [,]INT result = zig zag(dim);
 FOR i TO dim DO
   print((result[i,], new line))
 OD
  1. FI#</lang>
Output:
With formatted transput possible, e.g. ALGOL 68G not formatted transput possible, e.g. ELLA ALGOL 68
((  0,  1,  5,  6, 14),
 (  2,  4,  7, 13, 15),
 (  3,  8, 12, 16, 21),
 (  9, 11, 17, 20, 22),
 ( 10, 18, 19, 23, 24))
         +0          +1          +5          +6         +14
         +2          +4          +7         +13         +15
         +3          +8         +12         +16         +21
         +9         +11         +17         +20         +22
        +10         +18         +19         +23         +24

APL

Works with: Dyalog APL
Translation of: J

<lang apl> zz ← {⍵⍴⎕IO-⍨⍋⊃,/{(2|⍴⍵):⌽⍵⋄⍵}¨(⊂w)/¨⍨w{↓⍵∘.=⍨∪⍵}+/[1]⍵⊤w←⎕IO-⍨⍳×/⍵} ⍝ General zigzag (any rectangle)

     zzSq ←  {zz,⍨⍵}                                                           ⍝  Square zigzag
     zzSq 5
0  1  5  6 14
2  4  7 13 15
3  8 12 16 21
9 11 17 20 22

10 18 19 23 24</lang>

AppleScript

Here's a vector & matrix boundary detection approach to the Zig-zap matrix: <lang AppleScript>set n to 5 -- Size of zig-zag matrix (n^2 cells).

-- Create an empty matrix. set m to {} repeat with i from 1 to n set R to {} repeat with j from 1 to n set end of R to 0 end repeat set end of m to R end repeat

-- Populate the matrix in a zig-zag manner. set {x, y, v, d} to {1, 1, 0, 1} repeat while v < (n ^ 2) if 1 ≤ x and x ≤ n and 1 ≤ y and y ≤ n then set {m's item y's item x, x, y, v} to {v, x + d, y - d, v + 1} else if x > n then set {x, y, d} to {n, y + 2, -d} else if y > n then set {x, y, d} to {x + 2, n, -d} else if x < 1 then set {x, y, d} to {1, y, -d} else if y < 1 then set {x, y, d} to {x, 1, -d} end if end repeat --> R = {{0, 1, 5, 6, 14}, {2, 4, 7, 13, 15}, {3, 8, 12, 16, 21}, {9, 11, 17, 20, 22}, {10, 18, 19, 23, 24}}

-- Reformat the matrix into a table for viewing. repeat with i in m repeat with j in i set j's contents to (characters -(length of (n ^ 2 as string)) thru -1 of (" " & j)) as string end repeat set end of i to return end repeat return return & m as string</lang> But this can be improved upon by building the matrix by populating empty AppleScript lists (it's about 50% faster when n=50):<lang AppleScript>set n to 5

set m to {} repeat with i from 1 to n set end of m to {} -- Built a foundation for the matrix out of n empty lists. end repeat

set {v, d, i} to {0, -1, 1} repeat while v < n ^ 2 if length of m's item i < n then set {end of m's item i, i, v} to {f(v, n), i + d, v + 1} if i < 1 then set {i, d} to {1, -d} else if i > n then set {i, d} to {n, -d} else if i > 1 and (count of m's item (i - 1)) = 1 then set d to -d end if else set {i, d} to {i + 1, 1} end if end repeat

-- Handler/function to format the cells on the fly. on f(v, n) return (characters -(length of (n ^ 2 as string)) thru -1 of (" " & v)) as string end f

-- Reformat the matrix into a table for viewing. set text item delimiters to "" repeat with i in m set i's contents to (i as string) & return end repeat return return & m as string </lang>

Output:
for both scripts is
"
  0   1   5   6  14
  2   4   7  13  15
  3   8  12  16  21
  9  11  17  20  22
 10  18  19  23  24
"

Applesoft BASIC

<lang ApplesoftBasic>100 S = 5 110 S2 = S ^ 2 : REM SQUARED 120 H = S2 / 2 : REM HALFWAY 130 S2 = S2 - 1 140 DX = 1 : REM INITIAL 150 DY = 0 : REM DIRECTION 160 N = S - 1 170 DIM A%(N, N)

200 FOR I = 0 TO H 210 A%(X, Y) = I 220 A%(N - X, N - Y) = S2 - I 230 X = X + DX 240 Y = Y + DY 250 IF Y = 0 THEN DY = DY + 1 : IF DY THEN DX = -DX 260 IF X = 0 THEN DX = DX + 1 : IF DX THEN DY = -DY 270 NEXT I

300 FOR Y = 0 TO N 310 FOR X = 0 TO N 320 IF X THEN PRINT TAB(X * (LEN(STR$(S2)) + 1) + 1); 330 PRINT A%(X, Y); 340 NEXT X 350 PRINT 360 NEXT Y</lang>

AutoHotkey

Translation of: lisp

contributed by Laszlo on the ahk forum. <lang AutoHotkey>n = 5  ; size v := x := y := 1  ; initial values Loop % n*n {  ; for every array element

  a_%x%_%y% := v++             ; assign the next index
  If ((x+y)&1)                 ; odd diagonal
     If (x < n)                ; while inside the square
        y -= y<2 ? 0 : 1, x++  ; move right-up
     Else y++                  ; on the edge increment y, but not x: to even diagonal
  Else                         ; even diagonal
     If (y < n)                ; while inside the square
        x -= x<2 ? 0 : 1, y++  ; move left-down
     Else x++                  ; on the edge increment x, but not y: to odd diagonal

}

Loop %n% {  ; generate printout

  x := A_Index                 ; for each row
  Loop %n%                     ; and for each column
     t .= a_%x%_%A_Index% "`t" ; attach stored index
  t .= "`n"                    ; row is complete

} MsgBox %t%  ; show output</lang>

AutoIt

<lang autoit>

  1. include <Array.au3>

$Array = ZigZag(5) _ArrayDisplay($Array)

Func ZigZag($int) Local $av_array[$int][$int] Local $x = 1, $y = 1 For $I = 0 To $int ^ 2 -1 $av_array[$x-1][$y-1] = $I If Mod(($x + $y), 2) = 0 Then ;Even if ($y < $int) Then $y += 1 Else $x += 2 EndIf if ($x > 1) Then $x -= 1 Else ; ODD if ($x < $int) Then $x += 1 Else $y += 2 EndIf If $y > 1 Then $y -= 1 EndIf Next Return $av_array EndFunc  ;==>ZigZag </lang>

AWK

<lang AWK>

  1. syntax: GAWK -f ZIG-ZAG_MATRIX.AWK [-v offset={0|1}] [size]

BEGIN {

  1. offset: "0" prints 0 to size^2-1 while "1" prints 1 to size^2
   offset = (offset == "") ? 0 : offset
   size = (ARGV[1] == "") ? 5 : ARGV[1]
   if (offset !~ /^[01]$/) { exit(1) }
   if (size !~ /^[0-9]+$/) { exit(1) }
   width = length(size ^ 2 - 1 + offset) + 1
   i = j = 1
   for (n=0; n<=size^2-1; n++) { # build array
     arr[i-1,j-1] = n + offset
     if ((i+j) % 2 == 0) {
       if (j < size) { j++ } else { i+=2 }
       if (i > 1) { i-- }
     }
     else {
       if (i < size) { i++ } else { j+=2 }
       if (j > 1) { j-- }
     }
   }
   for (row=0; row<size; row++) { # show array
     for (col=0; col<size; col++) {
       printf("%*d",width,arr[row,col])
     }
     printf("\n")
   }
   exit(0)

} </lang>

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

BBC BASIC

<lang bbcbasic> Size% = 5

     DIM array%(Size%-1,Size%-1)
     
     i% = 1
     j% = 1
     FOR e% = 0 TO Size%^2-1
       array%(i%-1,j%-1) = e%
       IF ((i% + j%) AND 1) = 0 THEN
         IF j% < Size% j% += 1 ELSE i% += 2
         IF i% > 1 i% -= 1
       ELSE
         IF i% < Size% i% += 1 ELSE j% += 2
         IF j% > 1 j% -= 1
       ENDIF
     NEXT
     
     @% = &904
     FOR row% = 0 TO Size%-1
       FOR col% = 0 TO Size%-1
         PRINT array%(row%,col%);
       NEXT
       PRINT
     NEXT row%</lang>
Output:
   0   1   5   6  14
   2   4   7  13  15
   3   8  12  16  21
   9  11  17  20  22
  10  18  19  23  24

Befunge

The size, N, is specified by the first value on the stack - 5 in the example below. The upper limit is constrained only by the range of the playfield cells used for variables, since we're using an algorithm that calculates the values on the fly rather than building them up in memory. On an 8 bit interpreter this means an upper limit of at least 127, but with an extended cell range the size of N can be almost unlimited.

<lang befunge>>> 5 >>00p0010p:1:>20p030pv >0g-:0`*:*-:00g:*1-55+/>\55+/:v v:,*84< v:++!\**2p01:+1g01:g02$$_>>#^4#00#+p#1:#+1#g0#0g#3<^/+ 55\_$:>55+/\| >55+,20g!00g10g`>#^_$$$@^!`g03g00!g04++**2p03:+1g03!\*+1*2g01:g04.$<</lang>

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

C

<lang c>#include <stdio.h>

  1. include <stdlib.h>

int main(int c, char **v) { int i, j, m, n, *s;

/* default size: 5 */ if (c < 2 || ((m = atoi(v[1]))) <= 0) m = 5;

/* alloc array*/ s = malloc(sizeof(int) * m * m);

for (i = n = 0; i < m * 2; i++) for (j = (i < m) ? 0 : i-m+1; j <= i && j < m; j++) s[(i&1)? j*(m-1)+i : (i-j)*m+j ] = n++;

for (i = 0; i < m * m; putchar((++i % m) ? ' ':'\n')) printf("%3d", s[i]);

/* free(s) */ return 0; }</lang>

Output:
% ./a.out 7
  0  1  5  6 14 15 27
  2  4  7 13 16 26 28
  3  8 12 17 25 29 38
  9 11 18 24 30 37 39
 10 19 23 31 36 40 45
 20 22 32 35 41 44 46
 21 33 34 42 43 47 48

C++

<lang cpp>#include <vector>

  1. include <memory> // for auto_ptr
  2. include <cmath> // for the log10 and floor functions
  3. include <iostream>
  4. include <iomanip> // for the setw function

using namespace std;

typedef vector< int > IntRow; typedef vector< IntRow > IntTable;

auto_ptr< IntTable > getZigZagArray( int dimension ) { auto_ptr< IntTable > zigZagArrayPtr( new IntTable( dimension, IntRow( dimension ) ) );

// fill along diagonal stripes (oriented as "/") int lastValue = dimension * dimension - 1; int currNum = 0; int currDiag = 0; int loopFrom; int loopTo; int i; int row; int col; do { if ( currDiag < dimension ) // if doing the upper-left triangular half { loopFrom = 0; loopTo = currDiag; } else // doing the bottom-right triangular half { loopFrom = currDiag - dimension + 1; loopTo = dimension - 1; }

for ( i = loopFrom; i <= loopTo; i++ ) { if ( currDiag % 2 == 0 ) // want to fill upwards { row = loopTo - i + loopFrom; col = i; } else // want to fill downwards { row = i; col = loopTo - i + loopFrom; }

( *zigZagArrayPtr )[ row ][ col ] = currNum++; }

currDiag++; } while ( currDiag <= lastValue );

return zigZagArrayPtr; }

void printZigZagArray( const auto_ptr< IntTable >& zigZagArrayPtr ) { size_t dimension = zigZagArrayPtr->size();

int fieldWidth = static_cast< int >( floor( log10( static_cast< double >( dimension * dimension - 1 ) ) ) ) + 2;

size_t col; for ( size_t row = 0; row < dimension; row++ ) { for ( col = 0; col < dimension; col++ ) cout << setw( fieldWidth ) << ( *zigZagArrayPtr )[ row ][ col ]; cout << endl; } }

int main() { printZigZagArray( getZigZagArray( 5 ) ); }</lang>

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

C#

<lang csharp>public static int[,] ZigZag(int n) {

   int[,] result = new int[n, n];
   int i = 0, j = 0;
   int d = -1; // -1 for top-right move, +1 for bottom-left move
   int start = 0, end = n * n - 1;
   do
   {
       result[i, j] = start++;
       result[n - i - 1, n - j - 1] = end--;
       i += d; j -= d;
       if (i < 0)
       {
           i++; d = -d; // top reached, reverse
       }
       else if (j < 0)
       {
           j++; d = -d; // left reached, reverse
       }
   } while (start < end);
   if (start == end)
       result[i, j] = start;
   return result;

}</lang>

Clojure

Purely functional approach. <lang Clojure>(defn partitions [sizes coll]

 (lazy-seq
  (when-let [n (first sizes)]
    (when-let [s (seq coll)]
      (cons (take n coll)

(partitions (next sizes) (drop n coll)))))))

(defn take-from [n colls]

 (lazy-seq
  (when-let [s (seq colls)]
    (let [[first-n rest-n] (split-at n s)]
      (cons (map first first-n)

(take-from n (concat (filter seq (map rest first-n)) rest-n)))))))

(defn zig-zag [n]

 (->> (partitions (concat (range 1 (inc n)) (range (dec n) 0 -1)) (range (* n n)))
      (map #(%1 %2) (cycle [reverse identity]) ,)
      (take-from n ,)))

user> (zig-zag 5) (( 0 1 5 6 14)

( 2  4  7 13 15)
( 3  8 12 16 21)
( 9 11 17 20 22)
(10 18 19 23 24))

user> (zig-zag 6) (( 0 1 5 6 14 15)

( 2  4  7 13 16 25)
( 3  8 12 17 24 26)
( 9 11 18 23 27 32)
(10 19 22 28 31 33)
(20 21 29 30 34 35))</lang>

CoffeeScript

<lang coffeescript>

  1. Calculate a zig-zag pattern of numbers like so:
  2. 0 1 5
  3. 2 4 6
  4. 3 7 8
  5. There are many interesting ways to solve this; we
  6. try for an algebraic approach, calculating triangle
  7. areas, so that me minimize space requirements.

zig_zag_value = (x, y, n) ->

 upper_triangle_zig_zag = (x, y) ->
   # calculate the area of the triangle from the prior
   # diagonals
   diag = x + y
   triangle_area = diag * (diag+1) / 2
   # then add the offset along the diagonal
   if diag % 2 == 0
     triangle_area + y
   else
     triangle_area + x
   
 if x + y < n
   upper_triangle_zig_zag x, y
 else
   # For the bottom right part of the matrix, we essentially
   # use reflection to count backward.
   bottom_right_cell = n * n - 1
   n -= 1
   v = upper_triangle_zig_zag(n-x, n-y)
   bottom_right_cell - v
   

zig_zag_matrix = (n) ->

 row = (i) -> (zig_zag_value i, j, n for j in [0...n])
 (row i for i in [0...n])

do ->

 for n in [4..6]
   console.log "---- n=#{n}"
   console.log zig_zag_matrix(n)
   console.log "\n"

</lang>

Output:
> coffee zigzag.coffee 
---- n=4
[ [ 0, 1, 5, 6 ],
  [ 2, 4, 7, 12 ],
  [ 3, 8, 11, 13 ],
  [ 9, 10, 14, 15 ] ]


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


---- n=6
[ [ 0, 1, 5, 6, 14, 15 ],
  [ 2, 4, 7, 13, 16, 25 ],
  [ 3, 8, 12, 17, 24, 26 ],
  [ 9, 11, 18, 23, 27, 32 ],
  [ 10, 19, 22, 28, 31, 33 ],
  [ 20, 21, 29, 30, 34, 35 ] ]


Common Lisp

Translation of: Java
(but with zero-based indexes and combining the even and odd cases)

<lang lisp>(defun zigzag (n)

 (flet ((move (i j)
          (if (< j (1- n))
              (values (max 0 (1- i)) (1+ j))
              (values (1+ i) j))))
   (loop with a = (make-array (list n n) :element-type 'integer)
         with x = 0
         with y = 0
         for v from 0 below (* n n)
         do (setf (aref a x y) v)
            (if (evenp (+ x y))
                (setf (values x y) (move x y))
                (setf (values y x) (move y x)))
         finally (return a))))</lang>

An alternative approach

<lang lisp>

ZigZag
Nigel Galloway.
June 4th., 2012

(defun ZigZag (COLS)

 (let ((cs 2) (st '(1 2)) (dx '(-1 1)))
   (defun new_cx (i)
     (setq st (append st (list (setq cs (+ cs (* 2 i))) (setq cs (+ 1 cs))))
           dx (append dx '(-1 1))))
   (do ((i 2 (+ 2 i))) ((>= i COLS)) (new_cx i))
   (do ((i (- COLS 1 (mod COLS 2)) (+ -2 i))) ((<= i 0)) (new_cx i))
   (do ((i 0 (+ 1 i))) ((>= i COLS))
     (format t "~%")
     (do ((j i (+ 1 j))) ((>= j (+ COLS i)))
       (format t "~3d" (nth j st))
       (setf (nth j st) (+ (nth j st) (nth j dx))))))) 

</lang> (ZigZag 5) Produces:

  1  2  6  7 15
  3  5  8 14 16
  4  9 13 17 22
 10 12 18 21 23
 11 19 20 24 25

(ZigZag 8) Produces:

  1  2  6  7 15 16 28 29
  3  5  8 14 17 27 30 43
  4  9 13 18 26 31 42 44
 10 12 19 25 32 41 45 54
 11 20 24 33 40 46 53 55
 21 23 34 39 47 52 56 61
 22 35 38 48 51 57 60 62
 36 37 49 50 58 59 63 64

(ZigZag 9) Produces:

  1  2  6  7 15 16 28 29 45
  3  5  8 14 17 27 30 44 46
  4  9 13 18 26 31 43 47 60
 10 12 19 25 32 42 48 59 61
 11 20 24 33 41 49 58 62 71
 21 23 34 40 50 57 63 70 72
 22 35 39 51 56 64 69 73 78
 36 38 52 55 65 68 74 77 79
 37 53 54 66 67 75 76 80 81

D

Translation of: Common Lisp

<lang d>int[][] zigZag(in int n) pure nothrow @safe {

   static void move(in int n, ref int i, ref int j)
   pure nothrow @safe @nogc {
       if (j < n - 1) {
           if (i > 0) i--;
           j++;
       } else
           i++;
   }
   auto a = new int[][](n, n);
   int x, y;
   foreach (v; 0 .. n ^^ 2) {
       a[y][x] = v;
       (x + y) % 2 ? move(n, x, y) : move(n, y, x);
   }
   return a;

}

void main() {

   import std.stdio;
   writefln("%(%(%2d %)\n%)", 5.zigZag);

}</lang>

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

Alternative Version

Translation of: Scala

Same output. <lang d>import std.stdio, std.algorithm, std.range, std.array;

int[][] zigZag(in int n) pure nothrow {

   static struct P2 { int x, y; }
   const L = iota(n ^^ 2).map!(i => P2(i % n, i / n)).array
             .sort!q{ (a.x + a.y == b.x + b.y) ?
                      ((a.x + a.y) % 2 ? a.y < b.y : a.x < b.x) :
                      (a.x + a.y) < (b.x + b.y) }.release;
   auto result = new typeof(return)(n, n);
   foreach (immutable i, immutable p; L)
       result[p.y][p.x] = i;
   return result;

}

void main() {

   writefln("%(%(%2d %)\n%)", 5.zigZag);

}</lang>

E

First, some tools originally written for Spiral (only the array is used):

/** 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 }
  }
}
Then the code.
Translation of: D

<lang e>def zigZag(n) {

 def move(&i, &j) {
     if (j < (n - 1)) {
         i := 0.max(i - 1)
         j += 1
     } else {
         i += 1
     }
 }
 def array := makeFlex2DArray(n, n)
 var x := 0
 var y := 0
 for i in 1..n**2 {
     array[y, x] := i
     if ((x + y) % 2 == 0) {
         move(&x, &y)
     } else {
         move(&y, &x)
     }
 }
 return array

}</lang>

Elixir

<lang elixir>defmodule RC do

 require Integer
 def zigzag(n) do
   indices = for x <- 1..n, y <- 1..n, do: {x,y}
   sorted = Enum.sort_by(indices, fn{x,y}->{x+y, if(Integer.is_even(x+y), do: y, else: x)} end)
   sorted2 = Enum.sort(Enum.with_index(sorted))
   Enum.each(sorted2, fn {{_x,y},i} ->
     IO.write "#{i} "
     if y==n, do: IO.puts ""
   end)
 end

end

RC.zigzag(5)</lang>

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

Erlang

<lang Erlang> -module( zigzag ).

-export( [matrix/1, task/0] ).

matrix( N ) -> {{_X_Y, N}, Proplist} = lists:foldl( fun matrix_as_proplist/2, {{{0, 0}, N}, []}, lists:seq(0, (N * N) - 1) ), [columns( X, Proplist ) || X <- lists:seq(0, N - 1)].

task() -> matrix( 5 ).


columns( Column, Proplist ) -> lists:sort( [Value || {{_X, Y}, Value} <- Proplist, Y =:= Column] ).

matrix_as_proplist( N, {{X_Y, Max}, Acc} ) -> Next = next_indexes( X_Y, Max ), {{Next, Max}, [{X_Y, N} | Acc]}.

next_indexes( {X, Y}, Max ) when Y + 1 =:= Max, (X + Y) rem 2 =:= 0 -> {X + 1, Y - 1}; next_indexes( {X, Y}, Max ) when Y + 1 =:= Max, (X + Y) rem 2 =:= 1 -> {X + 1, Y}; next_indexes( {X, Y}, Max ) when X + 1 =:= Max, (X + Y) rem 2 =:= 0 -> {X, Y + 1}; next_indexes( {X, Y}, Max ) when X + 1 =:= Max, (X + Y) rem 2 =:= 1 -> {X - 1, Y + 1}; next_indexes( {X, 0}, _Max ) when X rem 2 =:= 0 -> {X + 1, 0}; next_indexes( {X, 0}, _Max ) when X rem 2 =:= 1 -> {X - 1, 1}; next_indexes( {0, Y}, _Max ) when Y rem 2 =:= 0 -> {1, Y - 1}; next_indexes( {0, Y}, _Max ) when Y rem 2 =:= 1 -> {0, Y + 1}; next_indexes( {X, Y}, _Max ) when (X + Y) rem 2 =:= 0 -> {X + 1, Y - 1}; next_indexes( {X, Y}, _Max ) when (X + Y) rem 2 =:= 1 -> {X - 1, Y + 1}. </lang>

Output:
71> zigzag:task().
[[0,1,5,6,14],
 [2,4,7,13,15],
 [3,8,12,16,21],
 [9,11,17,20,22],
 [10,18,19,23,24]]


ERRE

<lang ERRE>PROGRAM ZIG_ZAG

!$DYNAMIC

    DIM ARRAY%[0,0]

BEGIN

    SIZE%=5
    !$DIM ARRAY%[SIZE%-1,SIZE%-1]
    I%=1
    J%=1
    FOR E%=0 TO SIZE%^2-1 DO
         ARRAY%[I%-1,J%-1]=E%
         IF ((I%+J%) AND 1)=0 THEN
             IF J%<SIZE% THEN J%+=1 ELSE I%+=2 END IF
             IF I%>1 THEN I%-=1 END IF
          ELSE
             IF I%<SIZE% THEN I%+=1 ELSE J%+=2 END IF
             IF J%>1 THEN J%-=1 END IF
         END IF
    END FOR
    FOR ROW%=0 TO SIZE%-1 DO
        FOR COL%=0 TO SIZE%-1 DO
           WRITE("###";ARRAY%[ROW%,COL%];)
        END FOR
        PRINT
    END FOR

END PROGRAM</lang>

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

Euphoria

Translation of: C#

<lang Euphoria>function zigzag(integer size)

   sequence s
   integer i, j, d, max
   s = repeat(repeat(0,size),size)
   i = 1  j = 1  d = -1
   max = size*size
   for n = 1 to floor(max/2)+1 do
       s[i][j] = n
       s[size-i+1][size-j+1] = max-n+1
       i += d  j-= d
       if i < 1 then
           i += 1  d = -d
       elsif j < 1 then
           j += 1  d = -d
       end if
   end for
   return s

end function

? zigzag(5)</lang>

Output:
{
  {1,2,6,7,15},
  {3,5,8,14,16},
  {4,9,13,17,22},
  {10,12,18,21,23},
  {11,19,20,24,25}
}

F#

<lang fsharp> //Produce a zig zag matrix - Nigel Galloway: April 7th., 2015 let zz l a =

 let N = Array2D.create l a 0
 let rec gng (n, i, g, e) =
   N.[n,i] <- g
   match e with
   | _ when i=a-1 && n=l-1 -> N
   | 1 when n = l-1        -> gng (n, i+1, g+1, 2)
   | 2 when i = a-1        -> gng (n+1, i, g+1, 1)
   | 1 when i = 0          -> gng (n+1, 0, g+1, 2)
   | 2 when n = 0          -> gng (0, i+1, g+1, 1)
   | 1                     -> gng (n+1, i-1, g+1, 1)
   | _                     -> gng (n-1, i+1, g+1, 2)
 gng (0, 0, 0, 2)

</lang>

Output:

<lang fsharp>zz 5 5</lang>

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

<lang fsharp>zz 8 8</lang>

[[0; 1; 5; 6; 14; 15; 27; 28]
 [2; 4; 7; 13; 16; 26; 29; 42]
 [3; 8; 12; 17; 25; 30; 41; 43]
 [9; 11; 18; 24; 31; 40; 44; 53]
 [10; 19; 23; 32; 39; 45; 52; 54]
 [20; 22; 33; 38; 46; 51; 55; 60]
 [21; 34; 37; 47; 50; 56; 59; 61]
 [35; 36; 48; 49; 57; 58; 62; 63]]

Let's try something a little less square man <lang fsharp>zz 5 8</lang>

[[0; 1; 5; 6; 14; 15; 24; 25]
 [2; 4; 7; 13; 16; 23; 26; 33]
 [3; 8; 12; 17; 22; 27; 32; 34]
 [9; 11; 18; 21; 28; 31; 35; 38]
 [10; 19; 20; 29; 30; 36; 37; 39]]

Fan

<lang Fan>using gfx // for Point; convenient x/y wrapper

    • A couple methods for generating a 'zigzag' array like
    • 0 1 5 6
    • 2 4 7 12
    • 3 8 11 13
    • 9 10 14 15

class ZigZag {

 ** return an n x n array of uninitialized Int
 static Int[][] makeSquareArray(Int n)
 {
   Int[][] grid := Int[][,] {it.size=n}
   n.times |i| { grid[i] = Int[,] {it.size=n} }
   return grid
 }


 Int[][] zig(Int n)
 {
   grid := makeSquareArray(n)
   move := |Int i, Int j->Point|
   { return j < n - 1 ? Point(i <= 0 ? 0 : i-1, j+1) : Point(i+1, j) }
   pt := Point(0,0)
   (n*n).times |i| {
     grid[pt.y][pt.x] = i
     if ((pt.x+pt.y)%2 != 0) pt = move(pt.x,pt.y)
     else {tmp:= move(pt.y,pt.x); pt = Point(tmp.y, tmp.x) }
   }
   return grid
 }
 public static Int[][] zag(Int size)
 {
   data := makeSquareArray(size)
   Int i := 1
   Int j := 1
   for (element:=0; element < size * size; element++)
   {
     data[i - 1][j - 1] = element
     if((i + j) % 2 == 0) {
       // Even stripes
       if (j < size) {
         j++
       } else {
         i += 2
       }
       if (i > 1) {
         i--
       }
     } else {
       // Odd stripes
       if (i < size) {
         i++;
       } else {
         j += 2
       }
       if (j > 1) {
         j--
       }
     }
   }
   return data;
 }
 Void print(Int[][] data)
 {
   data.each |row|
   {
     buf := StrBuf()
     row.each |num|
     {
       buf.add(num.toStr.justr(3))
     }
     echo(buf)
   }
 }
 Void main()
 {
   echo("zig method:")
   print(zig(8))
   echo("\nzag method:")
   print(zag(8))
 }

}</lang>

Forth

<lang forth>0 value diag

south diag abs + cell+ ;

' cell+ value zig ' south value zag

init ( n -- )
 1- cells negate to diag
 ['] cell+ to zig
 ['] south to zag ;
swap-diag zig zag to zig to zag ;
put ( n addr -- n+1 addr )
 2dup !  swap 1+ swap ;
turn ( addr -- addr+E/S )
 zig execute  swap-diag
 diag negate to diag ;
zigzag ( matrix n -- )
 { n } n init
 0 swap
 n 1 ?do
   put turn
   i 0 do put diag + loop
 loop
 swap-diag
 n 1 ?do
   put turn
   n i 1+ ?do put diag + loop
 loop
 ! ;
.matrix ( n matrix -- )
 over 0 do
   cr
   over 0 do
     dup @ 3 .r cell+
   loop
 loop 2drop ;
test ( n -- ) here over zigzag here .matrix ;

5 test

 0  1  5  6 14
 2  4  7 13 15
 3  8 12 16 21
 9 11 17 20 22
10 18 19 23 24 ok</lang>


Fortran

Works with: Fortran version 90 and later

<lang fortran>PROGRAM ZIGZAG

 IMPLICIT NONE
   INTEGER, PARAMETER :: size = 5
   INTEGER :: zzarray(size,size), x(size*size), y(size*size), i, j
    
   ! index arrays
   x = (/ ((j, i = 1, size), j = 1, size) /)
   y = (/ ((i, i = 1, size), j = 1, size) /)
  
   ! Sort indices
   DO i = 2, size*size
      j = i - 1
      DO WHILE (j>=1 .AND. (x(j)+y(j)) > (x(i)+y(i)))
         j = j - 1
      END DO
      x(j+1:i) = cshift(x(j+1:i),-1)
      y(j+1:i) = cshift(y(j+1:i),-1)
   END DO

   ! Create zig zag array
   DO i = 1, size*size
      IF (MOD(x(i)+y(i), 2) == 0) THEN
         zzarray(x(i),y(i)) = i - 1
      ELSE
         zzarray(y(i),x(i)) = i - 1
      END IF
   END DO
 
   ! Print zig zag array
   DO j = 1, size
      DO i = 1, size
         WRITE(*, "(I5)", ADVANCE="NO") zzarray(i,j)
      END DO
      WRITE(*,*)
   END DO
 
END PROGRAM ZIGZAG</lang>

GAP

<lang gap>ZigZag := function(n)

 local a, i, j, k;
 a := NullMat(n, n);
 i := 1;
 j := 1;
 for k in [0 .. n*n - 1] do
   a[i][j] := k;
   if (i + j) mod 2 = 0 then
     if j < n then
       j := j + 1;
     else
       i := i + 2;
     fi;
     if i > 1 then
       i := i - 1;
     fi;
   else
     if i < n then
       i := i + 1;
     else
       j := j + 2;
     fi;
     if j > 1 then
       j := j - 1;
     fi;
   fi;
 od;
 return a;

end;

PrintArray(ZigZag(5));

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

Go

Translation of: Groovy
Edge direct algorithm

<lang go>package main

import (

   "fmt"
   "strconv"

)

func zz(n int) []int {

   r := make([]int, n*n)
   i := 0
   n2 := n * 2
   for d := 1; d <= n2; d++ {
       x := d - n
       if x < 0 {
           x = 0
       }
       y := d - 1
       if y > n-1 {
           y = n - 1
       }
       j := n2 - d
       if j > d {
           j = d
       }
       for k := 0; k < j; k++ {
           if d&1 == 0 {
               r[(x+k)*n+y-k] = i
           } else {
               r[(y-k)*n+x+k] = i
           }
           i++
       }
   }
   return r

}

func main() {

   const n = 5
   w := len(strconv.Itoa(n*n - 1))
   for i, e := range zz(n) {
       fmt.Printf("%*d ", w, e)
       if i%n == n-1 {
           fmt.Println("")
       }
   }

}</lang>

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

Groovy

Edge

An odd technique that traverses the grid edges directly and calculates the transform onto the grid.

<lang groovy>def zz = { n ->

 grid = new int[n][n]
 i = 0
 for (d in 1..n*2) {
   (x, y) = [Math.max(0, d - n), Math.min(n - 1, d - 1)]
    Math.min(d, n*2 - d).times {
      grid[d%2?y-it:x+it][d%2?x+it:y-it] = i++;
     }
 }
 grid

}</lang>

Output:
 > zz(5).each { it.each { print("${it}".padLeft(3)) }; println() }
  0  1  5  6 14
  2  4  7 13 15
  3  8 12 16 21
  9 11 17 20 22
 10 18 19 23 24

Cursor

Ported from the Java example

<lang groovy>def zz = { n->

 move = { i, j -> j < n - 1 ? [i <= 0 ? 0 : i-1, j+1] : [i+1, j] }
 grid = new int[n][n]
 (x, y) = [0, 0]
 (n**2).times {
   grid[y][x] = it
   if ((x+y)%2) (x,y) = move(x,y)
   else (y,x) = move(y,x)
 }
 grid

}</lang>

Output:
 > zz(5).each { it.each { print("${it}".padLeft(3)) }; println() }
  0  1  5  6 14
  2  4  7 13 15
  3  8 12 16 21
  9 11 17 20 22
 10 18 19 23 24

Sorting

Ported from the Python example with some input from J

<lang groovy>def zz = { n ->

 (0..<n*n).collect { [x:it%n,y:(int)(it/n)] }.sort { c->
   [c.x+c.y, (((c.x+c.y)%2) ? c.y : -c.y)]
 }.with { l -> l.inject(new int[n][n]) { a, c -> a[c.y][c.x] = l.indexOf(c); a } }

}</lang>

Output:
 > zz(5).each { it.each { print("${it}".padLeft(3)) }; println() }
  0  1  5  6 14
  2  4  7 13 15
  3  8 12 16 21
  9 11 17 20 22
 10 18 19 23 24

Haskell

Computing the array:

<lang haskell>import Data.Array (array, bounds, range, (!)) import Data.Monoid (mappend) import Data.List (sortBy)

compZig (x,y) (x',y') = compare (x+y) (x'+y')

                       `mappend` if even (x+y) then compare x x'
                                               else compare y y'

zigZag upper = array b $ zip (sortBy compZig (range b))

                            [0..]
 where b = ((0,0),upper)</lang>
  

compZig compares coordinates using the order of a zigzag walk: primarily, the antidiagonals; secondarily, alternating directions along them.

In zigZag, array takes the bounds and a list of indexes paired with values. We take the list of all indexes, range b, and sort it in the zigzag order, then zip that with the integers starting from 0. (This algorithm was inspired by the explanation of the J example.)

Displaying the array (not part of the task):

<lang haskell>import Text.Printf (printf)

-- format a 2d array of integers neatly show2d a = unlines [unwords [printf "%3d" (a ! (x,y) :: Integer) | x <- axis fst] | y <- axis snd]

 where (l, h) = bounds a
       axis f = [f l .. f h]

main = mapM_ (putStr . show2d . zigZag) [(3,3), (4,4), (10,2)]</lang>

Icon and Unicon

This solution works for both Icon and Unicon.

<lang icon>procedure main(args)

  n := integer(!args) | 5
  every !(A := list(n)) := list(n)
  A := zigzag(A)
  show(A)

end

procedure show(A)

   every writes(right(!A,5) | "\n")

end

procedure zigzag(A)

   x := [0,0]
   every i := 0 to (*A^2 -1) do {
       x := nextIndices(*A, x)
       A[x[1]][x[2]] := i
       }   
   return A

end

procedure nextIndices(n, x)

   return if (x[1]+x[2])%2 = 0
          then if x[2] = n then [x[1]+1, x[2]] else [max(1, x[1]-1), x[2]+1]
          else if x[1] = n then [x[1], x[2]+1] else [x[1]+1, max(1, x[2]-1)]

end</lang>

Output:
->zz
    0    1    5    6   14
    2    4    7   13   15
    3    8   12   16   21
    9   11   17   20   22
   10   18   19   23   24
->

J

A succinct way: <lang j> ($ [: /:@; <@|.`</.@i.)@,~ 5

0  1  5  6 14
2  4  7 13 15
3  8 12 16 21
9 11 17 20 22

10 18 19 23 24</lang>

This version is longer, but more "mathematical" and less "procedural": <lang j> ($ [: /:@; [: <@(A.~_2|#)/. i.)@,~ 5

0  1  5  6 14
2  4  7 13 15
3  8 12 16 21
9 11 17 20 22

10 18 19 23 24</lang>

Leveraging a useful relationship among the indices: <lang j> ($ ([: /:@;@(+/"1 <@|.`</. ]) (#: i.@(*/))))@,~ 5

0  1  5  6 14
2  4  7 13 15
3  8 12 16 21
9 11 17 20 22

10 18 19 23 24</lang>

By the way, all the edge cases are handled transparently, without any special checks. Furthermore, by simply removing the trailing @,~ from the solutions, they automatically generalize to rectangular (non-square) matrices: <lang j> ($ [: /:@; [: <@|.`</. i.) 5 3 0 1 5 2 4 6 3 7 11 8 10 12 9 13 14</lang>

Java

Translation of: Ada

<lang java>public static int[][] Zig_Zag(final int size) {

int[][] data = new int[size][size];
int i = 1;
int j = 1;
for (int element = 0; element < size * size; element++)
{
 data[i - 1][j - 1] = element;
 if ((i + j) % 2 == 0)
 {
  // Even stripes
  if (j < size)
   j++;
  else
   i+= 2;
  if (i > 1)
   i--;
 }
 else
 {
  // Odd stripes
  if (i < size)
   i++;
  else
   j+= 2;
  if (j > 1)
   j--;
 }
}
return data;

}</lang>

JavaScript

Imperative

Works with: SpiderMonkey
for the print() function.
Translation of: Java

Subclasses the Matrix class defined at Matrix Transpose#JavaScript <lang javascript>function ZigZagMatrix(n) {

   this.height = n;
   this.width = n;
   this.mtx = [];
   for (var i = 0; i < n; i++) 
       this.mtx[i] = [];
   var i=1, j=1;
   for (var e = 0; e < n*n; e++) {
       this.mtx[i-1][j-1] = e;
       if ((i + j) % 2 == 0) {
           // Even stripes
           if (j < n) j ++;
           else       i += 2;
           if (i > 1) i --;
       } else {
           // Odd stripes
           if (i < n) i ++;
           else       j += 2;
           if (j > 1) j --;
       }
   }

} ZigZagMatrix.prototype = Matrix.prototype;

var z = new ZigZagMatrix(5); print(z); print();

z = new ZigZagMatrix(4); print(z);</lang>

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

0,1,5,6
2,4,7,12
3,8,11,13
9,10,14,15

Functional (ES 5)

<lang JavaScript>(function (n) {

 // Read range of values into a series of 'diagonal rows'
 // for a square of given dimension,
 // starting at diagonal row i.
 // n -> n -> [n] -> n
 function diagonals(nEdge, iRow, lstRange) {
   var lng = (iRow > nEdge ? (2 * nEdge - iRow) : iRow);
   return lstRange.length ? [lstRange.slice(0, lng)].concat(
     diagonals(nEdge, iRow + 1, lstRange.slice(lng))
   ) : [];
 }
 // Recursively read off n heads from the diagonals (as rows)
 // n -> n -> n
 function nHeads(n, lst) {
   var zipEdge = lst.slice(0, n);
   return lst.length ? [zipEdge.map(function (x) {
     return x[0];
   })].concat(nHeads(n, [].concat.apply([], zipEdge.map(function (x) {
     return x.length > 1 ? [x.slice(1)] : [];
   })).concat(lst.slice(n)))) : [];
 }
 // [m..n]
 function range(m, n) {
   return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
     return m + i;
   });
 }
 // Recursively take n heads from the alternately reversed diagonals
 return nHeads(n, diagonals(n, 1, range(0, (n * n) - 1)).map(function (x, i) {
   i % 2 || x.reverse();
   return x;
 }));

})(5);</lang>

Output:

<lang JavaScript>[[0, 1, 5, 6, 14],

[2, 4, 7, 13, 15],
[3, 8, 12, 16, 21],
[9, 11, 17, 20, 22],
[10, 18, 19, 23, 24]]</lang>

Joy

<lang Joy> (*

   From the library.
  • )

DEFINE reverse == [] swap shunt;

      shunt   == [swons] step.

(*

   Split according to the parameter given.
  • )

DEFINE take-drop == [dup] swap dup [[] cons [take swap] concat concat] dip []

                    cons concat [drop] concat.

(*

   Take the first of a list of lists.
  • )

DEFINE take-first == [] cons 3 [dup] times [dup] swap concat [take [first] map

                    swap dup] concat swap concat [drop swap] concat swap
                    concat [take [rest] step []] concat swap concat [[cons]
                    times swap concat 1 drop] concat.

DEFINE zigzag ==

(*

   Use take-drop to generate a list of lists.
  • )

4 [dup] times 1 swap from-to-list swap pred 1 swap from-to-list reverse concat swap dup * pred 0 swap from-to-list swap [take-drop i] step [pop list] [cons] while

(*

   The odd numbers must be modified with reverse.
  • )

[dup size 2 div popd [1 =] [pop reverse] [pop] ifte] map

(*

   Take the first of the first of n lists.
  • )

swap dup take-first [i] cons times pop

(*

   Merge the n separate lists.
  • )

[] [pop list] [cons] while

(*

   And print them.
  • )

swap dup * pred 'd 1 1 format size succ [] cons 'd swons [1 format putchars] concat [step '\n putch] cons step.

11 zigzag.</lang>

jq

Infrastructure: <lang jq># 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 ;
  1. 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" ) ;

</lang> Create a zigzag matrix by zigzagging: <lang jq>def zigzag(n):

 # unless m == n*n, place m at (i,j), pointing
 # in the direction d, where d = [drow, dcolumn]:
 def _next(i; j; m; d):
   if m == (n*n) then . else .[i][j] = m end
   | if m == (n*n) - 1 then .
     elif i == n-1 then if j+1 < n then .[i][j+1] = m+1 | _next(i-1; j+2; m+2; [-1, 1]) else . end
     elif i ==   0 then if j+1 < n then .[i][j+1] = m+1 | _next(i+1; j  ; m+2; [ 1,-1])
                        else            .[i+1][j] = m+1 | _next(i+2; j-1; m+2; [ 1,-1]) end
     elif j == n-1 then if i+1 < n then .[i+1][j] = m+1 | _next(i+2; j-1; m+2; [ 1,-1]) else . end
     elif j ==   0 then if i+1 < n then .[i+1][j] = m+1 | _next(i;   j+1; m+2; [-1, 1])
                        else            .[i][j+1] = m+1 | _next(i-1; j+1; m+2; [-1, 1]) end 
     else _next(i+ d[0]; j+ d[1]; m+1;  d)
     end ;
 matrix(n;n;-1) | _next(0;0; 0; [0,1]) ;
  1. Example

zigzag(5) | neatly(4)</lang>

Output:
$ jq -n -r -f zigzag.jq
    0    1    5    6   14
    2    4    7   13   15
    3    8   12   16   21
    9   11   17   20   22
   10   18   19   23   24

Julia

Create an iterator that steps through a matrix's indices in the zig-zag pattern and use this to create zig-zag matrices and related objects.

Zig-Zag Iterator <lang Julia> immutable ZigZag

   m::Int
   n::Int
   diag::Array{Int,1}
   cmax::Int
   numd::Int
   lohi::(Int,Int)

end

function zigzag(m::Int, n::Int)

   0<m && 0<n || error("The matrix dimensions must be positive.")
   ZigZag(m, n, [-1,1], m*n, m+n-1, extrema([m,n]))

end zigzag(n::Int) = zigzag(n, n)

type ZZState

   cnt::Int
   cell::Array{Int,1}
   dir::Int
   dnum::Int
   dlen::Int
   dcnt::Int

end

Base.length(zz::ZigZag) = zz.cmax Base.start(zz::ZigZag) = ZZState(1, [1,1], 1, 1, 1, 1) Base.done(zz::ZigZag, zzs::ZZState) = zzs.cnt > zz.cmax

function Base.next(zz::ZigZag, zzs::ZZState)

   s = sub2ind((zz.m, zz.n), zzs.cell[1], zzs.cell[2])
   if zzs.dcnt == zzs.dlen
       if isodd(zzs.dnum)
           if zzs.cell[2] < zz.n
               zzs.cell[2] += 1
           else
               zzs.cell[1] += 1
           end
       else
           if zzs.cell[1] < zz.m
               zzs.cell[1] += 1
           else
               zzs.cell[2] += 1
           end
       end
       zzs.dcnt = 1
       zzs.dnum += 1
       zzs.dir = -zzs.dir
       if zzs.dnum <= zz.lohi[1]
           zzs.dlen += 1
       elseif zz.lohi[2] < zzs.dnum
           zzs.dlen -= 1
       end
   else
       zzs.cell += zzs.dir*zz.diag
       zzs.dcnt += 1
   end
   zzs.cnt += 1
   return (s, zzs)

end </lang>

Helper Functions <lang Julia> 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 </lang>

Main <lang Julia> n = 5 println("The n = ", n, " zig-zag matrix:") a = zeros(Int, (n, n)) for (i, s) in enumerate(zigzag(n))

   a[s] = i-1

end println(pretty(a))

m = 3 println() println("Generalize to a non-square matrix (", m, "x", n, "):") a = zeros(Int, (m, n)) for (i, s) in enumerate(zigzag(m, n))

   a[s] = i-1

end println(pretty(a))

p = primes(10^3) n = 7 println() println("An n = ", n, " prime spiral matrix:") a = zeros(Int, (n, n)) for (i, s) in enumerate(zigzag(n))

   a[s] = p[i]

end println(pretty(a)) </lang>

Output:
The n = 5 zig-zag matrix:
      0  1  5  6 14
      2  4  7 13 15
      3  8 12 16 21
      9 11 17 20 22
     10 18 19 23 24

Generalize to a non-square matrix (3x5):
      0  1  5  6 11
      2  4  7 10 12
      3  8  9 13 14

An n = 7 prime spiral matrix:
       2   3  13  17  47  53 107
       5  11  19  43  59 103 109
       7  23  41  61 101 113 167
      29  37  67  97 127 163 173
      31  71  89 131 157 179 199
      73  83 137 151 181 197 211
      79 139 149 191 193 223 227

Lasso

<lang lasso> var(

    'square'  = array
   ,'size'    = integer( 5 )// for a 5 X 5 square
   ,'row'     = array
   ,'x'       = integer( 1 )
   ,'y'       = integer( 1 )
   ,'counter' = integer( 1 )

);

// create place-holder matrix loop( $size );

  $row = array;
  loop( $size );
     $row->insert( 0 );
   /loop;
  $square->insert( $row );

/loop;

while( $counter < $size * $size );

  // check downward diagonal
  if(
        $x > 1
        &&
        $y < $square->size
        &&
        $square->get( $y + 1 )->get( $x - 1 ) == 0
     );
        $x -= 1;
        $y += 1;
  // check upward diagonal
  else(
        $x < $square->size
        &&
        $y > 1
        &&
        $square->get( $y - 1 )->get( $x + 1 ) == 0
     );
        $x += 1;
        $y -= 1;
  // check right
  else(
        (
           $y == 1
           ||
           $y == $square->size
        )
        &&
        $x < $square->size
        &&
        $square->get( $y )->get( $x + 1 ) == 0
     );
     $x += 1;
  // down
  else;
     $y += 1;
  /if;
  $square->get( $y )->get( $x ) = loop_count;
  $counter += 1;

/while;

$square; </lang>

Lua

<lang Lua> local zigzag = {}

function zigzag.new(n)

   local a = {}
   local i -- cols
   local j -- rows
   a.n = n
   a.val = {}
   for j = 1, n do
       a.val[j] = {}
       for i = 1, n do
           a.val[j][i] = 0
       end
   end
   i = 1
   j = 1
   local di
   local dj
   local k = 0
   while k < n * n do
       a.val[j][i] = k
       k = k + 1
       if i == n then
           j = j + 1
           a.val[j][i] = k
           k = k + 1
           di = -1
           dj = 1
       end
       if j == 1 then
           i = i + 1
           a.val[j][i] = k
           k = k + 1
           di = -1
           dj = 1
       end
       if j == n then
           i = i + 1
           a.val[j][i] = k
           k = k + 1
           di = 1
           dj = -1
       end
       if i == 1 then
           j = j + 1
           a.val[j][i] = k
           k = k + 1
           di = 1
           dj = -1
       end
       i = i + di
       j = j + dj
   end
   setmetatable(a, {__index = zigzag, __tostring = zigzag.__tostring})
   return a

end

function zigzag:__tostring()

   local s = {} 
   for j = 1, self.n do
       local row = {}
       for i = 1, self.n do
           row[i] = string.format('%d', self.val[j][i])
       end
       s[j] = table.concat(row, ' ')
   end
   return table.concat(s, '\n')

end

print(zigzag.new(5)) </lang>

M4

<lang M4>divert(-1)

define(`set2d',`define(`$1[$2][$3]',`$4')') define(`get2d',`defn(`$1[$2][$3]')') define(`for',

  `ifelse($#,0,``$0,
  `ifelse(eval($2<=$3),1,
  `pushdef(`$1',$2)$4`'popdef(`$1')$0(`$1',incr($2),$3,`$4')')')')

define(`show2d',

  `for(`x',0,decr($2),
     `for(`y',0,decr($3),`format(`%2d',get2d($1,x,y)) ')

')')

dnl <name>,<size> define(`zigzag',

  `define(`j',1)`'define(`k',1)`'for(`e',0,eval($2*$2-1),
     `set2d($1,decr(j),decr(k),e)`'ifelse(eval((j+k)%2),0,
        `ifelse(eval(k<$2),1,
           `define(`k',incr(k))',
           `define(`j',eval(j+2))')`'ifelse(eval(j>1),1,
           `define(`j',decr(j))')',
        `ifelse(eval(j<$2),1,
           `define(`j',incr(j))',
           `define(`k',eval(k+2))')`'ifelse(eval(k>1),1,
           `define(`k',decr(k))')')')')

divert

zigzag(`a',5) show2d(`a',5,5)</lang>

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

Mathematica / Wolfram Language

Rule-based implementation, the upper-left half is correctly calculated using a direct formula. The lower-right half is then 'mirrored' from the upper-left half. <lang Mathematica>ZigZag[size_Integer/;size>0]:=Module[{empty=ConstantArray[0,{size,size}]},

empty=ReplacePart[empty,{i_,j_}:>1/2 (i+j)^2-(i+j)/2-i (1-Mod[i+j,2])-j Mod[i+j,2]];
ReplacePart[empty,{i_,j_}/;i+j>size+1:> size^2-tmpsize-i+1,size-j+1-1]

]</lang> Ported from the java-example: <lang Mathematica>ZigZag2[size_] := Module[{data, i, j, elem},

data = ConstantArray[0, {size, size}];
i = j = 1;
For[elem = 0, elem < size^2, elem++,
 datai, j = elem;
 If[Mod[i + j, 2] == 0,
  If[j < size, j++, i += 2];
  If[i > 1, i--]
  ,
  If[i < size, i++, j += 2];
  If[j > 1, j--];
  ];
 ];
data
]</lang>

Examples: <lang Mathematica>ZigZag[5] // MatrixForm ZigZag2[6] // MatrixForm</lang> gives back:

MATLAB

This isn't the best way to solve this task and the algorithm is completely unintuitive without some major exploration of the code. But! It is pretty fast for n < 10000.

<lang MATLAB>function matrix = zigZag(n)

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

end</lang>

Output:
>> zigZag(5)

ans =

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


Maxima

<lang maxima>zigzag(n) := block([a, i, j], a: zeromatrix(n, n), i: 1, j: 1, for k from 0 thru n*n - 1 do (

  a[i, j]: k,
  if evenp(i + j) then (
     if j < n then j: j + 1 else i: i + 2,
     if i > 1 then i: i - 1      
  ) else (
     if i < n then i: i + 1 else j: j + 2,
     if j > 1 then j: j - 1
  )

), a)$

zigzag(5); /* matrix([ 0, 1, 5, 6, 14],

         [ 2,  4,  7, 13, 15],
         [ 3,  8, 12, 16, 21],
         [ 9, 11, 17, 20, 22],
         [10, 18, 19, 23, 24]) */</lang>

Modula-3

<lang modula3>MODULE ZigZag EXPORTS Main;

IMPORT IO, Fmt;

TYPE Matrix = REF ARRAY OF ARRAY OF CARDINAL;

PROCEDURE Create(size: CARDINAL): Matrix =

 PROCEDURE move(VAR i, j: INTEGER) =
   BEGIN
     IF j < (size - 1) THEN
       IF (i - 1) < 0 THEN
         i := 0;
       ELSE
         i := i - 1;
       END;
       INC(j);
     ELSE
       INC(i);
     END;
   END move;
   
 VAR data := NEW(Matrix, size, size);
     x, y: INTEGER := 0;
 BEGIN
   FOR v := 0 TO size * size - 1 DO
     data[y, x] := v;
     IF (x + y) MOD 2 = 0 THEN
       move(y, x);
     ELSE
       move(x, y);
     END;
   END;
   RETURN data;
 END Create;

PROCEDURE Print(data: Matrix) =

 BEGIN
   FOR i := FIRST(data^) TO LAST(data^) DO
     FOR j := FIRST(data[0]) TO LAST(data[0]) DO
       IO.Put(Fmt.F("%3s", Fmt.Int(data[i, j])));
     END;
     IO.Put("\n");
   END;
 END Print;

BEGIN

 Print(Create(5));

END ZigZag.</lang>

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

NetRexx

Translation of: REXX

<lang NetRexx>/* NetRexx */ options replace format comments java crossref savelog symbols binary

zigzag(5)

return

method zigzag(msize) public static

 row = 1
 col = 1
 ziggy = Rexx(0)
 loop j_ = 0 for msize * msize
   ziggy[row, col] = j_
   if (row + col) // 2 == 0 then do
     if col < msize then -
       col = col + 1
     else row = row + 2
     if row \== 1 then -
       row = row - 1
     end
   else do
     if row < msize then -
       row = row + 1
     else col = col + 2
     if col \== 1 then -
       col = col - 1
     end
   end j_
 L = (msize * msize - 1).length             /*for a constant element width.  */
 loop row = 1 for msize                     /*show all the matrix's rows.    */
   rowOut = 
   loop col = 1 for msize
     rowOut = rowOut ziggy[row, col].right(L)
     end col
   say rowOut
   end row
 return

</lang>

Nim

Translation of: Python

<lang nim>import algorithm, strutils

type Pos = tuple[x, y: int]

template newSeqWith(len: int, init: expr): expr =

 var result {.gensym.} = newSeq[type(init)](len)
 for i in 0 .. <len:
   result[i] = init
 result

proc `$`(m: seq[seq[int]]): string =

 result = ""
 for r in m:
   for c in r:
     result.add align($c, 2) & " "
   result.add "\n"

proc zigzagMatrix(n): auto =

 result = newSeqWith(n, newSeq[int](n))
 var indices = newSeq[Pos]()
 for x in 0 .. <n:
   for y in 0 .. <n:
     indices.add((x,y))
 sort(indices, proc(a, b: Pos): int =
   result = a.x + a.y - b.x - b.y
   if result == 0: result =
     (if (a.x + a.y) mod 2 == 0: a.y else: -a.y) -
     (if (b.x + b.y) mod 2 == 0: b.y else: -b.y))
 for i, p in indices:
   result[p.x][p.y] = i

echo zigzagMatrix(6)</lang>

Output:
 0  1  5  6 14 15 
 2  4  7 13 16 25 
 3  8 12 17 24 26 
 9 11 18 23 27 32 
10 19 22 28 31 33 
20 21 29 30 34 35

Objeck

Translation of: Java

<lang ocaml> function : native : ZigZag(size : Int) ~ Int[,] {

 data := Int->New[size, size];
 i := 1;
 j := 1;
 
 max := size * size;
 for(element := 0; element < max ; element += 1;) {
   data[i - 1, j - 1] := element;
   
   if((i + j) % 2 = 0) {
     # even stripes
     if(j < size){
       j += 1;
     }
     else{
       i+= 2;
     };
     
     if(i > 1) {
       i -= 1;
     };
   }
   else{
     # ddd stripes
     if(i < size){
       i += 1;
     }
     else{
       j+= 2;
     };
     
     if(j > 1){
       j -= 1;
     };
   };
 };
 
 return data;

} </lang>


OCaml

Translation of: Common Lisp

<lang ocaml>let zigzag n =

 (* move takes references and modifies them directly *)
 let move i j =
   if !j < n - 1 then begin
     i := max 0 (!i - 1);
     incr j
   end else
     incr i
 in
 let a = Array.make_matrix n n 0
 and x = ref 0 and y = ref 0 in
 for v = 0 to n * n - 1 do
   a.(!x).(!y) <- v;
   if (!x + !y) mod 2 = 0 then
     move x y
   else
     move y x
 done;
 a</lang>

Octave

See the MATLAB solution, which works perfectly in Octave too.

ooRexx

Translation of: Java

<lang ooRexx> call printArray zigzag(3) say call printArray zigzag(4) say call printArray zigzag(5)

routine zigzag
 use strict arg size
 data = .array~new(size, size)
 row = 1
 col = 1
 loop element = 0 to (size * size) - 1
     data[row, col] = element
     -- even stripes
     if (row + col) // 2 = 0 then do
         if col < size then col += 1
         else row += 2
         if row > 1 then row -= 1
     end
     -- odd rows
     else do
         if row < size then row += 1
         else col += 2
         if col > 1 then col -= 1
     end
 end
 return data
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

</lang>

Output:
|  0  1  5 |
|  2  4  6 |
|  3  7  8 |

|  0  1  5  6 |
|  2  4  7 12 |
|  3  8 11 13 |
|  9 10 14 15 |

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

Oz

Implemented as a state machine: <lang oz>declare

 %%            state          move   success     failure
 States = unit(right:        [ 1# 0  downLeft    downInstead]
               downInstead:  [ 0# 1  downLeft    terminate]
               downLeft:     [~1# 1  downLeft    down]
               down:         [ 0# 1  topRight    rightInstead]
               rightInstead: [ 1# 0  topRight    terminate]
               topRight:     [ 1#~1  topRight    right])
 fun {CreateZigZag N}
    ZZ = {Create2DTuple N N}
    %% recursively walk through 2D tuple and set values
    proc {Walk Pos=X#Y Count State}
       [Dir Success Failure] = States.State
       NextPos = {Record.zip Pos Dir Number.'+'}
       Valid = {Record.all NextPos fun {$ C} C > 0 andthen C =< N end}
       NewPos = if Valid then NextPos else Pos end
       NewCount = if Valid then Count + 1 else Count end
       NewState = if Valid then Success else Failure end
    in
       ZZ.Y.X = Count
       if NewState \= terminate then
          {Walk NewPos NewCount NewState}
       end
    end
 in
    {Walk 1#1 0 right}
    ZZ
 end
 fun {Create2DTuple W H}
    T = {MakeTuple unit H}
 in
    {Record.forAll T fun {$} {MakeTuple unit W} end}
    T
 end

in

 {Inspect {CreateZigZag 5}}</lang>

PARI/GP

Translation of: C.23

<lang parigp>zz(n)={ my(M=matrix(n,n),i,j,d=-1,start,end=n^2-1); while(ct--, M[i+1,j+1]=start; M[n-i,n-j]=end; start++; end--; i+=d; j-=d; if(i<0, i++; d=-d , if(j<0, j++; d=-d ) ); if(start>end,return(M)) ) };</lang>

Pascal

<lang Pascal>Program zigzag;

const

 size = 5;

var

 zzarray: array [1..size, 1..size] of integer;
 element, i, j: integer;
 direction: integer;

begin

 i := 1;
 j := 1;
 direction := 1;
 for element := 1 to size*size do
 begin
   zzarray[i,j] := element;
   i := i + direction;
   j := j - direction;
   if (i = 0) then
   begin
     direction := -direction;
     i := i + 1;
   end;
   if (i = size +1) then
   begin
     direction := -direction;
     i := i - 1;
     j := j + 2;
   end;
   if (j = 0) then
   begin
     direction := -direction;
     j := j + 1;
   end;
   if (j = size + 1) then
   begin
     direction := -direction;
     j := j - 1;
     i := i + 2;
   end;
 end;
 for j := 1 to size do
 begin
   for i := 1 to size do
     write(zzarray[i,j]:3);
   writeln;
 end;

end.</lang>

Output:
  1  2  6  7 15
  3  5  8 14 16
  4  9 13 17 22
 10 12 18 21 23
 11 19 20 24 25

Perl

<lang perl>use 5.010;

sub zig_zag {

   my $n          = shift;
   my $max_number = $n**2;
   my @matrix;
   my $number = 0;
   for my $j ( 0 .. --$n ) {
       for my $i (
           $j % 2
           ? 0 .. $j
           : reverse 0 .. $j
         )
       {
           $matrix[$i][ $j - $i ] = $number++;
           #next if $j == $n;
           $matrix[ $n - $i ][ $n - ( $j - $i ) ] = $max_number - $number;
       }
   }
   return @matrix;

}

my @zig_zag_matrix = zig_zag(5); say join "\t", @{$_} foreach @zig_zag_matrix; </lang>


Translation of: Haskell

<lang perl>sub zig_zag {

   my ($w, $h, @r, $n) = @_;
   $r[ $_->[1] ][ $_->[0] ] = $n++	for
   	sort {	$a->[0] + $a->[1] <=> $b->[0] + $b->[1]	  or

($a->[0] + $a->[1]) % 2 ? $a->[1] <=> $b->[1] : $a->[0] <=> $b->[0] } map { my $e = $_; map{ [$e, $_] } 0 .. $w-1 } 0 .. $h - 1;

   @r

}

print map{ "@$_\n" } zig_zag(3, 5);</lang>

Perl 6

Assuming the same Turtle class that is used in Spiral_matrix: <lang perl6>sub MAIN($size as Int) {

   my $t = Turtle.new(dir => northeast);
   my $counter = 0;
   for 1 ..^ $size -> $run {

for ^$run { $t.lay-egg($counter++); $t.forward; } my $yaw = $run %% 2 ?? -1 !! 1; $t.turn-right($yaw * 135); $t.forward; $t.turn-right($yaw * 45);

   }
   for $size ... 1 -> $run {

for ^$run -> $ { $t.lay-egg($counter++); $t.forward; } $t.turn-left(180); $t.forward; my $yaw = $run %% 2 ?? 1 !! -1; $t.turn-right($yaw * 45); $t.forward; $t.turn-left($yaw * 45);

   }
   $t.showmap;

}</lang>

Phix

Translation of: C#

<lang Phix>integer n = 9 integer zstart = 0, zend = n*n-1 --integer zstart = 1, zend = n*n string fmt = sprintf("%%%dd",length(sprintf("%d",zend))) sequence m = repeat(repeat("??",n),n) integer x = 1, y = 1, d = -1 while 1 do

   m[x][y] = sprintf(fmt,zstart)
   if zstart=zend then exit end if
   zstart += 1
   m[n-x+1][n-y+1] = sprintf(fmt,zend)
   zend -= 1
   x += d
   y -= d
   if x<1 then
       x += 1
       d = -d
   elsif y<1 then
       y += 1
       d = -d
   end if

end while

for i=1 to n do

   m[i] = join(m[i])

end for puts(1,join(m,"\n"))</lang> Alternative: <lang Phix>integer n = 5 string fmt = sprintf("%%%dd",length(sprintf("%d",n*n-1))) sequence m = repeat(repeat("??",n),n) integer x = 1, y = 1 for d=0 to n*n-1 do

   m[y][x] = sprintf(fmt,d)
   if mod(x+y,2) then
       {x,y} = iff(y<n?{x-(x>1),y+1}:{x+1,y})
   else
       {x,y} = iff(x<n?{x+1,y-(y>1)}:{x,y+1})
   end if

end for

for i=1 to n do

   m[i] = join(m[i])

end for puts(1,join(m,"\n"))</lang>

PHP

<lang php>function ZigZagMatrix($num) {

   $matrix = array();
   for ($i = 0; $i < $num; $i++){

$matrix[$i] = array(); }

   $i=1;

$j=1;

   for ($e = 0; $e < $num*$num; $e++) {
       $matrix[$i-1][$j-1] = $e;
       if (($i + $j) % 2 == 0) {
           if ($j < $num){

$j++; }else{ $i += 2; }

           if ($i > 1){ 

$i --; }

       } else {
           if ($i < $num){ 

$i++; }else{ $j += 2; }

           if ($j > 1){

$j --; }

       }
   }

return $matrix; }</lang>

PicoLisp

This example uses 'grid' from "lib/simul.l", which maintains a two-dimensional structure and is normally used for simulations and board games. <lang PicoLisp>(load "@lib/simul.l")

(de zigzag (N)

  (prog1 (grid N N)
     (let (D '(north west  south east  .)  E '(north east .)  This 'a1)
        (for Val (* N N)
           (=: val Val)
           (setq This
              (or
                 ((cadr D) ((car D) This))
                 (prog
                    (setq D (cddr D))
                    ((pop 'E) This) )
                 ((pop 'E) This) ) ) ) ) ) )

(mapc

  '((L)
     (for This L (prin (align 3 (: val))))
     (prinl) )
  (zigzag 5) )</lang>
Output:
  1  2  6  7 15
  3  5  8 14 16
  4  9 13 17 22
 10 12 18 21 23
 11 19 20 24 25

PL/I

<lang pli>/* Fill a square matrix with the values 0 to N**2-1, */ /* in a zig-zag fashion. */ /* 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 matrix:');
  get list (n);

begin;

  declare A(n,n) fixed binary;
  declare (i, j, inc, q) fixed binary;
  on subrg snap begin;
     declare i fixed binary;
     do  i = 1 to n;
        put skip edit (a(i,*)) (f(4));
     end;
     stop;
  end;
  A = -1;
  inc = -1;
  i, j = 1;

loop:

  do q = 0 to n**2-1;
     a(i,j) = q;
     if q = n**2-1 then leave;
     if i = 1 & j = n then
        if iand(j,1) = 1 then /* odd-sided matrix */
           do; i = i + 1; inc = -inc; iterate loop; end;
        else  /* an even-sided matrix */
           do; i = i + inc; j = j - inc; iterate loop; end;
     if inc = -1 then if i+inc < 1 then
        do; inc = -inc; j = j + 1; a(i,j) = q; iterate loop; end;
     if inc = 1 then if i+inc > n then
        do; inc = -inc; j = j + 1; a(i,j) = q; iterate loop; end;
     if inc = 1 then if j-inc < 1 then
        do; inc = -inc; i = i + 1; a(i,j) = q; iterate loop; end;
     if inc = -1 then if j - inc > n then
        do; inc = -inc; i = i + 1; a(i,j) = q; iterate loop; end;
     i = i + inc; j = j - inc;
  end;
  /* Display the square. */
  do  i = 1 to n;
     put skip edit (a(i,*)) (f(4));
  end;

end;</lang>

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

PostScript

This implementation is far from being elegant or smart, but it builds the zigzag how a human being could do, and also draws lines to show the path.

<lang postscript>%!PS %%BoundingBox: 0 0 300 200 /size 9 def % defines row * column (9*9 -> 81 numbers,

           % from 0 to 80)

/itoa { 2 string cvs } bind def % visual bounding box... % 0 0 moveto 300 0 lineto 300 200 lineto 0 200 lineto % closepath stroke 20 150 translate % it can be easily enhanced to support more columns and % rows. This limit is put here just to avoid more than 2 % digits, mainly because of formatting size size mul 99 le {

  /Helvetica findfont 14 scalefont setfont
  /ulimit size size mul def
  /sizem1 size 1 sub def
  % prepare the number list
  0 ulimit 1 sub { dup 1 add } repeat
  ulimit array astore
  /di -1 def /dj 1 def
  /ri 1 def /rj 0 def /pus true def
  0 0 moveto
  /i 0 def /j 0 def
  {  % can be rewritten a lot better :)
     0.8 setgray i 30 mul j 15 mul neg lineto stroke
     0 setgray i 30 mul j 15 mul neg moveto itoa show
     i 30 mul j 15 mul neg moveto
     pus {
        i ri add size ge {
            /ri 0 def /rj 1 def
        } if
        j rj add size ge {
            /ri 1 def /rj 0 def
        } if
        /pus false def
        /i i ri add def
        /j j rj add def
        /ri rj /rj ri def def
     } {
         i di add dup    0 le
                 exch sizem1 ge or
         j dj add dup    0 le
                 exch sizem1 ge or
            or {
               /pus true def
               /i i di add def /j j dj add def
               /di di neg def /dj dj neg def
         } {
               /i i di add def /j j dj add def
         } ifelse
     } ifelse
  } forall
  stroke showpage

} if %%EOF</lang>

PowerShell

<lang PowerShell>function zigzag( [int] $n ) {

   $zigzag=New-Object 'Object[,]' $n,$n
   $nodd = $n -band 1
   $nm1 = $n - 1
   $i=0;
   $j=0;
   foreach( $k in 0..( $n * $n - 1 ) ) {
       $zigzag[$i,$j] = $k
       $iodd = $i -band 1
       $jodd = $j -band 1
       if( ( $j -eq $nm1 ) -and ( $iodd -ne $nodd ) ) {
           $i++
       } elseif( ( $i -eq $nm1 ) -and ( $jodd -eq $nodd ) ) {
           $j++
       } elseif( ( $i -eq 0 ) -and ( -not $jodd ) ) {
           $j++
       } elseif( ( $j -eq 0 ) -and $iodd ) {
           $i++
       } elseif( $iodd -eq $jodd ) {
           $i--
           $j++
       } else {
           $i++
           $j--
       }
   }
   ,$zigzag

}

function displayZigZag( [int] $n ) {

   $a = zigzag $n
   0..$n | ForEach-Object {
       $b=$_
       $pad=($n*$n-1).ToString().Length
       "$(0..$n | ForEach-Object {
           "{0,$pad}" -f $a[$b,$_]
       } )"
   }

}</lang>

Prolog

Works with: SWi-Prolog

<lang Prolog>zig_zag(N) :- zig_zag(N, N).

% compute zig_zag for a matrix of Lig lines of Col columns zig_zag(Lig, Col) :- length(M, Lig), maplist(init(Col), M), fill(M, 0, 0, 0, Lig, Col, up), % display the matrix maplist(print_line, M).


fill(M, Cur, L, C, NL, NC, _) :- L is NL - 1, C is NC - 1, nth0(L, M, Line), nth0(C, Line, Cur).

fill(M, Cur, L, C, NL, NC, Sens) :- nth0(L, M, Line), nth0(C, Line, Cur), Cur1 is Cur + 1, compute_next(NL, NC, L, C, Sens, L1, C1, Sens1), fill(M, Cur1, L1, C1, NL, NC, Sens1).


init(N, L) :- length(L, N).

% compute_next % arg1 : Number of lnes of the matrix % arg2 : number of columns of the matrix % arg3 : current line % arg4 : current column % arg5 : current direction of movement % arg6 : nect line % arg7 : next column % arg8 : next direction of movement compute_next(_NL, NC, 0, Col, up, 0, Col1, down) :- Col < NC - 1, Col1 is Col+1.

compute_next(_NL, NC, 0, Col, up, 1, Col, down) :- Col is NC - 1.

compute_next(NL, _NC, Lig, 0, down, Lig1, 0, up) :- Lig < NL - 1, Lig1 is Lig+1.

compute_next(NL, _NC, Lig, 0, down, Lig, 1, up) :- Lig is NL - 1.

compute_next(NL, _NC, Lig, Col, down, Lig1, Col1, down) :- Lig < NL - 1, Lig1 is Lig + 1, Col1 is Col-1.

compute_next(NL, _NC, Lig, Col, down, Lig, Col1, up) :- Lig is NL - 1, Col1 is Col+1.

compute_next(_NL, NC, Lig, Col, up, Lig1, Col1, up) :- Col < NC - 1, Lig1 is Lig - 1, Col1 is Col+1.

compute_next(_NL, NC, Lig, Col, up, Lig1, Col, down) :- Col is NC - 1, Lig1 is Lig + 1.


print_line(L) :- maplist(print_val, L), nl.

print_val(V) :- writef('%3r ', [V]). </lang>

Output:
?- zig_zag(5).
  0   1   5   6  14 
  2   4   7  13  15 
  3   8  12  16  21 
  9  11  17  20  22 
 10  18  19  23  24 
true .

?- zig_zag(5, 7).
  0   1   5   6  14  15  24 
  2   4   7  13  16  23  25 
  3   8  12  17  22  26  31 
  9  11  18  21  27  30  32 
 10  19  20  28  29  33  34 
true .

?- zig_zag(7,5).
  0   1   5   6  14 
  2   4   7  13  15 
  3   8  12  16  24 
  9  11  17  23  25 
 10  18  22  26  31 
 19  21  27  30  32 
 20  28  29  33  34 
true .

PureBasic

Translation of: AutoHotkey

<lang purebasic>Procedure zigZag(size)

 Protected i, v, x, y
 
 Dim a(size - 1, size - 1)
 
 x = 1
 y = 1
 For i = 1 To  size * size  ;loop once for each element
   a(x - 1, y - 1) = v      ;assign the next index
   
   If (x + y) & 1 = 0       ;even diagonal (zero based count)
     If x < size            ;while inside the square
       If y > 1             ;move right-up
         y - 1
       EndIf 
       x + 1
     Else
       y + 1                ;on the edge increment y, but not x until diagonal is odd
     EndIf 
   Else                     ;odd diagonal (zero based count)
     If y < size            ;while inside the square
       If x > 1             ;move left-down
         x - 1
       EndIf  
       y + 1
     Else
       x + 1                ;on the edge increment x, but not y until diagonal is even
     EndIf 
   EndIf 
   v + 1
 Next 
 
 ;generate and show printout
 PrintN("Zig-zag matrix of size " + Str(size) + #CRLF$)
 maxDigitCount = Len(Str(size * size)) + 1
 For y = 0 To size - 1 
   For x = 0 To size - 1
     Print(RSet(Str(a(x, y)), maxDigitCount, " "))
   Next 
   PrintN("")
 Next
 PrintN("")

EndProcedure

If OpenConsole()

 zigZag(5)
 zigZag(6)
 
 Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
 Input()
 CloseConsole()

EndIf</lang>

Output:
Zig-zag matrix of size 5

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

Zig-zag matrix of size 6

  0  1  5  6 14 15
  2  4  7 13 16 25
  3  8 12 17 24 26
  9 11 18 23 27 32
 10 19 22 28 31 33
 20 21 29 30 34 35

Python

Python: By sorting indices

There is a full explanation of the algorithm used by paddy3118. <lang python>def zigzag(n):

   indexorder = sorted(((x,y) for x in range(n) for y in range(n)),
                   key = lambda (x,y): (x+y, -y if (x+y) % 2 else y) )
   return {index: n for n,index in enumerate(indexorder)}

def printzz(myarray):

   n = int(len(myarray)** 0.5 +0.5)
   for x in range(n):
       for y in range(n):
               print "%2i" % myarray[(x,y)],
       print

printzz(zigzag(6))</lang>

Output:
     0  1  5  6 14 15
     2  4  7 13 16 25
     3  8 12 17 24 26
     9 11 18 23 27 32
    10 19 22 28 31 33
    20 21 29 30 34 35

Alternative version,
Translation of: Common Lisp

<lang python>def zigzag(n):

   def move(i, j):
       if j < (n - 1):
           return max(0, i-1), j+1
       else:
           return i+1, j
   a = [[0] * n for _ in xrange(n)]
   x, y = 0, 0
   for v in xrange(n * n):
       a[y][x] = v
       if (x + y) & 1:
           x, y = move(x, y)
       else:
           y, x = move(y, x)
   return a

from pprint import pprint pprint(zigzag(5))</lang>

Output:

<lang python>[[0, 1, 5, 6, 14],

[2, 4, 7, 13, 15],
[3, 8, 12, 16, 21],
[9, 11, 17, 20, 22],
[10, 18, 19, 23, 24]]</lang>

Alternative version, inspired by the Common Lisp Alternative Approach

<lang python> COLS = 9 def CX(x, ran):

 while True:
   x += 2 * next(ran)
   yield x
   x += 1
   yield x

ran = [] d = -1 for V in CX(1,iter(list(range(0,COLS,2)) + list(range(COLS-1-COLS%2,0,-2)))):

 ran.append(iter(range(V, V+COLS*d, d)))
 d *= -1

for x in range(0,COLS):

 for y in range(x, x+COLS):
   print(repr(next(ran[y])).rjust(3), end = ' ')
 print()

</lang>

Output:
COLS = 5 Produces
  1   2   6   7  15 
  3   5   8  14  16 
  4   9  13  17  22 
 10  12  18  21  23 
 11  19  20  24  25 
Output:
COLS = 8 Produces
  1   2   6   7  15  16  28  29 
  3   5   8  14  17  27  30  43 
  4   9  13  18  26  31  42  44 
 10  12  19  25  32  41  45  54 
 11  20  24  33  40  46  53  55 
 21  23  34  39  47  52  56  61 
 22  35  38  48  51  57  60  62 
 36  37  49  50  58  59  63  64 
Output:
COLS = 9 Produces
  1   2   6   7  15  16  28  29  45 
  3   5   8  14  17  27  30  44  46 
  4   9  13  18  26  31  43  47  60 
 10  12  19  25  32  42  48  59  61 
 11  20  24  33  41  49  58  62  71 
 21  23  34  40  50  57  63  70  72 
 22  35  39  51  56  64  69  73  78 
 36  38  52  55  65  68  74  77  79 
 37  53  54  66  67  75  76  80  81 

Rascal

This example is incorrect. Please fix the code and remove this message.
Details: Output is striped rather than zig-zag i.e. your numbers always increase going diagonally down and to the left when it should alternativly increase/decrease.

This is a translation of the Python example. As explained on the Talk page, the key way to understand a zig-zag matrix is to write down an example with coordinates: <lang rascal>0 (0,0), 1 (0,1), 3 (0,2) 2 (1,0), 4 (1,1), 6 (1,2) 5 (2,0), 7 (2,1), 8 (2,2)</lang> If you order these coordinates on the number, you create the order: <lang rascal> 0 (0,0), 1 (0,1), 2 (1,0), 3 (0,2), 4 (1,1), 5 (2,0), 6 (1,2), 7 (2,1), 8 (2,2)</lang> One can observe that this increases with the sum of the coordinates, and secondly with the the first number of the coordinates. The Rascal example uses this phenomenon: <lang rascal>import util::Math; import List; import Set; import IO;

alias cd = tuple[int,int];

public rel[cd, int] zz(int n){ indexorder = sort([<x,y>| x <- [0..n], y <- [0..n]], bool (cd a, cd b){ if (a[0]+a[1] > b[0]+b[1]) return false; elseif(a[0] < b[0]) return false; else return true; ; }); return {<indexorder[z] , z> | z <- index(indexorder)}; }

public void printzz(rel[cd, int] myarray){

   n = floor(sqrt(size(myarray)));
   for (x <- [0..n-1]){
       for (y <- [0..n-1]){
               print("<myarray[<y,x>]>\t");}
       println();}

}</lang>

Output:

<lang rascal>rascal>printzz(zz(4)) {0} {1} {3} {6} {10} {2} {4} {7} {11} {15} {5} {8} {12} {16} {19} {9} {13} {17} {20} {22} {14} {18} {21} {23} {24} ok</lang>

Qi

This is a purely functional, very inefficient, and straight forward solution. The code can probably be simplified somewhat.

<lang qi> (define odd? A -> (= 1 (MOD A 2))) (define even? A -> (= 0 (MOD A 2)))

(define zigzag-val

 0 0 N -> 0
 X 0 N -> (1+ (zigzag-val (1- X) 0 N)) where (odd? X)
 X 0 N -> (1+ (zigzag-val (1- X) 1 N)) 
 0 Y N -> (1+ (zigzag-val 1 (1- Y) N)) where (odd? Y)
 0 Y N -> (1+ (zigzag-val 0 (1- Y) N))
 X Y N -> (1+ (zigzag-val (MAX 0 (1- X)) (MIN (1- N) (1+ Y)) N)) where (even? (+ X Y))
 X Y N -> (1+ (zigzag-val (MIN (1- N) (1+ X)) (MAX 0 (1- Y)) N)))

(define range

 E E -> []
 S E -> [S|(range (1+ S) E)])

(define zigzag

 N -> (map (/. Y 
               (map (/. X 
                        (zigzag-val X Y N)) 
                    (range 0 N)))
           (range 0 N)))

</lang>

R

Translation of: Java

<lang R>zigzag <- function(size) {

  digits <- seq_len(size^2) - 1
  mat <- matrix(0, nrow = size, ncol=size)
  i <- 1
  j <- 1
  for(element in digits)
  {
     mat[i,j] <- element
     if((i + j) %% 2 == 0)
     {
        # Even stripes
        if(j < size) j <- j + 1 else i <- i + 2
        if(i > 1) i <- i - 1
     } else
     {
        # Odd stripes
        if(i < size) i <- i + 1 else j <- j + 2
        if(j > 1) j <- j - 1
     }
  }
  mat

}

zigzag(5)</lang>

Racket

<lang racket>

  1. lang racket

(define/match (compare i j)

 [((list x y) (list a b)) (or (< x a) (and (= x a) (< y b)))])

(define/match (key i)

 [((list x y)) (list (+ x y) (if (even? (+ x y)) (- y) y))])

(define (zigzag-ht n)

 (define indexorder
   (sort (for*/list ([x n] [y n]) (list x y))
         compare #:key key))
 (for/hash ([(n i) (in-indexed indexorder)]) (values n i)))
      

(define (zigzag n)

 (define ht (zigzag-ht n))
 (for/list ([x n]) 
   (for/list ([y n])
     (hash-ref ht (list x y)))))

(zigzag 4) </lang>

Output:

<lang racket> '((0 2 3 9)

 (1 4 8 10)
 (5 7 11 14) 
 (6 12 13 15))

</lang>

REXX

<lang rexx>/*REXX program produces and displays a zig─zag matrix (a square array). */ parse arg n start inc . /*obtain optional arguments from the CL*/ if n== then n=5 /*Not specified? Then use the default.*/ if start== then start=0 /* " " " " " " */ if inc== then inc=1 /* " " " " " " */ row=1; col=1 /*start with the 1st row, 1st column.*/ size=n**2 /*size of array.*/

          do j=start  by inc  for size;    @.row.col=j
          if (row+col)//2==0 then do
                                  if col<n    then col=col+1
                                              else row=row+2
                                  if row\==1  then row=row-1
                                  end
                             else do
                                  if row<n    then row=row+1
                                              else col=col+2
                                  if col\==1  then col=col-1
                                  end
          end   /*j*/

w=max(length(start), length(start+size*inc)) /*maximum width of any element.*/

 do       row=1  for n;   _=          /*show all the rows of the matrix.     */
       do col=1  for n;   _=_ right(@.row.col,w);    end  /*col*/
 say _                                /*show the matrix row just constructed.*/
 end   /*row*/                        /*stick a fork in it,  we're all done. */</lang>

output   when using the default input of:   5

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

Ruby

Translation of: Python

<lang ruby>def zigzag(n)

 (seq=*0...n).product(seq)
   .sort_by {|x,y| [x+y, (x+y).even? ? y : -y]}
   .each_with_index.sort.map(&:last).each_slice(n).to_a

end

def print_matrix(m)

 format = "%#{m.flatten.max.to_s.size}d " * m[0].size
 puts m.map {|row| format % row}

end

print_matrix zigzag(5)</lang>

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

Scala

Uses the array indices sort solution used by others here.

<lang scala>def zigzag(n:int) = {

 var l = List[Tuple2[int,int]]()
 (0 until n*n) foreach {i=>l = l + (i%n,i/n)}
 l = l.sort{case ((x,y),(u,v)) => if (x+y == u+v) 
                                    if ((x+y) % 2 == 0) x<u else y<v 
                                  else (x+y) < (u+v) }
 var a = new Array[Array[int]](n,n)
 l.zipWithIndex foreach {case ((x,y),i) => a(y)(x) = i}
 a

}</lang>

Or, compressed into just one statement

<lang scala>def zigzag(n:int) = {

var indices = List[Tuple2[Int,Int]]()
var array = new Array[Array[Int]](n,n)
(0 until n*n).foldLeft(indices)((l,i) => l + (i%n,i/n)).
  sort{case ((x,y),(u,v)) => if (x+y == u+v) 
                   		if ((x+y) % 2 == 0) x<u else y<v 
                             else (x+y) < (u+v) }.
  zipWithIndex.foldLeft(array) {case (a,((x,y),i)) => a(y)(x) = i; a}

} </lang>

Seed7

<lang seed7>$ include "seed7_05.s7i";

const type: matrix is array array integer;

const func matrix: zigzag (in integer: size) is func

 result
   var matrix: s is matrix.value;
 local
   var integer: i is 1;
   var integer: j is 1;
   var integer: d is -1;
   var integer: max is 0;
   var integer: n is 0;
 begin
   s := size times size times 0;
   max := size ** 2;
   for n range 1 to max div 2 + 1 do
     s[i][j] := n;
     s[size - i + 1][size - j + 1] := max - n + 1;
     i +:= d;
     j -:= d;
     if i < 1 then
       incr(i);
       d := -d;
     elsif j < 1 then
       incr(j);
       d := -d;
     end if;
   end for;
 end func;

const proc: main is func

 local
   var matrix: s is matrix.value;
   var integer: i is 0;
   var integer: num is 0;
 begin
   s := zigzag(7);
   for i range 1 to length(s) do
     for num range s[i] do
       write(num lpad 4);
     end for;
     writeln;
   end for;
 end func;</lang>
Output:
   1   2   6   7  15  16  28
   3   5   8  14  17  27  29
   4   9  13  18  26  30  39
  10  12  19  25  31  38  40
  11  20  24  32  37  41  46
  21  23  33  36  42  45  47
  22  34  35  43  44  48  49

Sidef

Translation of: Perl

<lang ruby>func zig_zag(w, h) {

   var r = [];
   var n = 0;
   h.of { |e|
       w.of { |f|
           [e-1, f-1]
       }
   }
   -> reduce('+')
   -> sort { |a, b|
          (a[0]+a[1] <=> b[0]+b[1])
       || (a[0]+a[1] -> is_even ? a[0]<=>b[0]
                                : a[1]<=>b[1])
   }
   -> each { |a|
      r[a[1]][a[0]] = n++;
   }
   return r;

}

zig_zag(5, 5).each {say .join(, {|i| "%4i" % i})};</lang>

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

Tcl

Using print_matrix from Matrix Transpose… <lang tcl>proc zigzag {size} {

   set m [lrepeat $size [lrepeat $size .]]
   set x 0; set dx -1
   set y 0; set dy 1
   
   for {set i 0} {$i < $size ** 2} {incr i} {
       if {$x >= $size} {
           incr x -1
           incr y 2
           negate dx dy
       } elseif {$y >= $size} {
           incr x 2
           incr y -1
           negate dx dy
       } elseif {$x < 0 && $y >= 0} {
           incr x
           negate dx dy
       } elseif {$x >= 0 && $y < 0} {
           incr y
           negate dx dy
       }
       lset m $x $y $i
       incr x $dx
       incr y $dy
   }
   return $m

}

proc negate {args} {

   foreach varname $args {
       upvar 1 $varname var
       set var [expr {-1 * $var}]
   }

}

print_matrix [zigzag 5]</lang>

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

uBasic/4tH

Translation of: BBC BASIC

<lang>S = 5

i = 1 j = 1

For e = 0 To (S*S)-1

 @((i-1) * S + (j-1)) = e
 If (i + j) % 2 = 0 Then
   If j < S Then
     j = j + 1
   Else
     i = i + 2
   EndIf
   If i > 1 Then
     i = i - 1
   EndIf
 Else
   If i < S
     i = i + 1
   Else
     j = j + 2
   EndIf
   If j > 1
     j = j - 1
   EndIf
 EndIf

Next

For r = 0 To S-1

 For c = 0 To S-1
   Print Using "___#";@(r * S + c);
 Next
 Print

Next</lang>

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

0 OK, 0:428

Ursala

adapted from the J solution <lang Ursala>#import std

  1. import nat

zigzag = ~&mlPK2xnSS+ num+ ==+sum~~|=xK9xSL@iiK0+ iota</lang> test program (three examples): <lang Ursala>#cast %nLLL

tests = zigzag* <4,5,6></lang>

Output:
<
   <
      <0,1,5,6>,
      <2,4,7,12>,
      <3,8,11,13>,
      <9,10,14,15>>,
   <
      <0,1,5,6,14>,
      <2,4,7,13,15>,
      <3,8,12,16,21>,
      <9,11,17,20,22>,
      <10,18,19,23,24>>,
   <
      <0,1,5,6,14,15>,
      <2,4,7,13,16,25>,
      <3,8,12,17,24,26>,
      <9,11,18,23,27,32>,
      <10,19,22,28,31,33>,
      <20,21,29,30,34,35>>>

VBA

<lang VBA> Public Sub zigzag(n) Dim a() As Integer 'populate a (1,1) to a(n,n) in zigzag pattern

'check if n too small If n < 1 Then

 Debug.Print "zigzag: enter a number greater than 1"
 Exit Sub

End If

'initialize ReDim a(1 To n, 1 To n) i = 1 'i is the row j = 1 'j is the column P = 0 'P is the next number a(i, j) = P 'fill in initial value

'now zigzag through the matrix and fill it in Do While (i <= n) And (j <= n)

 'move one position to the right or down the rightmost column, if possible
 If j < n Then
   j = j + 1
 ElseIf i < n Then
   i = i + 1
 Else
   Exit Do
 End If
 'fill in
 P = P + 1: a(i, j) = P
 'move down to the left
 While (j > 1) And (i < n)
   i = i + 1: j = j - 1
   P = P + 1: a(i, j) = P
 Wend
 'move one position down or to the right in the bottom row, if possible
 If i < n Then
   i = i + 1
 ElseIf j < n Then
   j = j + 1
 Else
   Exit Do
 End If
 P = P + 1: a(i, j) = P
 'move back up to the right
 While (i > 1) And (j < n)
   i = i - 1: j = j + 1
   P = P + 1: a(i, j) = P
 Wend

Loop

'print result Debug.Print "Result for n="; n; ":" For i = 1 To n

 For j = 1 To n
   Debug.Print a(i, j),
 Next
 Debug.Print

Next End Sub </lang>

Output:
zigzag 5
Result for n= 5 :
 0             1             5             6             14           
 2             4             7             13            15           
 3             8             12            16            21           
 9             11            17            20            22           
 10            18            19            23            24           

zigzag 6
Result for n= 6 :
 0             1             5             6             14            15           
 2             4             7             13            16            25           
 3             8             12            17            24            26           
 9             11            18            23            27            32           
 10            19            22            28            31            33           
 20            21            29            30            34            35           

VBScript

Translation of: BBC BASIC

<lang vb>ZigZag(Cint(WScript.Arguments(0)))

Function ZigZag(n) Dim arrZ() ReDim arrZ(n-1,n-1) i = 1 j = 1 For e = 0 To (n^2) - 1 arrZ(i-1,j-1) = e If ((i + j ) And 1) = 0 Then If j < n Then j = j + 1 Else i = i + 2 End If If i > 1 Then i = i - 1 End If Else If i < n Then i = i + 1 Else j = j + 2 End If If j > 1 Then j = j - 1 End If End If Next For k = 0 To n-1 For l = 0 To n-1 WScript.StdOut.Write Right(" " & arrZ(k,l),3) Next WScript.StdOut.WriteLine Next End Function</lang>

Output:
C:\>cscript /nologo ZigZag.vbs 5
  0  1  5  6 14
  2  4  7 13 15
  3  8 12 16 21
  9 11 17 20 22
 10 18 19 23 24

C:\>cscript /nologo ZigZag.vbs 7
  0  1  5  6 14 15 27
  2  4  7 13 16 26 28
  3  8 12 17 25 29 38
  9 11 18 24 30 37 39
 10 19 23 31 36 40 45
 20 22 32 35 41 44 46
 21 33 34 42 43 47 48

XPL0

<lang XPL0>include c:\cxpl\codes; def N=6; int A(N,N), X, Y, I, D; [I:=0; X:=0; Y:=0; D:=1; repeat A(X,Y):=I;

       case of
        X+D>=N: [D:=-D; Y:=Y+1];
        Y-D>=N: [D:=-D; X:=X+1];
        X+D<0:  [D:=-D; Y:=Y+1];
        Y-D<0:  [D:=-D; X:=X+1]
       other    [X:=X+D; Y:=Y-D];
       I:=I+1;

until I>=N*N; for Y:=0 to N-1 do

   [for X:=0 to N-1 do
       [I:=A(X,Y);
       ChOut(0,^ );
       if I<10 then ChOut(0,^ );
       IntOut(0, I);
       ];
   CrLf(0);
   ];

]</lang>

Output:
  0  1  5  6 14 15
  2  4  7 13 16 25
  3  8 12 17 24 26
  9 11 18 23 27 32
 10 19 22 28 31 33
 20 21 29 30 34 35

zkl

Translation of: Groovy

<lang zkl>fcn zz(n){

  grid := (0).pump(n,List, (0).pump(n,List).copy).copy();
  ri := Ref(0);
  foreach d in ([1..n*2]){
     x:=(0).max(d - n); y:=(n - 1).min(d - 1);
     (0).pump(d.min(n*2 - d),Void,'wrap(it){
        grid[if(d%2)y-it else x+it][if(d%2)x+it else y-it] = ri.inc();
     });
  }
  grid.pump(String,'wrap(r){("%3s"*n+"\n").fmt(r.xplode())});

}</lang>

Translation of: C

Using list comprehension (and side effects) for the double loop, the resulting list is just thrown away, which is easier than creating an enumerated list and sorting. <lang zkl>fcn ceg(m){

  s  := (0).pump(m*m,List).copy(); // copy to make writable
  rn := Ref(0);
  [[(i,j); [0..m*2-1]; '{[(0).max(i-m+1) .. i.min(m-1)]};
        '{ s[ if(i.isOdd) j*(m-1)+i else (i-j)*m+j ] = rn.inc(); }]];
  s.pump(String,T(Void.Read,m-1), ("%3s"*m+"\n").fmt);

}</lang> To be pedantic, the same as above, but using the output of the list comprehension: <lang zkl>fcn ceg2(m){

  rn := Ref(0);
  [[(i,j); [0..m*2-1]; '{[(0).max(i-m+1) .. i.min(m-1)]};
        '{ T( if(i.isOdd) j*(m-1)+i else (i-j)*m+j;, rn.inc() ) }]]
  .sort(fcn([(a,_)], [(b,_)]){ a<b }).apply("get",1)
  .pump(String,T(Void.Read,m-1), ("%3s"*m+"\n").fmt);

}</lang>

Output:
The results are the same
zz(5).println();
  0  1  5  6 14
  2  4  7 13 15
  3  8 12 16 21
  9 11 17 20 22
 10 18 19 23 24