# Zig-zag matrix

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 array's   anti-diagonals.

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

## 360 Assembly

*        Zig-zag matrix            15/08/2015
ZIGZAGMA CSECT
USING ZIGZAGMA,R12 set base register
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
N EQU 5 matrix size
BUFFER DS CL80
XDEC DS CL12
T DS (N*N)H t(n,n) matrix
YREGS
END ZIGZAGMA
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

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 --;
}
}
}
}
}

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;

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

## Agena

Tested with Agena 2.9.5 Win32

# zig-zag matrix

makeZigZag := proc( n :: number ) :: table is

local move := proc( x :: number, y :: number, upRight :: boolean ) is
if y = n then
upRight := not upRight;
x := x + 1
elif x = 1 then
upRight := not upRight;
y := y + 1
else
x := x - 1;
y := y + 1
fi;
return x, y, upRight
end ;

# create empty table
local result := [];
for i to n do
result[ i ] := [];
for j to n do result[ i, j ] := 0 od
od;

# fill the table
local x, y, upRight := 1, 1, true;
for i to n * n do
result[ x, y ] := i - 1;
if upRight then
x, y, upRight := move( x, y, upRight )
else
y, x, upRight := move( y, x, upRight )
fi
od;

return result
end;

scope
local m := makeZigZag( 5 );
for i to size m do
for j to size m do
printf( " %3d", m[ i, j ] )
od;
print()
od
epocs
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
PROC zig zag = (INT n)[,]INT: (
PROC move = (REF INT i, j)VOID: (
IF j < n THEN
i := ( i <= 1 | 1 | i-1 );
j +:= 1
ELSE
i +:= 1
FI
);

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

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

INT dim = 5;
#IF formatted transput possible THEN
FORMAT d = $z-d$;
FORMAT row = $"("n(dim-1)(f(d)",")f(d)")"$;
FORMAT block = $"("n(dim-1)(f(row)","lx)f(row)")"l$;

printf((block, zig zag(dim)))
ELSE#

[,]INT result = zig zag(dim);
FOR i TO dim DO
print((result[i,], new line))
OD
#FI#
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

## ALGOL W

Based on the Agena sample.

begin % zig-zag matrix %
% z is returned holding a zig-zag matrix of order n, z must be at least n x n %
procedure makeZigZag ( integer value n
; integer array z( *, * )
) ;
begin
procedure move ;
begin
if y = n then begin
upRight := not upRight;
x := x + 1
end
else if x = 1 then begin
upRight := not upRight;
y := y + 1
end
else begin
x := x - 1;
y := y + 1
end
end move ;
procedure swapXY ;
begin
integer swap;
swap := x;
x  := y;
y  := swap;
end swapXY ;
integer x, y;
logical upRight;
% initialise the n x n matrix in z %
for i := 1 until n do for j := 1 until n do z( i, j ) := 0;
% fill in the zig-zag matrix %
x := y := 1;
upRight := true;
for i := 1 until n * n do begin
z( x, y ) := i - 1;
if upRight then move
else begin
swapXY;
move;
swapXY
end;
end;
end makeZigZap ;

begin
integer array zigZag( 1 :: 10, 1 :: 10 );
for n := 5 do begin
makeZigZag( n, zigZag );
for i := 1 until n do begin
write( i_w := 4, s_w := 1, zigZag( i, 1 ) );
for j := 2 until n do writeon( i_w := 4, s_w := 1, zigZag( i, j ) );
end
end
end

end.
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

## APL

Works with: Dyalog APL
Translation of: J
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

## AppleScript

### Iterative

Here's a vector & matrix boundary detection approach to the Zig-zap matrix:

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
But this can be improved upon by building the matrix by populating empty AppleScript lists (it's about 50% faster when n=50):
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

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
"

### Recursive

By functional composition:

-- zigzagMatrix
on zigzagMatrix(n)

-- diagonals :: n -> [[n]]
script diagonals
on |λ|(n)
script mf
on diags(xs, iCol, iRow)
if (iCol < length of xs) then
if iRow < n then
set iNext to iCol + 1
else
set iNext to iCol - 1
end if

set {headList, tail} to splitAt(iCol, xs)
{headList} & diags(tail, iNext, iRow + 1)
else
{xs}
end if
end diags
end script

diags(enumFromTo(0, n * n - 1), 1, 1) of mf
end |λ|
end script

-- oddReversed :: [a] -> Int -> [a]
script oddReversed
on |λ|(lst, i)
if i mod 2 = 0 then
lst
else
reverse of lst
end if
end |λ|
end script

rowsFromDiagonals(n, map(oddReversed, |λ|(n) of diagonals))

end zigzagMatrix

-- Rows of given length from list of diagonals
-- rowsFromDiagonals :: Int -> [[a]] -> [[a]]
on rowsFromDiagonals(n, lst)
if length of lst > 0 then

-- lengthOverOne :: [a] -> Bool
script lengthOverOne
on |λ|(lst)
length of lst > 1
end |λ|
end script

set {edge, residue} to splitAt(n, lst)

rowsFromDiagonals(n, ¬
map(my tail, ¬
filter(lengthOverOne, edge)) & residue)
else
{}
end if
end rowsFromDiagonals

-- TEST -----------------------------------------------------------------------
on run

zigzagMatrix(5)

end run

-- GENERIC FUNCTIONS ----------------------------------------------------------

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if n < m then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo

-- filter :: (a -> Bool) -> [a] -> [a]
on filter(f, xs)
tell mReturn(f)
set lst to {}
set lng to length of xs
repeat with i from 1 to lng
set v to item i of xs
if |λ|(v, i, xs) then set end of lst to v
end repeat
return lst
end tell
end filter

-- head :: [a] -> a
if length of xs > 0 then
item 1 of xs
else
missing value
end if

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- splitAt:: n -> list -> {n items from start of list, rest of list}
-- splitAt :: Int -> [a] -> ([a], [a])
on splitAt(n, xs)
if n > 0 and n < length of xs then
{items 1 thru n of xs, items (n + 1) thru -1 of xs}
else
if n < 1 then
{{}, xs}
else
{xs, {}}
end if
end if
end splitAt

-- tail :: [a] -> [a]
on tail(xs)
if length of xs > 1 then
items 2 thru -1 of xs
else
{}
end if
end tail
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}}

## Applesoft BASIC

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 ## ATS (* ****** ****** *) // #include "share/atspre_define.hats" // defines some names #include "share/atspre_staload.hats" // for targeting C #include "share/HATS/atspre_staload_libats_ML.hats" // for ... // (* ****** ****** *) // extern fun Zig_zag_matrix(n: int): void // (* ****** ****** *) fun max(a: int, b: int): int = if a > b then a else b fun movex(n: int, x: int, y: int): int = if y < n-1 then max(0, x-1) else x+1 fun movey(n: int, x: int, y: int): int = if y < n-1 then y+1 else y fun zigzag(n: int, i: int, row: int, x: int, y: int): void = if i = n*n then () else let val () = (if x = row then begin print i; print ','; end else ()) //val () = (begin print x; print ' '; print y; print ' '; print i; print ' '; end) val nextX: int = if ((x+y) % 2) = 0 then movex(n, x, y) else movey(n, y, x) val nextY: int = if ((x+y) % 2) = 0 then movey(n, x, y) else movex(n, y, x) in zigzag(n, i+1, row, nextX, nextY) end implement Zig_zag_matrix(n) = let fun loop(row: int): void = if row = n then () else let val () = zigzag(n, 0, row, 0, 0) val () = println!(" ") in loop(row + 1) end in loop(0) end (* ****** ****** *) implement main0() = () where { val () = Zig_zag_matrix(5) } (* end of [main0] *) (* ****** ****** *) ## AutoHotkey Translation of: lisp contributed by Laszlo on the ahk forum. 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 ## AutoIt #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

## AWK

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

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

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%
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.

>> 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\_$:>55+/\| >55+,20g!00g10g>#^[email protected]^!g03g00!g04++**2p03:+1g03!\*+1*2g01:g04.$<
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

#include <stdio.h>
#include <stdlib.h>

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

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

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

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

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

/* free(s) */
return 0;
}
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++

#include <vector>
#include <memory> // for auto_ptr
#include <cmath> // for the log10 and floor functions
#include <iostream>
#include <iomanip> // for the setw function

using namespace std;

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

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

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

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

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

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

return zigZagArrayPtr;
}

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

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

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

int main()
{
printZigZagArray( getZigZagArray( 5 ) );
}
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#

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;
}

## Ceylon

class ZigZag(Integer size) {

value data = Array {
for (i in 0:size)
Array.ofSize(size, 0)
};

variable value i = 1;
variable value j = 1;

for (element in 0 : size^2) {
data[j - 1]?.set(i - 1, element);
if ((i + j).even) {
if (j < size) {
j++;
}
else {
i += 2;
}
if (i > 1) {
i--;
}
}
else {
if (i < size) {
i++;
}
else {
j += 2;
}
if (j > 1) {
j--;
}
}
}

shared void display() {
for (row in data) {
for (element in row) {
}
print(""); //newline
}
}
}

shared void run() {
value zz = ZigZag(5);
zz.display();
}

## Clojure

Purely functional approach.

(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))

## CoffeeScript

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

zig_zag_value = (x, y, n) ->

upper_triangle_zig_zag = (x, y) ->
# calculate the area of the triangle from the prior
# diagonals
diag = x + y
triangle_area = diag * (diag+1) / 2
# then add the offset along the diagonal
if diag % 2 == 0
triangle_area + y
else
triangle_area + x

if x + y < n
upper_triangle_zig_zag x, y
else
# For the bottom right part of the matrix, we essentially
# use reflection to count backward.
bottom_right_cell = n * n - 1
n -= 1
v = upper_triangle_zig_zag(n-x, n-y)
bottom_right_cell - v

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

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

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)

(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))))

### An alternative approach

; 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)))))))

(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
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);
}
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.

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);
}

## 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
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
}

## Elena

Translation of: C#

ELENA 3.4:

import extensions.

extension<int> op
{
zigzagMatrix
[
auto result := IntMatrix new(self, self).

int i := 0.
int j := 0.
int d := -1.
int start := 0.
int end := self*self - 1.

while (start < end)
[
result write(i, j, start). start += 1.
result write(self - i - 1, self - j - 1, end). end -= 1.

i := i + d.
j := j - d.
if (i < 0)
[
i:=i+1. d := d negative
];
[
if (j < 0)
[
j := j + 1. d := d negative
]
]
].

if (start == end)
[
result write(i, j, start).
].

^ result
]
}

public program
[
]

## Elixir

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

RC.zigzag(5)
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

-module( zigzag ).

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)].

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}.

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]]

## 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
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#
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)
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#

//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)

Output:
zz 5 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]]
zz 8 8
[[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

zz 5 8
[[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

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|
{
}
echo(buf)
}
}

Void main()
{
echo("zig method:")
print(zig(8))
echo("\nzag method:")
print(zag(8))
}
}

## 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 ;

2dup ! swap 1+ swap ;

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

## Fortran

Works with: Fortran version 90 and later
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
END DO
WRITE(*,*)
END DO

END PROGRAM ZIGZAG

## FreeBASIC

' FB 1.05.0 Win64

Dim As Integer n

Do
Input "Enter size of matrix "; n
Loop Until n > 0

Dim zigzag(1 To n, 1 To n) As Integer '' all zero by default

' enter the numbers 0 to (n^2 - 1) in the matrix's anti-diagonals
zigzag(1, 1) = 0
If n > 1 Then
Dim As Integer row = 0, col = 3
Dim As Boolean down = true, increment = true
Dim As Integer i = 0, j = 2, k
Do
If down Then
For k = 1 To j
i += 1
row += 1
col -= 1
zigzag(row, col) = i
Next
down = false
Else
For k = 1 To j
i += 1
row -= 1
col += 1
zigzag(row, col) = i
Next
down = true
End If
If increment Then
j += 1
If j > n Then
j = n - 1
increment = false
End If
Else
j -= 1
If j = 0 Then Exit Do
End If
If down AndAlso increment Then
col += 2
row -= 1
ElseIf Not Down AndAlso increment Then
row += 2
col -= 1
ElseIf down AndAlso Not increment Then
col += 1
Else '' Not down AndAlso NotIncrement
row += 1
End If
Loop
End If

' print zigzag matrix if n < 20
Print
If n < 20 Then
For i As Integer = 1 To n
For j As Integer = 1 To n
Print Using "####"; zigzag(i, j);
Next j
Print
Next i
Else
Print "Matrix is too big to display on 80 column console"
End If

Print
Print "Press any key to quit"
Sleep
Output:
Enter size of matrix ? 8

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

## 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));
# [ [ 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 ] ]

## Go

Translation of: Groovy
Edge direct algorithm
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("")
}
}
}
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.

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
}
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

### Sorting

Ported from the Python example with some input from J

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 } }
}
Output:
> zz(5).each { it.each { print("${it}".padLeft(3)) }; println() } 0 1 5 6 14 2 4 7 13 15 3 8 12 16 21 9 11 17 20 22 10 18 19 23 24 ## Haskell Computing the array: import Data.Array (array, bounds, range, (!)) import Data.Monoid (mappend) import Data.List (sortBy) compZig (x,y) (x',y') = compare (x+y) (x'+y') mappend if even (x+y) then compare x x' else compare y y' zigZag upper = array b$ zip (sortBy compZig (range b))
[0..]
where b = ((0,0),upper)

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):

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)]

Or, building a list of lists with mapAccumL:

import Data.List (mapAccumL)
import Data.Text (justifyRight, pack, unpack)

zigZag :: Int -> [[Int]]
zigZag n = horizontals n (diagonals n)
where

diagonals :: Int -> [[Int]]
diagonals n =
snd $mapAccumL (\xs h -> let (grp, rst) = splitAt h xs in ( rst , (if mod h 2 /= 0 then reverse else id) grp)) [0 .. (n * n) - 1] (slope ++ [n] ++ reverse slope) where slope = [1 .. n - 1] horizontals :: Int -> [[Int]] -> [[Int]] horizontals n xss = if not (null xss) then let (edge, rst) = splitAt n xss in (head <$> edge) :
horizontals n (dropWhile null (tail <$> edge) ++ rst) else [] main :: IO () main = putStrLn$
unlines $(concat . (unpack <$>)) . ((justifyRight 3 ' ' . pack . show) <$>) <$>
zigZag 5
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

## Icon and Unicon

This solution works for both Icon and Unicon.

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
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
->

## IS-BASIC

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

## J

A succinct way:

($[: /:@; <@|.</[email protected])@,~ 5 0 1 5 6 14 2 4 7 13 15 3 8 12 16 21 9 11 17 20 22 10 18 19 23 24 This version is longer, but more "mathematical" and less "procedural": ($ [: /:@; [: <@(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

Leveraging a useful relationship among the indices:

($([: /:@;@(+/"1 <@|.</. ]) (#: [email protected](*/))))@,~ 5 0 1 5 6 14 2 4 7 13 15 3 8 12 16 21 9 11 17 20 22 10 18 19 23 24 By the way, all the edge cases are handled transparently, without any special checks. Furthermore, by simply removing the trailing @,~ from the solutions, they automatically generalize to rectangular (non-square) matrices: ($ [: /:@; [: <@|.</. i.) 5 3
0 1 5
2 4 6
3 7 11
8 10 12
9 13 14

## 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;
}

## JavaScript

### Imperative

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

Subclasses the Matrix class defined at Matrix Transpose#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);
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

#### ES5

(function (n) {

// Read range of values into a series of 'diagonal rows'
// for a square of given dimension,
// starting at diagonal row i.
// [
// [0],
// [1, 2],
// [3, 4, 5],
// [6, 7, 8, 9],
// [10, 11, 12, 13, 14],
// [15, 16, 17, 18],
// [19, 20, 21],
// [22, 23],
// [24]
// ]

// diagonals :: n -> [[n]]
function diagonals(n) {
function diags(xs, iCol, iRow) {
if (iCol < xs.length) {
var xxs = splitAt(iCol, xs);

return [xxs[0]].concat(diags(
xxs[1],
(iCol + (iRow < n ? 1 : -1)),
iRow + 1
));
} else return [xs];
}

return diags(range(0, n * n - 1), 1, 1);
}

// n -> [[n]] -> [[n]]
var zipEdge = lst.slice(0, n);

return lst.length ? [zipEdge.map(function (x) {
return x[0];
x) {
return x.length > 1 ? [x.slice(1)] : [];
}))
.concat(lst.slice(n)))) : [];
}

// range(intFrom, intTo, optional intStep)
// Int -> Int -> Maybe Int -> [Int]
function range(m, n, delta) {
var d = delta || 1,
blnUp = n > m,
lng = Math.floor((blnUp ? n - m : m - n) / d) + 1,
a = Array(lng),
i = lng;

if (blnUp)
while (i--) a[i] = (d * i) + m;
else
while (i--) a[i] = m - (d * i);
return a;
}

// splitAt :: Int -> [a] -> ([a],[a])
function splitAt(n, xs) {
return [xs.slice(0, n), xs.slice(n)];
}

// Recursively take n heads from the alternately reversed diagonals

// [ [
// [0], -> [0, 1, 5, 6, 14] and:
// [1, 2], [2],
// [5, 4, 3], [4, 3],
// [6, 7, 8, 9], [7, 8, 9],
// [14, 13, 12, 11, 10], [13, 12, 11, 10],
// [15, 16, 17, 18], [15, 16, 17, 18],
// [21, 20, 19], [21, 20, 19],
// [22, 23], [22, 23],
// [24] [24]
// ] ]
//
// In the next recursion with the remnant on the right, the next
// 5 heads will be [2, 4, 7, 13, 15] - the second row of our zig zag matrix.
// (and so forth)

.map(function (x, i) {
i % 2 || x.reverse();
return x;
}));

})(5);
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]]

#### ES6

(n => {

// diagonals :: n -> [[n]]
function diagonals(n) {
let diags = (xs, iCol, iRow) => {
if (iCol < xs.length) {
let xxs = splitAt(iCol, xs);

return [xxs[0]].concat(diags(
xxs[1],
iCol + (iRow < n ? 1 : -1),
iRow + 1
));
} else return [xs];
}

return diags(range(0, n * n - 1), 1, 1);
}

// rowsFromDiagonals :: n -> [[n]] -> [[n]]
function rowsFromDiagonals(n, lst) {
if (lst.length) {
let [edge, rest] = splitAt(n, lst);

return [edge.map(x => x[0])]
.concat(rowsFromDiagonals(n,
edge.filter(x => x.length > 1)
.map(x => x.slice(1))
.concat(rest)
));
} else return [];
}

// GENERIC FUNCTIONS

// splitAt :: Int -> [a] -> ([a],[a])
function splitAt(n, xs) {
return [xs.slice(0, n), xs.slice(n)];
}

// range :: From -> To -> Maybe Step -> [Int]
// range :: Int -> Int -> Maybe Int -> [Int]
function range(m, n, step) {
let d = (step || 1) * (n >= m ? 1 : -1);

return Array.from({
length: Math.floor((n - m) / d) + 1
}, (_, i) => m + (i * d));
}

// ZIG-ZAG MATRIX

return rowsFromDiagonals(n,
diagonals(n)
.map((x, i) => (i % 2 || x.reverse()) && x)
);

})(5);
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]]

## 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.

## jq

Infrastructure:

# Create an m x n matrix
def matrix(m; n; init):
if m == 0 then []
elif m == 1 then [range(0;n)] | map(init)
elif m > 0 then
matrix(1;n;init) as $row | [range(0;m)] | map($row )
else error("matrix\(m);_;_) invalid")
end ;

# Print a matrix neatly, each cell occupying n spaces
def neatly(n):
def right: tostring | ( " " * (n-length) + .);
. as $in | length as$length
| reduce range (0;$length) as$i
(""; . + reduce range(0;$length) as$j
(""; "\(.) \($in[$i][$j] | right )" ) + "\n" ) ; Create a zigzag matrix by zigzagging: def zigzag(n): # unless m == n*n, place m at (i,j), pointing # in the direction d, where d = [drow, dcolumn]: def _next(i; j; m; d): if m == (n*n) then . else .[i][j] = m end | if m == (n*n) - 1 then . elif i == n-1 then if j+1 < n then .[i][j+1] = m+1 | _next(i-1; j+2; m+2; [-1, 1]) else . end elif i == 0 then if j+1 < n then .[i][j+1] = m+1 | _next(i+1; j ; m+2; [ 1,-1]) else .[i+1][j] = m+1 | _next(i+2; j-1; m+2; [ 1,-1]) end elif j == n-1 then if i+1 < n then .[i+1][j] = m+1 | _next(i+2; j-1; m+2; [ 1,-1]) else . end elif j == 0 then if i+1 < n then .[i+1][j] = m+1 | _next(i; j+1; m+2; [-1, 1]) else .[i][j+1] = m+1 | _next(i-1; j+1; m+2; [-1, 1]) end else _next(i+ d[0]; j+ d[1]; m+1; d) end ; matrix(n;n;-1) | _next(0;0; 0; [0,1]) ; # Example zigzag(5) | neatly(4) Output:$ 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

### another solution

#!/usr/bin/env jq -Mnrc -f
#
# solve zigzag matrix by constructing list of 2n+1 column "runs"
# and then shifting them into final form.
#
# e.g. for n=3 initial runs are [[0],[1,2],[3,4,5],[6,7],[8]]
# runs below are shown as columns:
#
# initial column runs 0 1 3 6 8
# 2 4 7
# 5
#
# reverse cols 0,2,4 0 1 5 6 8
# 2 4 7
# 3
#
# shift cols 3,4 down 0 1 5
# 2 4 6
# 3 7 8
#
# shift rows left 0 1 5
# to get final zigzag 2 4 6
# 3 7 8

def N: $n ; # size of matrix def NR: 2*N - 1; # number of runs def abs: if .<0 then -. else . end ; # absolute value def runlen: N-(N-.|abs) ; # length of run def makeruns: [ foreach range(1;NR+1) as$r ( # for each run
{c:0} # state counter
; .l = ($r|runlen) # length of this run | .r = [range(.c;.c+.l)] # values in this run | .c += .l # increment counter ; .r # produce run ) ] ; # collect into array def even: .%2==0 ; # is input even? def reverseruns: # reverse alternate runs .[keys|map(select(even))[]] |= reverse ; def zeros: [range(.|N-length)|0] ; # array of padding zeros def shiftdown: def pad($r): # pad run with zeros
if $r < N # determine where zeros go then . = . + zeros # at back for left runs else . = zeros + . # at front for right runs end ; reduce keys[] as$r (.;.[$r] |= pad($r)); # shift rows down with pad
def shiftleft: [
range(N) as $r | [ range($r;$r+N) as$c
| .[$c][$r]
]
] ;
def width: [.[][]]|max|tostring|1+length; # width of largest value
def justify($w): (($w-length)*" ") + . ; # leading spaces
def format:
width as $w # compute width | map(map(tostring | justify($w)))[] # justify values
| join(" ")
;
makeruns # create column runs
| reverseruns # reverse alternate runs
| shiftdown # shift right runs down
| shiftleft # shift rows left
| format # format final result

Output:
$./zigzag.jq --argjson n 8 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 ## Julia ### simple solution function zigzag_matrix(n::Int) matrix = zeros(Int, n, n) x, y = 1, 1 for i = 0:(n*n-1) matrix[y,x] = i if (x + y) % 2 == 0 # Even stripes if x < n x += 1 y -= (y > 1) else y += 1 end else # Odd stripes if y < n x -= (x > 1) y += 1 else x += 1 end end end return matrix end Output: julia> zigzag_matrix(5) 5×5 Array{Int64,2}: 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 ### a more generic solution 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 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 Helper Functions using Formatting function width{T<:Integer}(n::T) w = ndigits(n) n < 0 || return w return w + 1 end function pretty{T<:Integer}(a::Array{T,2}, indent::Int=4) lo, hi = extrema(a) w = max(width(lo), width(hi)) id = " "^indent fe = FormatExpr(@sprintf(" {:%dd}", w)) s = id nrow = size(a)[1] for i in 1:nrow for j in a[i,:] s *= format(fe, j) end i != nrow || continue s *= "\n"*id end return s end Main n = 5 println("The n = ", n, " 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)) 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 ## Kotlin // version 1.1.3 typealias Vector = IntArray typealias Matrix = Array<Vector> fun zigzagMatrix(n: Int): Matrix { val result = Matrix(n) { Vector(n) } var down = false var count = 0 for (col in 0 until n) { if (down) for (row in 0..col) result[row][col - row] = count++ else for (row in col downTo 0) result[row][col - row] = count++ down = !down } for (row in 1 until n) { if (down) for (col in n - 1 downTo row) result[row + n - 1 - col][col] = count++ else for (col in row until n) result[row + n - 1 - col][col] = count++ down = !down } return result } fun printMatrix(m: Matrix) { for (i in 0 until m.size) { for (j in 0 until m.size) print("%2d ".format(m[i][j])) println() } println() } fun main(args: Array<String>) { printMatrix(zigzagMatrix(5)) printMatrix(zigzagMatrix(10)) } 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 14 15 27 28 44 45 2 4 7 13 16 26 29 43 46 63 3 8 12 17 25 30 42 47 62 64 9 11 18 24 31 41 48 61 65 78 10 19 23 32 40 49 60 66 77 79 20 22 33 39 50 59 67 76 80 89 21 34 38 51 58 68 75 81 88 90 35 37 52 57 69 74 82 87 91 96 36 53 56 70 73 83 86 92 95 97 54 55 71 72 84 85 93 94 98 99 ## 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; ## 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)) ## 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) 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. ZigZag[size_Integer/;size>0]:=Module[{empty=ConstantArray[0,{size,size}]}, empty=ReplacePart[empty,{i_,j_}:>1/2 (i+j)^2-(i+j)/2-i (1-Mod[i+j,2])-j Mod[i+j,2]]; ReplacePart[empty,{i_,j_}/;i+j>size+1:> size^2-tmp[[size-i+1,size-j+1]]-1] ] Ported from the java-example: ZigZag2[size_] := Module[{data, i, j, elem}, data = ConstantArray[0, {size, size}]; i = j = 1; For[elem = 0, elem < size^2, elem++, data[[i, j]] = elem; If[Mod[i + j, 2] == 0, If[j < size, j++, i += 2]; If[i > 1, i--] , If[i < size, i++, j += 2]; If[j > 1, j--]; ]; ]; data ] Examples: ZigZag[5] // MatrixForm ZigZag2[6] // MatrixForm gives back: ${\displaystyle \left({\begin{array}{ccccc}0&1&5&6&14\\2&4&7&13&15\\3&8&12&16&21\\9&11&17&20&22\\10&18&19&23&24\end{array}}\right)}$ ${\displaystyle \left({\begin{array}{cccccc}0&1&5&6&14&15\\2&4&7&13&16&25\\3&8&12&17&24&26\\9&11&18&23&27&32\\10&19&22&28&31&33\\20&21&29&30&34&35\end{array}}\right)}$ ## 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. 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 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 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]) */

## Modula-3

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.
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
/* 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

## Nim

Translation of: Python
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) & " "

proc zigzagMatrix(n): auto =
result = newSeqWith(n, newSeq[int](n))

var indices = newSeq[Pos]()

for x in 0 .. <n:
for y in 0 .. <n:

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)
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

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;
}

## OCaml

Translation of: Common Lisp
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

## Octave

Translation of: Stata
function a = zigzag1(n)
j = 1:n;
u = repmat([-1; 1], n, 1);
v = j.*(2*j-3);
v = reshape([v; v+1], 2*n, 1);
a = zeros(n, n);
for i = 1:n
a(:, i) = v(i+j);
v += u;
endfor
endfunction

function a = zigzag2(n)
a = zigzag1(n);
v = (1:n-1)'.^2;
for i = 2:n
a(n+2-i:n, i) -= v(1:i-1);
endfor
endfunction

>> zigzag2(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

Alternate solution, filling pairs of diagonals.

function a = zigzag3(n)
a = zeros(n, n);
for k=1:n
d = (2*(j = mod(k, 2))-1)*(n-1);
m = (n-1)*(k-1);
a(k+(1-j)*m:d:k+j*m) = k*(k-1)/2:k*(k+1)/2-1;
a(n*(n+1-k)+(1-j)*m:d:n*(n+1-k)+j*m) = n*n-k*(k+1)/2:n*n-k*(k-1)/2-1;
endfor
endfunction

>> zigzag3(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

## ooRexx

Translation of: Java

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

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:

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}}

## PARI/GP

Translation of: C.23
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))
)
};

## Pascal

Program zigzag( input, output );

const
size = 5;
var
zzarray: array [1..size, 1..size] of integer;
element, i, j: integer;
direction: integer;
width, n: integer;

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

width := 2;
n := size;
while (n > 0) do
begin
width := width + 1;
n := n div 10;
end;
for j := 1 to size do
begin
for i := 1 to size do
write(zzarray[i,j]:width);
writeln;
end;
end.
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
Output:
with size set to 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

Translation of: Seed7

Program zigzag;
{$APPTYPE CONSOLE} const size = 5; var s: array [1..size, 1..size] of integer; i, j, d, max, n: integer; begin i := 1; j := 1; d := -1; max := 0; n := 0; max := size * size; for n := 1 to (max div 2)+1 do begin s[i,j] := n; s[size - i + 1,size - j + 1] := max - n + 1; i:=i+d; j:=j-d; if i < 1 then begin inc(i); d := -d; end else if j < 1 then begin inc(j); d := -d; end; end; for j := 1 to size do begin for i := 1 to size do write(s[i,j]:4); writeln; end; end. Output: Size 5 1 3 4 10 11 2 5 9 12 19 6 8 13 18 20 7 14 17 21 24 15 16 22 23 25 Output: Size 8 1 3 4 10 11 21 22 36 2 5 9 12 20 23 35 37 6 8 13 19 24 34 38 49 7 14 18 25 33 39 48 50 15 17 26 32 40 47 51 58 16 27 31 41 46 52 57 59 28 30 42 45 53 56 60 63 29 43 44 54 55 61 62 64 ## Perl use 5.010; sub zig_zag { my$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", @{$_} foreach @zig_zag_matrix; Translation of: Haskell sub zig_zag { my ($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{ "@$_\n" } zig_zag(3, 5); ## Perl 6 Using the same Turtle class as in the Spiral matrix task: class Turtle { my @dv = [0,-1], [1,-1], [1,0], [1,1], [0,1], [-1,1], [-1,0], [-1,-1]; my$points = 8; # 'compass' points of neighbors on grid: north=0, northeast=1, east=2, etc.

has @.loc = 0,0;
has $.dir = 0; has %.world; has$.maxegg;
has $.range-x; has$.range-y;

method turn-left ($angle = 90) {$!dir -= $angle / 45;$!dir %= $points; } method turn-right($angle = 90) { $!dir +=$angle / 45; $!dir %=$points; }

method lay-egg($egg) { %!world{~@!loc} =$egg;
$!maxegg max=$egg;
$!range-x minmax= @!loc[0];$!range-y minmax= @!loc[1];
}

method look($ahead = 1) { my$there = @!loc »+« @dv[$!dir] »*»$ahead;
%!world{~$there}; } method forward($ahead = 1) {
my $there = @!loc »+« @dv[$!dir] »*» $ahead; @!loc = @($there);
}

method showmap() {
my $form = "%{$!maxegg.chars}s";
my $endx =$!range-x.max;
for $!range-y.list X$!range-x.list -> ($y,$x) {
print (%!world{"$x$y"} // '').fmt($form); print$x == $endx ?? "\n" !! ' '; } } } sub MAIN(Int$size = 5) {
my $t = Turtle.new(dir => 1); my$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;
}

## Phix

Translation of: C#
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"))

Alternative:

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"))

## 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;
}

## PicoLisp

This example uses 'grid' from "lib/simul.l", which maintains a two-dimensional structure and is normally used for simulations and board games.

(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
(prog
(setq D (cddr D))
((pop 'E) This) )
((pop 'E) This) ) ) ) ) ) )

(mapc
'((L)
(for This L (prin (align 3 (: val))))
(prinl) )
(zigzag 5) )
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

/* 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;
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

## Plain TeX

The code works with any etex engine.

\long\def\antefi#1#2\fi{#2\fi#1}
\def\fornum#1=#2to#3(#4){%
\edef#1{\number\numexpr#2}\edef\fornumtemp{\noexpand\fornumi\expandafter\noexpand\csname fornum\string#1\endcsname
{\number\numexpr#3}{\ifnum\numexpr#4<0 <\else>\fi}{\number\numexpr#4}\noexpand#1}\fornumtemp
}
\long\def\fornumi#1#2#3#4#5#6{\def#1{\unless\ifnum#5#3#2\relax\antefi{#6\edef#5{\number\numexpr#5+(#4)\relax}#1}\fi}#1}
\def\elem(#1,#2){\numexpr(#1+#2)*(#1+#2-1)/2-(\ifodd\numexpr#1+#2\relax#1\else#2\fi)\relax}
\def\zzmat#1{%
\noindent% quit vertical mode
\fornum\yy=1to#1(+1){%
\fornum\xx=1to#1(+1){%
\ifnum\numexpr\xx+\yy\relax<\numexpr#1+2\relax
\hbox to 2em{\hfil\number\elem(\xx,\yy)}%
\else
\hbox to 2em{\hfil\number\numexpr#1*#1-1-\elem(#1+1-\xx,#1+1-\yy)\relax}%
\fi
}%
\par\noindent% next line + quit vertical mode
}\par
}
\zzmat{5}
\bye

pdf 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.

%!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
/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
/di di neg def /dj dj neg def
} {
} ifelse
} ifelse
} forall
stroke showpage
} if
%%EOF

## 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,$_] } )" } } ### An Alternate Display Display the zig-zag matrix using the Format-Wide cmdlet: zigzag 5 | Format-Wide {"{0,2}" -f$_} -Column 5 -Force

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

## Prolog

Works with: SWi-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]).

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

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 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. 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)) 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 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)) 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, inspired by the Common Lisp Alternative Approach 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() 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 ### Another alternative version from __future__ import print_function import math def zigzag( dimension): ''' generate the zigzag indexes for a square array Exploiting the fact that an array is symmetrical around its centre ''' NUMBER_INDEXES = dimension ** 2 HALFWAY = NUMBER_INDEXES // 2 KERNEL_ODD = dimension & 1 xy = [0 for _ in range(NUMBER_INDEXES)] # start at 0,0 ix = 0 iy = 0 # 'fake' that we are going up and right direction = 1 # the first index is always 0, so start with the second # until halfway for i in range(1, HALFWAY + KERNEL_ODD): if direction > 0: # going up and right if iy == 0: # are at top ix += 1 direction = -1 else: ix += 1 iy -= 1 else: # going down and left if ix == 0: # are at left iy += 1 direction = 1 else: ix -= 1 iy += 1 # update the index position xy[iy * dimension + ix] = i # have first half, but they are scattered over the list # so find the zeros to replace for i in range(1, NUMBER_INDEXES): if xy[i] == 0 : xy[i] = NUMBER_INDEXES - 1 - xy[NUMBER_INDEXES - 1 - i] return xy def main(dim): zz = zigzag(dim) print( 'zigzag of {}:'.format(dim)) width = int(math.ceil(math.log10(dim**2))) for j in range(dim): for i in range(dim): print('{:{width}}'.format(zz[j * dim + i], width=width), end=' ') print() if __name__ == '__main__': main(5) zigzag 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 ## 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: 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) If you order these coordinates on the number, you create the order: 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) 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: 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();} } Output: 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 ## Qi This is a purely functional, very inefficient, and straight forward solution. The code can probably be simplified somewhat. (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))) ## R Translation of: Java 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) ## Racket #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) Output: '((0 2 3 9) (1 4 8 10) (5 7 11 14) (6 12 13 15)) ## REXX This REXX version allows the optional specification of the start and increment values. /*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=='' | n=="," then n=5 /*Not specified? Then use the default.*/ if start=='' | start=="," then start=0 /* " " " " " " */ if inc=='' | inc=="," then inc=1 /* " " " " " " */ row=1; col=1 /*start with the 1st row, 1st column.*/ size=n**2 /*the 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*/ /* [↑] // is REXX ÷ remainder.*/ w=max(length(start), length(start + size*inc) ) /*maximum width of any matrix element. */ do r=1 for n ; _= right(@.r.1, w) /*show all the rows of the matrix. */ do c=2 for n-1; _=_ right(@.r.c, w) /*build a line for the output for a row*/ end /*c*/ /* [↑] matrix elements are aligned. */ say _ /*show the matrix row just constructed.*/ end /*r*/ /*stick a fork in it, we're all done. */ 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 ## Ring # Project Zig-zag matrix load "guilib.ring" load "stdlib.ring" new qapp { win1 = new qwidget() { setwindowtitle("Zig-zag matrix") setgeometry(100,100,600,400) n = 5 a = newlist(n,n) zigzag = newlist(n,n) for j = 1 to n for i = 1 to n a[j][i] = 0 next next i = 1 j = 1 k = 1 while k < n * n a[j][i] = k k = k + 1 if i = n j = j + 1 a[j][i] = k k = k + 1 di = -1 dj = 1 ok if j = 1 i = i + 1 a[j][i] = k k = k + 1 di = -1 dj = 1 ok if j = n i = i + 1 a[j][i] = k k = k + 1 di = 1 dj = -1 ok if i = 1 j = j + 1 a[j][i] = k k = k + 1 di = 1 dj = -1 ok i = i + di j = j + dj end for p = 1 to n for m = 1 to n zigzag[p][m] = new qpushbutton(win1) { x = 150+m*40 y = 30 + p*40 setgeometry(x,y,40,40) settext(string(a[p][m])) } next next show() } exec() } Output: ## Ruby Translation of: Python 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) 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. def zigzag(n: Int): Array[Array[Int]] = { val l = for (i <- 0 until n*n) yield (i%n, i/n) val lSorted = l.sortWith { 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 } val res = Array.ofDim[Int](n, n) lSorted.zipWithIndex foreach { case ((x,y), i) => res(y)(x) = i } res } zigzag(5).foreach{ ar => ar.foreach(x => print("%3d".format(x))) println } 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 ## Scilab Translation of: Octave function a = zigzag3(n) a = zeros(n, n) for k=1:n j = modulo(k, 2) d = (2*j-1)*(n-1) m = (n-1)*(k-1) a(k+(1-j)*m:d:k+j*m) = k*(k-1)/2:k*(k+1)/2-1 a(n*(n+1-k)+(1-j)*m:d:n*(n+1-k)+j*m) = n*n-k*(k+1)/2:n*n-k*(k-1)/2-1 end endfunction -->zigzag3(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. ## 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
end for;
writeln;
end for;
end func;
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
func zig_zag(w, h) {

var r = []
var n = 0

h.of { |e|
w.of { |f|
[e, f]
}
}.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}) }
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

## Stata

The requested zig-zag matrix can be constructed as a correction of another zig-zag matrix, which is a square "view" of the infinite zig-zag matrix. Here is the latter:

function zigzag1(n) {
j = 0::n-1
u = J(1, n, (-1, 1))
v = (j:*(2:*j:+3))
v = rowshape((v,v:+1), 1)
a = J(n, n, .)
for (i=1; i<=n; i++) {
a[i, .] = v[j:+i]
v = v+u
}
return(a)
}

zigzag1(5)
1 2 3 4 5
+--------------------------+
1 | 0 1 5 6 14 |
2 | 2 4 7 13 16 |
3 | 3 8 12 17 25 |
4 | 9 11 18 24 31 |
5 | 10 19 23 32 40 |
+--------------------------+

Now the corrected matrix, which solves the task:

function zigzag2(n) {
a = zigzag1(n)
v = (1..n-1):^2
for (i=1; i<n; i++) {
a[n-i+1, i+1..n] = a[n-i+1, i+1..n] - v[1..n-i]
}
return(a)
}

zigzag2(5)
1 2 3 4 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 |
+--------------------------+

The correction is given by the difference:

zigzag1(5)-zigzag2(5)
[symmetric]
1 2 3 4 5
+--------------------------+
1 | 0 |
2 | 0 0 |
3 | 0 0 0 |
4 | 0 0 1 4 |
5 | 0 1 4 9 16 |
+--------------------------+

## Tcl

Using print_matrix from Matrix Transpose

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]
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
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
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

#import std
#import nat

zigzag = ~&mlPK2xnSS+ num+ ==+sum~~|[email protected]+ iota

test program (three examples):

#cast %nLLL

tests = zigzag* <4,5,6>
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

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

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
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
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

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);
];
]
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

## Yabasic

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 and((i + j), 1) = 0 THEN
IF j < Size then j = j + 1 ELSE i = i + 2 end if
IF i > 1 i = i - 1
ELSE
IF i < Size then i = i + 1 ELSE j = j + 2 end if
IF j > 1 j = j - 1
ENDIF
NEXT e

FOR row = 0 TO Size-1
FOR col = 0 TO Size-1
PRINT array(row,col) USING "##";
NEXT col
PRINT
NEXT row

## zkl

Translation of: Groovy
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())});
}
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.

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(); }]];
}

To be pedantic, the same as above, but using the output of the list comprehension:

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)