Zig-zag matrix
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Produce a zig-zag array.
A zig-zag array is a square arrangement of the first N2 natural numbers, 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
- Related tasks
- See also
- Wiktionary entry: anti-diagonals
11l
F zigzag(n)
F compare(xy)
V (x, y) = xy
R (x + y, I (x + y) % 2 {-y} E y)
V xs = 0 .< n
R Dict(enumerate(sorted((multiloop(xs, xs, (x, y) -> (x, y))), key' compare)), (n, index) -> (index, n))
F printzz(myarray)
V n = Int(myarray.len ^ 0.5 + 0.5)
V xs = 0 .< n
print((xs.map(y -> @xs.map(x -> ‘#3’.format(@@myarray[(x, @y)])).join(‘’))).join("\n"))
printzz(zigzag(6))- Output:
0 2 3 9 10 20 1 4 8 11 19 21 5 7 12 18 22 29 6 13 17 23 28 30 14 16 24 27 31 34 15 25 26 32 33 35
360 Assembly
* Zig-zag matrix 15/08/2015
ZIGZAGMA CSECT
USING ZIGZAGMA,R12 set base register
LR R12,R15 establish addressability
LA R9,N n : matrix size
LA R6,1 i=1
LA R7,1 j=1
LR R11,R9 n
MR R10,R9 *n
BCTR R11,0 R11=n**2-1
SR R8,R8 k=0
LOOPK CR R8,R11 do k=0 to n**2-1
BH ELOOPK k>limit
LR R1,R6 i
BCTR R1,0 -1
MR R0,R9 *n
LR R2,R7 j
BCTR R2,0 -1
AR R1,R2 (i-1)*n+(j-1)
SLA R1,1 index=((i-1)*n+j-1)*2
STH R8,T(R1) t(i,j)=k
LR R2,R6 i
AR R2,R7 i+j
LA R1,2 2
SRDA R2,32 shift right r1 to r2
DR R2,R1 (i+j)/2
LTR R2,R2 if mod(i+j,2)=0
BNZ ELSEMOD
CR R7,R9 if j<n
BNL ELSE1
LA R7,1(R7) j=j+1
B EIF1
ELSE1 LA R6,2(R6) i=i+2
EIF1 CH R6,=H'1' if i>1
BNH NOT1
BCTR R6,0 i=i-1
NOT1 B NOT2
ELSEMOD CR R6,R9 if i<n
BNL ELSE2
LA R6,1(R6) i=i+1
B EIF2
ELSE2 LA R7,2(R7) j=j+2
EIF2 CH R7,=H'1' if j>1
BNH NOT2
BCTR R7,0 j=j-1
NOT2 LA R8,1(R8) k=k+1
B LOOPK
ELOOPK LA R6,1 end k; i=1
LOOPI CR R6,R9 do i=1 to n
BH ELOOPI i>n
LA R10,0 ibuf=0 buffer index
MVC BUFFER,=CL80' '
LA R7,1 j=1
LOOPJ CR R7,R9 do j=1 to n
BH ELOOPJ j>n
LR R1,R6 i
BCTR R1,0 -1
MR R0,R9 *n
LR R2,R7 j
BCTR R2,0 -1
AR R1,R2 (i-1)*n+(j-1)
SLA R1,1 index=((i-1)*n+j-1)*2
LH R2,T(R1) t(i,j)
LA R3,BUFFER
AR R3,R10
XDECO R2,XDEC edit t(i,j) length=12
MVC 0(4,R3),XDEC+8 move in buffer length=4
LA R10,4(R10) ibuf=ibuf+1
LA R7,1(R7) j=j+1
B LOOPJ
ELOOPJ XPRNT BUFFER,80 end j
LA R6,1(R6) i=i+1
B LOOPI
ELOOPI XR R15,R15 end i; return_code=0
BR R14 return to caller
N EQU 5 matrix size
BUFFER DS CL80
XDEC DS CL12
T DS (N*N)H t(n,n) matrix
YREGS
END ZIGZAGMA- 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
Action!
DEFINE MAX_SIZE="10"
DEFINE MAX_MATRIX_SIZE="100"
INT FUNC Index(BYTE size,x,y)
RETURN (x+y*size)
PROC PrintMatrix(BYTE ARRAY a BYTE size)
BYTE i,j,v
FOR j=0 TO size-1
DO
FOR i=0 TO size-1
DO
v=a(Index(size,i,j))
IF v<10 THEN
Print(" ")
ELSE
Print(" ")
FI
PrintB(v)
OD
PutE()
OD
RETURN
PROC FillMatrix(BYTE ARRAY a BYTE size)
BYTE start,end
INT dir,i,j
start=0 end=size*size-1
i=0 j=0 dir=1
DO
a(Index(size,i,j))=start
a(Index(size,size-1-i,size-1-j))=end
start==+1 end==-1
i==+dir j==-dir
IF i<0 THEN
i==+1 dir=-dir
ELSEIF j<0 THEN
j==+1 dir=-dir
FI
UNTIL start>=end
OD
IF start=end THEN
a(Index(size,i,j))=start
FI
RETURN
PROC Test(BYTE size)
BYTE ARRAY mat(MAX_MATRIX_SIZE)
PrintF("Matrix size: %B%E",size)
FillMatrix(mat,size)
PrintMatrix(mat,size)
PutE()
RETURN
PROC Main()
Test(5)
Test(6)
RETURN- Output:
Screenshot from Atari 8-bit computer
Matrix size: 5 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 Matrix 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
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 --;
}
}
}
}
}
Ada
with Ada.Text_IO; use Ada.Text_IO;
procedure Test_Zig_Zag is
type Matrix is array (Positive range <>, Positive range <>) of Natural;
function Zig_Zag (Size : Positive) return Matrix is
Data : Matrix (1..Size, 1..Size);
I, J : Integer := 1;
begin
Data (1, 1) := 0;
for Element in 1..Size**2 - 1 loop
if (I + J) mod 2 = 0 then
-- Even stripes
if J < Size then
J := J + 1;
else
I := I + 2;
end if;
if I > 1 then
I := I - 1;
end if;
else
-- Odd stripes
if I < Size then
I := I + 1;
else
J := J + 2;
end if;
if J > 1 then
J := J - 1;
end if;
end if;
Data (I, J) := Element;
end loop;
return Data;
end Zig_Zag;
procedure Put (Data : Matrix) is
begin
for I in Data'Range (1) loop
for J in Data'Range (2) loop
Put (Integer'Image (Data (I, J)));
end loop;
New_Line;
end loop;
end Put;
begin
Put (Zig_Zag (5));
end Test_Zig_Zag;
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
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((IF i = 1 THEN "((" ELSE " (" FI));
FOR j TO dim DO
print(( whole( result[i,j], -3 ), IF j /= dim THEN "," ELSE "" FI ))
OD;
print((IF i = dim THEN "))" ELSE ")," FI, new line))
OD
#FI#- 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 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
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)
{map(my head, edge)} & ¬
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
on head(xs)
if length of xs > 0 then
item 1 of xs
else
missing value
end if
end head
-- 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}}
Optimised iterative
This is an optimised version of the second iterative script above, with the rendition to text kept separate and corrected. With n = 50, it's about 7.6 times as fast as the script on which it's based.
on zigzagMatrix(n)
script o
property matrix : {} -- Matrix list.
property row : missing value -- Row sublist.
end script
repeat n times
set end of o's matrix to {} -- Build a foundation for the matrix out of n empty lists.
end repeat
set {r, d} to {1, -1} -- Row index and direction to next insertion row (negative = row above).
repeat with v from 0 to (n ^ 2) - 1 -- Values to insert.
set o's row to o's matrix's item r
repeat while ((count o's row) = n)
set r to r + 1
set d to 1
set o's row to o's matrix's item r
end repeat
set end of o's row to v
set r to r + d
if (r < 1) then
set r to 1
set d to -d
else if (r > n) then
set r to n
set d to -d
else if ((r > 1) and ((count o's matrix's item (r - 1)) = 1)) then
set d to -d
end if
end repeat
return o's matrix
end zigzagMatrix
-- Demo:
on matrixToText(matrix, w)
script o
property matrix : missing value
property row : missing value
end script
set o's matrix to matrix
set padding to " "
repeat with r from 1 to (count o's matrix)
set o's row to o's matrix's item r
repeat with i from 1 to (count o's row)
set o's row's item i to text -w thru end of (padding & o's row's item i)
end repeat
set o's matrix's item r to join(o's row, "")
end repeat
return join(o's matrix, linefeed)
end matrixToText
on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join
set n to 5
set matrix to zigzagMatrix(n)
linefeed & matrixToText(matrix, (count (n ^ 2 - 1 as integer as text)) + 2) & linefeed
- 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 YArturo
zigzag: function [n][
result: map 1..n 'x -> map 1..n => 0
x: 1, y: 1, v: 0, d: 1
while [v < n^2][
if? all? @[1 =< x x =< n 1 =< y y =< n][
set get result (y-1) (x-1) v
x: x + d, y: y - d, v: v + 1
]
else[if? x > n [x: n, y: y + 2, d: neg d]
else[if? y > n [x: x + 2, y: n, d: neg d]
else[if? x < 1 [x: 1, d: neg d]
else[if y < 1 [y: 1, d: neg d]
]
]
]
]
]
result
]
zz: zigzag 5
loop zz 'row -> print map row 'col [pad to :string col 3]
- 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
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
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
Beads
This is a translation of the C++ example.
beads 1 program 'Zig-zag Matrix'
calc main_init
var test : array^2 of num = create_array(5)
printMatrix(test)
calc create_array(
dimension:num
):array^2 of num
var
result : array^2 of num
lastValue = dimension^2 - 1
loopFrom
loopTo
row
col
currDiag = 0
currNum = 0
loop
if (currDiag < dimension) // if doing the upper-left triangular half
loopFrom = 1
loopTo = currDiag + 1
else // doing the bottom-right triangular half
loopFrom = currDiag - dimension + 2
loopTo = dimension
loop count:c from:loopFrom to:loopTo
var i = loopFrom + c - 1
if (rem(currDiag, 2) == 0) // want to fill upwards
row = loopTo - i + loopFrom
col = i
else // want to fill downwards
row = i
col = loopTo - i + loopFrom
result[row][col] = currNum
inc currNum
inc currDiag
if (currNum > lastValue)
exit
return result
calc printMatrix(
matrix:array^2 of num
)
var dimension = tree_count(matrix)
var maxDigits = 1 + lg((dimension^2-1), base:10)
loop across:matrix ptr:rowp index:row
var tempstr : str
loop across:rowp index:col
tempstr = tempstr & " " & to_str(matrix[row][col], min:maxDigits)
log(tempstr)- 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$$_>>#^4#00#+p#1:#+1#g0#0g#3<^/+ 55\_$:>55+/\|
>55+,20g!00g10g`>#^_$$$@^!`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
BQN
Flip ← {m←2|+⌜˜↕≠𝕩 ⋄ (⍉𝕩׬m)+𝕩×m}
Zz ← {Flip ⍋∘⍋⌾⥊+⌜˜↕𝕩}
Example:
Zz 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
#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#
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;
}
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
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) {
process.write(element.string.pad(3));
}
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
(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
Crystal
def zigzag(n)
(seq=(0...n).to_a).product(seq)
.sort_by {|x,y| [x+y, (x+y).even? ? y : -y]}
.map_with_index{|v, i| {v, i}}.sort.map(&.last).each_slice(n).to_a
end
def print_matrix(m)
format = "%#{m.flatten.max.to_s.size}d " * m[0].size
m.each {|row| puts 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
D
int[][] zigZag(in int n) pure nothrow @safe {
static void move(in int n, ref int i, ref int j)
pure nothrow @safe @nogc {
if (j < n - 1) {
if (i > 0) i--;
j++;
} else
i++;
}
auto a = new int[][](n, n);
int x, y;
foreach (v; 0 .. n ^^ 2) {
a[y][x] = v;
(x + y) % 2 ? move(n, x, y) : move(n, y, x);
}
return a;
}
void main() {
import std.stdio;
writefln("%(%(%2d %)\n%)", 5.zigZag);
}
- 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
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.
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
}Delphi
type TMatrix = array of array of double;
procedure DisplayMatrix(Memo: TMemo; Mat: TMatrix);
{Display specified matrix}
var X,Y: integer;
var S: string;
begin
S:='';
for Y:=0 to High(Mat[0]) do
begin
S:=S+'[';
for X:=0 to High(Mat) do
S:=S+Format('%4.0f',[Mat[X,Y]]);
S:=S+']'+#$0D#$0A;
end;
Memo.Lines.Add(S);
end;
procedure ZigzagMatrix(Memo: TMemo);
var Mat: TMatrix;
var X,Y,Inx,Dir: integer;
const Size = 10;
procedure Toggle(var I: integer);
{Toggle Direction and increment I}
begin
Dir:=-Dir;
Inc(I);
end;
procedure Step(var X,Y: integer);
{Take one step "Dir" direction}
begin
X:=X+Dir;
Y:=Y-Dir;
end;
begin
SetLength(Mat,Size,Size);
Inx:=0; X:=0; Y:=0; Dir:=1;
repeat
begin
Mat[X,Y]:=Inx;
if (X+Dir)>=Size then Toggle(Y)
else if (Y-Dir)>=Size then Toggle(X)
else if (X+Dir)<0 then Toggle(Y)
else if (Y-Dir)<0 then Toggle(X)
else Step(X,Y);
Inc(Inx);
end
until Inx>=Size*Size;
DisplayMatrix(Memo,Mat);
end;
- Output:
[ 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] Elapsed Time: 1.576 ms.
EasyLang
func sumto n .
return n * (n + 1) div 2
.
func coord2num row col n .
diag = col + row
if diag < n
start = sumto diag
if diag mod 2 = 0
offs = col
else
offs = row
.
else
start = n * n - sumto (2 * n - 1 - diag)
offs = n - 1
if diag mod 2 = 0
offs -= row
else
offs -= col
.
.
return start + offs
.
n = 6
numfmt 0 3
for row = 0 to n - 1
for col = 0 to n - 1
write coord2num row col n
.
print ""
.
- 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
Elena
ELENA 5.0:
import extensions;
extension op : IntNumber
{
zigzagMatrix()
{
auto result := IntMatrix.allocate(self, self);
int i := 0;
int j := 0;
int d := -1;
int start := 0;
int end := self*self - 1;
while (start < end)
{
result.setAt(i, j, start); start += 1;
result.setAt(self - i - 1, self - j - 1, end); end -= 1;
i := i + d;
j := j - d;
if (i < 0)
{
i:=i+1; d := d.Negative
}
else if (j < 0)
{
j := j + 1; d := d.Negative
}
};
if (start == end)
{
result.setAt(i, j, start)
};
^ result
}
}
public program()
{
console.printLine(5.zigzagMatrix()).readChar()
}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
EMal
fun zigzag = List by int n
List matrix = List[].with(n)
for int y = 0; y < n; y++ do matrix[y] = int[].with(n) end
int y, x = 1
for int value = 0; value < n * n; value++
matrix[y - 1][x - 1] = value
if (y + x) % 2 == 0
if x < n do x++
else do y += 2 end
if y > 1 do y-- end
else
if y < n do y++
else do x += 2 end
if x > 1 do x-- end
end
end
return matrix
end
fun dump = void by List matrix
int max = length(text!(matrix.length ** 2)) + 1
for each List row in matrix
for each int value in row
write(" " * (max - length(text!value)) + value)
end
writeLine()
end
end
dump(zigzag(5))
writeLine()
dump(zigzag(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
Erlang
-module( zigzag ).
-export( [matrix/1, task/0] ).
matrix( N ) ->
{{_X_Y, N}, Proplist} = lists:foldl( fun matrix_as_proplist/2, {{{0, 0}, N}, []}, lists:seq(0, (N * N) - 1) ),
[columns( X, Proplist ) || X <- lists:seq(0, N - 1)].
task() -> matrix( 5 ).
columns( Column, Proplist ) -> lists:sort( [Value || {{_X, Y}, Value} <- Proplist, Y =:= Column] ).
matrix_as_proplist( N, {{X_Y, Max}, Acc} ) ->
Next = next_indexes( X_Y, Max ),
{{Next, Max}, [{X_Y, N} | Acc]}.
next_indexes( {X, Y}, Max ) when Y + 1 =:= Max, (X + Y) rem 2 =:= 0 -> {X + 1, Y - 1};
next_indexes( {X, Y}, Max ) when Y + 1 =:= Max, (X + Y) rem 2 =:= 1 -> {X + 1, Y};
next_indexes( {X, Y}, Max ) when X + 1 =:= Max, (X + Y) rem 2 =:= 0 -> {X, Y + 1};
next_indexes( {X, Y}, Max ) when X + 1 =:= Max, (X + Y) rem 2 =:= 1 -> {X - 1, Y + 1};
next_indexes( {X, 0}, _Max ) when X rem 2 =:= 0 -> {X + 1, 0};
next_indexes( {X, 0}, _Max ) when X rem 2 =:= 1 -> {X - 1, 1};
next_indexes( {0, Y}, _Max ) when Y rem 2 =:= 0 -> {1, Y - 1};
next_indexes( {0, Y}, _Max ) when Y rem 2 =:= 1 -> {0, Y + 1};
next_indexes( {X, Y}, _Max ) when (X + Y) rem 2 =:= 0 -> {X + 1, Y - 1};
next_indexes( {X, Y}, _Max ) when (X + Y) rem 2 =:= 1 -> {X - 1, Y + 1}.
- Output:
71> zigzag:task(). [[0,1,5,6,14], [2,4,7,13,15], [3,8,12,16,21], [9,11,17,20,22], [10,18,19,23,24]]
ERRE
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
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]]
Factor
This version follows the algorithm laid out in the comments of the first JavaScript (ES5) functional example, though it is not exactly a straight translation.
USING: columns fry kernel make math math.ranges prettyprint
sequences sequences.cords sequences.extras ;
IN: rosetta-code.zig-zag-matrix
: [1,b,1] ( n -- seq )
[1,b] dup but-last-slice <reversed> cord-append ;
: <reversed-evens> ( seq -- seq' )
[ even? [ <reversed> ] when ] map-index ;
: diagonals ( n -- seq )
[ sq <iota> ] [ [1,b,1] ] bi
[ [ cut [ , ] dip ] each ] { } make nip <reversed-evens> ;
: zig-zag-matrix ( n -- seq )
[ diagonals ] [ dup ] bi '[
[
dup 0 <column> _ head ,
[ _ < [ rest-slice ] when ] map-index harvest
] until-empty
] { } make ;
: zig-zag-demo ( -- ) 5 zig-zag-matrix simple-table. ;
MAIN: zig-zag-demo
- 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
The following example is an implementation of a J routine with an excellent walkthrough on the talk page. Luckily, we can mimic the "classification" step with the composition of 3 existing Factor words: zip-index expand-keys-push-at values and the inverse-permutation word is the same concept as J's grade, so this is fairly succinct.
USING: assocs assocs.extras grouping io kernel math
math.combinatorics math.matrices prettyprint sequences ;
: <zig-zag-matrix> ( n -- matrix )
[
dup [ + ] <matrix-by-indices> concat zip-index
expand-keys-push-at values [ even? [ reverse ] when ]
map-index concat inverse-permutation
] [ group ] bi ;
5 <zig-zag-matrix> simple-table.
- 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
Fan
using gfx // for Point; convenient x/y wrapper
**
** A couple methods for generating a 'zigzag' array like
**
** 0 1 5 6
** 2 4 7 12
** 3 8 11 13
** 9 10 14 15
**
class ZigZag
{
** return an n x n array of uninitialized Int
static Int[][] makeSquareArray(Int n)
{
Int[][] grid := Int[][,] {it.size=n}
n.times |i| { grid[i] = Int[,] {it.size=n} }
return grid
}
Int[][] zig(Int n)
{
grid := makeSquareArray(n)
move := |Int i, Int j->Point|
{ return j < n - 1 ? Point(i <= 0 ? 0 : i-1, j+1) : Point(i+1, j) }
pt := Point(0,0)
(n*n).times |i| {
grid[pt.y][pt.x] = i
if ((pt.x+pt.y)%2 != 0) pt = move(pt.x,pt.y)
else {tmp:= move(pt.y,pt.x); pt = Point(tmp.y, tmp.x) }
}
return grid
}
public static Int[][] zag(Int size)
{
data := makeSquareArray(size)
Int i := 1
Int j := 1
for (element:=0; element < size * size; element++)
{
data[i - 1][j - 1] = element
if((i + j) % 2 == 0) {
// Even stripes
if (j < size) {
j++
} else {
i += 2
}
if (i > 1) {
i--
}
} else {
// Odd stripes
if (i < size) {
i++;
} else {
j += 2
}
if (j > 1) {
j--
}
}
}
return data;
}
Void print(Int[][] data)
{
data.each |row|
{
buf := StrBuf()
row.each |num|
{
buf.add(num.toStr.justr(3))
}
echo(buf)
}
}
Void main()
{
echo("zig method:")
print(zig(8))
echo("\nzag method:")
print(zag(8))
}
}
Forth
0 value diag
: south diag abs + cell+ ;
' cell+ value zig
' south value zag
: init ( n -- )
1- cells negate to diag
['] cell+ to zig
['] south to zag ;
: swap-diag zig zag to zig to zag ;
: put ( n addr -- n+1 addr )
2dup ! swap 1+ swap ;
: turn ( addr -- addr+E/S )
zig execute swap-diag
diag negate to diag ;
: zigzag ( matrix n -- )
{ n } n init
0 swap
n 1 ?do
put turn
i 0 do put diag + loop
loop
swap-diag
n 1 ?do
put turn
n i 1+ ?do put diag + loop
loop
! ;
: .matrix ( n matrix -- )
over 0 do
cr
over 0 do
dup @ 3 .r cell+
loop
loop 2drop ;
: test ( n -- ) here over zigzag here .matrix ;
5 test
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24 ok
Fortran
PROGRAM ZIGZAG
IMPLICIT NONE
INTEGER, PARAMETER :: size = 5
INTEGER :: zzarray(size,size), x(size*size), y(size*size), i, j
! index arrays
x = (/ ((j, i = 1, size), j = 1, size) /)
y = (/ ((i, i = 1, size), j = 1, size) /)
! Sort indices
DO i = 2, size*size
j = i - 1
DO WHILE (j>=1 .AND. (x(j)+y(j)) > (x(i)+y(i)))
j = j - 1
END DO
x(j+1:i) = cshift(x(j+1:i),-1)
y(j+1:i) = cshift(y(j+1:i),-1)
END DO
! Create zig zag array
DO i = 1, size*size
IF (MOD(x(i)+y(i), 2) == 0) THEN
zzarray(x(i),y(i)) = i - 1
ELSE
zzarray(y(i),x(i)) = i - 1
END IF
END DO
! Print zig zag array
DO j = 1, size
DO i = 1, size
WRITE(*, "(I5)", ADVANCE="NO") zzarray(i,j)
END DO
WRITE(*,*)
END DO
END PROGRAM ZIGZAG
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
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:
> zz(5).each { it.each { print("${it}".padLeft(3)) }; println() }
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24
Cursor
Ported from the Java example
def zz = { n->
move = { i, j -> j < n - 1 ? [i <= 0 ? 0 : i-1, j+1] : [i+1, j] }
grid = new int[n][n]
(x, y) = [0, 0]
(n**2).times {
grid[y][x] = it
if ((x+y)%2) (x,y) = move(x,y)
else (y,x) = move(y,x)
}
grid
}
- Output:
> zz(5).each { it.each { print("${it}".padLeft(3)) }; println() }
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24
Sorting
Ported from the Python example with some input from J
def zz = { n ->
(0..<n*n).collect { [x:it%n,y:(int)(it/n)] }.sort { c->
[c.x+c.y, (((c.x+c.y)%2) ? c.y : -c.y)]
}.with { l -> l.inject(new int[n][n]) { a, c -> a[c.y][c.x] = l.indexOf(c); a } }
}
- Output:
> zz(5).each { it.each { print("${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, array, bounds, range, (!))
import Text.Printf (printf)
import Data.List (sortBy)
compZig :: (Int, Int) -> (Int, Int) -> Ordering
compZig (x, y) (x_, y_) = compare (x + y) (x_ + y_) <> go x y
where
go x y
| even (x + y) = compare x x_
| otherwise = compare y y_
zigZag :: (Int, Int) -> Array (Int, Int) Int
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):
-- 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 . ('\n' :) . show2d . zigZag) [(3, 3), (4, 4), (10, 2)]
Or, building a list of lists with mapAccumL:
import Data.Text (justifyRight, pack, unpack)
import Data.List (mapAccumL)
import Data.Bool (bool)
zigZag :: Int -> [[Int]]
zigZag = go <*> diagonals
where
go _ [] = []
go n xss = (head <$> edge) : go n (dropWhile null (tail <$> edge) <> rst)
where
(edge, rst) = splitAt n xss
diagonals :: Int -> [[Int]]
diagonals n =
snd $ mapAccumL go [0 .. (n * n) - 1] (slope <> [n] <> reverse slope)
where
slope = [1 .. n - 1]
go xs h = (rst, bool id reverse (0 /= mod h 2) grp)
where
(grp, rst) = splitAt h xs
main :: IO ()
main =
putStrLn $
unlines $
concatMap unpack . fmap (justifyRight 3 ' ' . pack . show) <$> zigZag 5
- Output:
0 1 5 6 14 2 4 7 13 15 3 8 12 16 21 9 11 17 20 22 10 18 19 23 24
Icon and Unicon
This solution works for both Icon and Unicon.
- Output:
->zz
0 1 5 6 14
2 4 7 13 15
3 8 12 16 21
9 11 17 20 22
10 18 19 23 24
->
IS-BASIC
100 PROGRAM "ZigZag.bas"
110 LET SIZE=5
120 NUMERIC A(1 TO SIZE,1 TO SIZE)
130 LET I,J=1
140 FOR E=0 TO SIZE^2-1
150 LET A(I,J)=E
160 IF ((I+J) BAND 1)=0 THEN
170 IF J<SIZE THEN
180 LET J=J+1
190 ELSE
200 LET I=I+2
210 END IF
220 IF I>1 THEN LET I=I-1
230 ELSE
240 IF I<SIZE THEN
250 LET I=I+1
260 ELSE
270 LET J=J+2
280 END IF
290 IF J>1 THEN LET J=J-1
300 END IF
310 NEXT
320 FOR ROW=1 TO SIZE
330 FOR COL=1 TO SIZE
340 PRINT USING " ##":A(ROW,COL);
350 NEXT
360 PRINT
370 NEXTJ
A succinct way:
($ [: /:@; <@|.`</.@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
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 <@|.`</. ]) (#: 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
(Also, of course, ($ [: /:@; <@|.`</.@i.)@,~0 creates a result with 0 rows and 0 columns. And, with an argument of 1, the result has one row and one column with the value 0. And, the other expressions behave the same.)
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
for the print() function.
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);
}
// Recursively read off n heads from the diagonals (as rows)
// n -> [[n]] -> [[n]]
function nHeads(n, lst) {
var zipEdge = lst.slice(0, n);
return lst.length ? [zipEdge.map(function (x) {
return x[0];
})].concat(nHeads(n, [].concat.apply([], zipEdge.map(function (
x) {
return x.length > 1 ? [x.slice(1)] : [];
}))
.concat(lst.slice(n)))) : [];
}
// 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)
return nHeads(n, diagonals(n)
.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);
}
// Recursively read off n heads of diagonal lists
// 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
Klingphix
include ..\Utilitys.tlhy
%Size 5 !Size
0 ( $Size dup ) dim
%i 1 !i %j 1 !j
$Size 2 power [
1 -
( $i $j ) set
$i $j + 1 band 0 == (
[$j $Size < ( [$j 1 + !j] [$i 2 + !i] ) if
$i 1 > [ $i 1 - !i] if ]
[$i $Size < ( [$i 1 + !i] [$j 2 + !j] ) if
$j 1 > [ $j 1 - !j] if ]
) if
] for
$Size [
%row !row
$Size [
%col !col
( $row $col ) get tostr 32 32 chain chain 1 3 slice print drop
] for
nl
] for
nl "End " input- Output:
0 1 5 6 14 2 4 7 13 15 3 8 12 16 21 9 11 17 20 22 10 18 19 23 24 End
K
Works with: ngn/k
f:{grid:+x#<<a,'(!#a)*- 2!a:+/!x,:x
padded:(-#$-1+*/x)$$grid
`0:" "/'padded}
f 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
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
Ksh
#!/bin/ksh
# Produce a zig-zag array.
# # Variables:
#
integer DEF_SIZE=5 # Default size = 5
arr_size=${1:-$DEF_SIZE} # $1 = size, or default
# # Externals:
#
# # Functions:
#
######
# main #
######
integer i j n
typeset -a zzarr
for (( i=n=0; i<arr_size*2; i++ )); do
for (( j= (i<arr_size) ? 0 : i-arr_size+1; j<=i && j<arr_size; j++ )); do
(( zzarr[(i&1) ? j*(arr_size-1)+i : (i-j)*arr_size+j] = n++ ))
done
done
for ((i=0; i<arr_size*arr_size; i++)); do
printf "%3d " ${zzarr[i]}
(( (i+1)%arr_size == 0 )) && printf "\n"
done
- Output:
0 1 5 6 14 2 4 7 13 15 3 8 12 16 21 9 11 17 20 22 10 18 19 23 240 1 5 6 14 15 27 28 44 2 4 7 13 16 26 29 43 45 3 8 12 17 25 30 42 46 59 9 11 18 24 31 41 47 58 60 10 19 23 32 40 48 57 61 70 20 22 33 39 49 56 62 69 71 21 34 38 50 55 63 68 72 77 35 37 51 54 64 67 73 76 7836 52 53 65 66 74 75 79 80
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))
M2000 Interpreter
Module Lib1 {
Module Global PrintArray(&Ar()) {
if dimension(Ar())<>2 then Error "This is for 2D arrays"
integer i, j, n=dimension(Ar(),1), n1=dimension(Ar(),2)
for i=1 to n
for j=1 to n1
print Ar(i, j),
next
print
next
}
Function Global MakeArray(n as integer=5) {
dim a(1 to n, 1 to n) as integer=0
integer i=1, j=1, z, t1=1
boolean ch=true
for z=0 to n*n-1
if ch then a(i,j)=z else a(j,i)=z
j++
if j>t1 then t1++: j=1:i=t1: ch~ else i--
if i<1 then i=t1 else.if i>n then i=n: j++
if j>n then j=i+2: i=n:ch~
next
=a() // return array (as a pointer)
}
}
Module Zig_Zag_Matrix (n as integer=5) {
Pen 15 {Report "matrix "+n+"x"+n}
integer old_column=tab
Print $(,4) // set column to 4 chars
if random(1,2)=2 then
dim ret()
ret()=makeArray(n) // this get a copy
else
object a=makeArray(n) // but this get the copy of pointer
link a to ret() // ret() is reference to a, to array
end if
PrintArray &ret()
Print $(,old_column)
}
Inline Code Lib1 // just execute the code from module lib1 like was here
Form 60, 36 \\ console 60x36 characters
Report 2, "Zig-zag matrix" // 2 for center
Pen 14 {Zig_Zag_Matrix 1}
Pen 11 {Zig_Zag_Matrix 2}
Pen 14 {Zig_Zag_Matrix 3}
Pen 11 {Zig_Zag_Matrix 4}
Pen 14 {Zig_Zag_Matrix 5}
Pen 11 {Zig_Zag_Matrix 10}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
Maple
Here values are starting at 1. Replace <v+~1,v+~2> with <v,v+~1> to start at 0.
zigzag1:=proc(n)
uses ArrayTools;
local i,u,v,a;
u:=Replicate(<-1,1>,n):
v:=Vector[row](1..n,i->i*(2*i-3)):
v:=Reshape(<v+~1,v+~2>,2*n):
a:=Matrix(n,n):
for i to n do
a[...,i]:=v[i+1..i+n];
v+=u
od:
a
end:
zigzag2:=proc(n)
local i,v,a;
a:=zigzag1(n);
v:=Vector(1..n-1,i->i^2);
for i from 2 to n do
a[n+2-i..n,i]-=v[1..i-1]
od;
a
end:zigzag1(6);- Output:
Matrix(6, 6, [[ 1, 2, 6, 7, 15, 16],
[ 3, 5, 8, 14, 17, 27],
[ 4, 9, 13, 18, 26, 31],
[10, 12, 19, 25, 32, 42],
[11, 20, 24, 33, 41, 50],
[21, 23, 34, 40, 51, 61]])
zigzag2(6);- Output:
Matrix(6, 6, [[ 1, 2, 6, 7, 15, 16],
[ 3, 5, 8, 14, 17, 26],
[ 4, 9, 13, 18, 25, 27],
[10, 12, 19, 24, 28, 33],
[11, 20, 23, 29, 32, 34],
[21, 22, 30, 31, 35, 36]])
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:
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]) */
MiniZinc
%Zigzag Matrix. Nigel Galloway, February 3rd., 2020
int: Size;
array [1..Size,1..Size] of var 1..Size*Size: zigzag;
constraint zigzag[1,1]=1 /\ zigzag[Size,Size]=Size*Size;
constraint forall(n in {2*g | g in 1..Size div 2})(zigzag[1,n]=zigzag[1,n-1]+1 /\ forall(g in 2..n)(zigzag[g,n-g+1]=zigzag[g-1,n-g+2]+1));
constraint forall(n in {2*g + ((Size-1) mod 2) | g in 1..(Size-1) div 2})(zigzag[n,Size]=zigzag[n-1,Size]+1 /\ forall(g in 1..Size-n)(zigzag[n+g,Size-g]=zigzag[n+g-1,Size-g+1]+1));
constraint forall(n in {2*g+1 | g in 1..(Size-1) div 2})(zigzag[n,1]=zigzag[n-1,1]+1 /\ forall(g in 2..n)(zigzag[n-g+1,g]=zigzag[n-g+2,g-1]+1));
constraint forall(n in {2*g+((Size) mod 2) | g in 1..(Size-1) div 2})(zigzag[Size,n]=zigzag[Size,n-1]+1 /\ forall(g in 1..Size-n)(zigzag[Size-g,n+g]=zigzag[Size-g+1,n+g-1]+1));
output [show2d(zigzag)];{out}
minizinc -DSize=5 zigzag.mzn
[| 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 |]
----------
minizinc -DSize=6 zigzag.mzn
[| 1, 2, 6, 7, 15, 16 |
3, 5, 8, 14, 17, 26 |
4, 9, 13, 18, 25, 27 |
10, 12, 19, 24, 28, 33 |
11, 20, 23, 29, 32, 34 |
21, 22, 30, 31, 35, 36 |]
----------
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
/* 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
from algorithm import sort
from strutils import align
from sequtils import newSeqWith
type Pos = tuple[x, y: int]
proc `<` (a, b: Pos): bool =
a.x + a.y < b.x + b.y or
a.x + a.y == b.x + b.y and (a.x < b.x xor (a.x + a.y) mod 2 == 0)
proc zigzagMatrix(n: int): auto =
var indices = newSeqOfCap[Pos](n*n)
for x in 0 ..< n:
for y in 0 ..< n:
indices.add((x,y))
sort(indices)
result = newSeqWith(n, newSeq[int](n))
for i, p in indices:
result[p.x][p.y] = i
proc `$`(m: seq[seq[int]]): string =
let Width = len($m[0][^1]) + 1
for r in m:
for c in r:
result.add align($c, Width)
result.add "\n"
echo zigzagMatrix(6)
- Output:
0 1 5 6 14 15 2 4 7 13 16 25 3 8 12 17 24 26 9 11 18 23 27 32 10 19 22 28 31 33 20 21 29 30 34 35
Direct coord to number
This calculates the number for each coordinate directly. This allows to create very large zig-zag matrices. Generates the same output as above.
import strutils
func sumTo(n: Natural): Natural = n * (n+1) div 2
func coord2num(row, col, N: Natural): Natural =
var start, offset: Natural
let diag = col + row
if diag < N:
start = sumTo(diag)
offset = if diag mod 2 == 0: col else: row
else:
# N * (2*diag+1-N) - sumTo(diag), but with smaller itermediates
start = N*N - sumTo(2*N-1-diag)
offset = N-1 - (if diag mod 2 == 0: row else: col)
start + offset
let N = 6
let width = (N*N).`$`.len + 1
for row in 0 ..< N:
for col in 0 ..< N:
stdout.write(coord2num(row, col, N).`$`.align(width))
stdout.write("\n")
Objeck
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
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
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
Inspired by Rascal
#{
Produce a zigzag matrix. Nigel Galloway, January 26th., 2020.
At the time of writing the Rascal solution is yellow flagged for producing a striped matrix.
Let me make the same faux pas.
#}
n=5; g=1;
for e=1:n i=1; for l=e:-1:1 zig(i++,l)=g++; endfor endfor
for e=2:n i=e; for l=n:-1:e zig(i++,l)=g++; endfor endfor
#{
I then have the following, let me call it zig.
1 2 4 7 11
3 5 8 12 16
6 9 13 17 20
10 14 18 21 23
15 19 22 24 25
To avoid being yellow flagged I must convert this striped matrix into a zigzag matrix.
#}
zag=zig'
#{
So zag is the transpose of zig.
1 3 6 10 15
2 5 9 14 19
4 8 13 18 22
7 12 17 21 24
11 16 20 23 25
#}
for e=1:n for g=1:n if(mod(e+g,2))==0 zagM(e,g)=1; endif endfor endfor; zigM=1-zagM;
#{
I now have 2 masks:
zigM =
0 1 0 1 0
1 0 1 0 1
0 1 0 1 0
1 0 1 0 1
0 1 0 1 0
zagM =
1 0 1 0 1
0 1 0 1 0
1 0 1 0 1
0 1 0 1 0
1 0 1 0 1
#}
zigzag=zag.*zagM+zig.*zigM;
#{
zigzag =
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
#}
ooRexx
call printArray zigzag(3)
say
call printArray zigzag(4)
say
call printArray zigzag(5)
::routine zigzag
use strict arg size
data = .array~new(size, size)
row = 1
col = 1
loop element = 0 to (size * size) - 1
data[row, col] = element
-- even stripes
if (row + col) // 2 = 0 then do
if col < size then col += 1
else row += 2
if row > 1 then row -= 1
end
-- odd rows
else do
if row < size then row += 1
else col += 2
if col > 1 then col -= 1
end
end
return data
::routine printArray
use arg array
dimension = array~dimension(1)
loop i = 1 to dimension
line = "|"
loop j = 1 to dimension
line = line array[i, j]~right(2)
end
line = line "|"
say line
end
- 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 {$} {MakeTuple unit W} end}
T
end
in
{Inspect {CreateZigZag 5}}PARI/GP
zz(n)={
my(M=matrix(n,n),i,j,d=-1,start,end=n^2-1);
while(ct--,
M[i+1,j+1]=start;
M[n-i,n-j]=end;
start++;
end--;
i+=d;
j-=d;
if(i<0,
i++;
d=-d
,
if(j<0,
j++;
d=-d
)
);
if(start>end,return(M))
)
};Pascal
Program zigzag( input, output );
const
size = 5;
var
zzarray: array [1..size, 1..size] of integer;
element, i, j: integer;
direction: integer;
width, n: integer;
begin
i := 1;
j := 1;
direction := 1;
for element := 0 to (size*size) - 1 do
begin
zzarray[i,j] := element;
i := i + direction;
j := j - direction;
if (i = 0) then
begin
direction := -direction;
i := 1;
if (j > size) then
begin
j := size;
i := 2;
end;
end
else if (i > size) then
begin
direction := -direction;
i := size;
j := j + 2;
end
else if (j = 0) then
begin
direction := -direction;
j := 1;
if (i > size) then
begin
j := 2;
i := size;
end;
end
else if (j > size) then
begin
direction := -direction;
j := size;
i := i + 2;
end;
end;
width := 2;
n := size;
while (n > 0) do
begin
width := width + 1;
n := n div 10;
end;
for j := 1 to size do
begin
for i := 1 to size do
write(zzarray[i,j]:width);
writeln;
end;
end.
- Output:
0 1 5 6 14 2 4 7 13 15 3 8 12 16 21 9 11 17 20 22 10 18 19 23 24
- Output:
with size set to 6
0 1 5 6 14 15 2 4 7 13 16 25 3 8 12 17 24 26 9 11 18 23 27 32 10 19 22 28 31 33 20 21 29 30 34 35
Program zigzag;
{$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;
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);
Phix
with javascript_semantics 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"))
Phixmonti
5 var Size
0 Size repeat Size repeat
1 var i 1 var j
Size 2 power for
swap i get rot j set i set
i j + 1 bitand 0 == IF
j Size < IF j 1 + var j ELSE i 2 + var i ENDIF
i 1 > IF i 1 - var i ENDIF
ELSE
i Size < IF i 1 + var i ELSE j 2 + var j ENDIF
j 1 > IF j 1 - var j ENDIF
ENDIF
endfor
Size FOR
var row
Size FOR
var col
row get col get tostr 32 32 chain chain 1 3 slice print drop drop
ENDFOR
nl
ENDFORPHP
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.
(load "@lib/simul.l")
(de zigzag (N)
(prog1 (grid N N)
(let (D '(north west south east .) E '(north east .) This 'a1)
(for Val (* N N)
(=: val Val)
(setq This
(or
((cadr D) ((car D) This))
(prog
(setq D (cddr D))
((pop 'E) This) )
((pop 'E) This) ) ) ) ) ) )
(mapc
'((L)
(for This L (prin (align 3 (: val))))
(prinl) )
(zigzag 5) )- 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
/i i ri add def
/j j rj add def
/ri rj /rj ri def def
} {
i di add dup 0 le
exch sizem1 ge or
j dj add dup 0 le
exch sizem1 ge or
or {
/pus true def
/i i di add def /j j dj add def
/di di neg def /dj dj neg def
} {
/i i di add def /j j dj add def
} ifelse
} ifelse
} forall
stroke showpage
} if
%%EOF
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
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
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):
'''zigzag rows'''
def compare(xy):
x, y = xy
return (x + y, -y if (x + y) % 2 else y)
xs = range(n)
return {index: n for n, index in enumerate(sorted(
((x, y) for x in xs for y in xs),
key=compare
))}
def printzz(myarray):
'''show zigzag rows as lines'''
n = int(len(myarray) ** 0.5 + 0.5)
xs = range(n)
print('\n'.join(
[''.join("%3i" % myarray[(x, y)] for x in xs) for y in xs]
))
printzz(zigzag(6))
- Output:
0 2 3 9 10 20 1 4 8 11 19 21 5 7 12 18 22 29 6 13 17 23 28 30 14 16 24 27 31 34 15 25 26 32 33 35
Alternative version,
# pylint: disable=invalid-name
# pylint: disable=unused-argument
"ZigZag iterator."
import sys
if sys.version_info[0] >= 3:
xrange = range
def move(x, y, columns, rows):
"Tells us what to do next with x and y."
if y < (rows - 1):
return max(0, x-1), y+1
return x+1, y
def zigzag(rows, columns):
"ZigZag iterator, yields indices."
x, y = 0, 0
size = rows * columns
for _ in xrange(size):
yield y, x
if (x + y) & 1:
x, y = move(x, y, columns, rows)
else:
y, x = move(y, x, rows, columns)
# test code
i, rows, cols = 0, 5, 5
mat = [[0 for x in range(cols)] for y in range(rows)]
for (y, x) in zigzag(rows, cols):
mat[y][x], i = i, i + 1
from pprint import pprint
pprint(mat)
- 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
Quackery
Sorting Indices
[ ]'[ tuck do dip do ] is with2 ( x x --> x x )
[ dup temp put
[] swap
dup * times [ i^ join ]
sortwith
[ with2
[ temp share /mod
tuck + 1 &
if negate ]
> ]
sortwith
[ with2
[ temp share /mod + ]
> ]
dup witheach
[ i^ unrot poke ]
[] swap
temp share times
[ temp share split
dip [ nested join ] ]
drop
temp release ] is zigzag ( n --> [ )
10 zigzag
witheach
[ witheach
[ dup 10 < if sp
echo sp ]
cr ]- Output:
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
Turtle style
Adapted from Spiral matrix#Quackery
The sequence of turns for the first half of the matrix is east to southwest to south to northeast to east. In the second half the order of turns is reversed.
[ stack ] is stepcount ( --> s )
[ stack ] is position ( --> s )
[ stack ] is heading ( --> s )
[ heading take
behead join
heading put ] is turn ( --> )
[ heading share 0 peek
unrot times
[ position share
stepcount share
unrot poke
over position tally
1 stepcount tally ]
nip ] is walk ( [ n --> [ )
[ dip [ temp put [] ]
temp share times
[ temp share split
dip
[ nested join ] ]
drop temp release ] is matrixify ( n [ --> [ )
[ 0 stepcount put ( set up... )
0 position put
' [ 1 ]
over 1 - join
over join
over 1 - negate join
heading put
0 over dup * of
over 1 - times ( turtle draws first half of zigzag )
[ 1 walk turn
i^ 1+ walk turn ]
heading take ( reverse the sequence of turns )
reverse heading put
over 1 - times ( turtle draws second half of zigzag )
[ turn 1 walk
turn i walk ]
1 walk
matrixify ( ...tidy up )
heading release
position release
stepcount release ] is zigzag ( n --> [ )
10 zigzag
witheach
[ witheach
[ dup 10 < if sp echo sp ]
cr ]- Output:
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
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
zigzag1 <- function(n) {
j <- seq(n)
u <- rep(c(-1, 1), n)
v <- j * (2 * j - 1) - 1
v <- as.vector(rbind(v, v + 1))
a <- matrix(0, n, n)
for (i in seq(n)) {
a[i, ] <- v[j + i - 1]
v <- v + u
}
a
}
zigzag1(5)
- Output:
[,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
zigzag2 <- function(n) {
a <- zigzag1(n)
v <- seq(n - 1)^2
for (i in seq(n - 1)) {
a[n - i + 1, seq(i + 1, n)] <- a[n - i + 1, seq(i + 1, n)] - v[seq(n - i)]
}
a
}
zigzag2(5)
- Output:
[,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
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))
Raku
(formerly 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;
}Rascal
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
REXX
This REXX version allows the optional specification of the start and increment values.
Version 1
/*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; size= n**2 /*start: 1st row & column; array size.*/
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.*/
call show /*display a (square) matrix──►terminal.*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: w= max(length(start), length(start+size*inc)) /*max width of any matrix elements,*/
do r=1 for n ; _= right(@.r.1, w) /*show the rows of the matrix. */
do c=2 for n-1; _= _ right(@.r.c, w) /*build a line for output of a row.*/
end /*c*/; say _ /* [↑] align the matrix elements. */
end /*r*/; return- output when using the default inputs:
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 when using the inputs of: 5 1
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 when using the inputs of: 4 -1000 -1
-1000 -1001 -1005 -1006 -1002 -1004 -1007 -1012 -1003 -1008 -1011 -1013 -1009 -1010 -1014 -1015
Version 2 - simplified logic
/*REXX program produces and displays a zig-zag matrix (a square array) */
Parse Arg n start inc . /* obtain optional arguments from command line */
if n=='' | n=="," then n= 5 /*Not specified? use the default*/
if start=='' | start=="," then start= 0 /* " " " " " */
if inc=='' | inc=="," then inc= 1 /* " " " " " */
Parse Value 1 1 n**2 With row col size
Do x=start By inc For size
m.row.col=x
If (row+col)//2=0 Then do /* moving upward */
Select
when row=1 Then Do /* at upper bound */
If col<n Then
col=col+1 /* move right */
Else
row=2 /* move down */
End
when col=n Then /* at right border */
row=row+1 /* move down */
Otherwise Do /* in all other cases */
row=row-1 /* move up */
col=col+1 /* and to the right */
End
End
End
Else Do /* moving downward */
Select
When col=1 Then Do /* at lower bound */
If row=n Then /* in bottom row */
col=2 /* move right */
Else /* otherwise */
row=row+1 /* move down */
End
When row=n Then /* at lower bound */
col=col+1 /* move right */
Otherwise Do /* in all other cases */
row=row+1 /* move down */
col=col-1 /* and to the left */
End
End
End
End
Call show
Exit
/*-----------------------------------------------------------------------*/
show:
w=length(start+size*inc) /* max width of any matrix element */
Do row=1 To n /* loop over rows */
line=right(m.row.1,w) /* first element */
Do column=2 To n /* loop over other elements */
line=line right(m.row.column,w) /* build output line */
End
Say line
End /* display the line */
ReturnRing
# 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:
RPL
Turtle's way.
« 1 -1 → n way val
« n DUP 2 →LIST 0 CON
2 n DUP + FOR s
n s 1 - MIN s OVER -
IF way 0 > THEN SWAP END
FOR j
j s OVER - 2 →LIST 'val' INCR PUT
way STEP
'way' SNEG
NEXT
» » 'ZIGZAG' STO
6 ZIGZAG
- Output:
1: [[0 2 3 9 10 20]
[1 4 8 11 19 21]
[5 7 12 18 22 29]
[6 13 17 23 28 30]
[14 16 24 27 31 34]
[15 25 26 32 33 35]]
Ruby
def zigzag(n)
(seq=*0...n).product(seq)
.sort_by {|x,y| [x+y, (x+y).even? ? y : -y]}
.each_with_index.sort.map(&:last).each_slice(n).to_a
end
def print_matrix(m)
format = "%#{m.flatten.max.to_s.size}d " * m[0].size
puts m.map {|row| format % row}
end
print_matrix zigzag(5)- 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
Rust
use std::cmp::Ordering;
use std::cmp::Ordering::{Equal, Greater, Less};
use std::iter::repeat;
#[derive(Debug, PartialEq, Eq)]
struct SortIndex {
x: usize,
y: usize,
}
impl SortIndex {
fn new(x: usize, y: usize) -> SortIndex {
SortIndex { x, y }
}
}
impl PartialOrd for SortIndex {
fn partial_cmp(&self, other: &SortIndex) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for SortIndex {
fn cmp(&self, other: &SortIndex) -> Ordering {
let lower = if self.x + self.y == other.x + other.y {
if (self.x + self.y) % 2 == 0 {
self.x < other.x
} else {
self.y < other.y
}
} else {
(self.x + self.y) < (other.x + other.y)
};
if lower {
Less
} else if self == other {
Equal
} else {
Greater
}
}
}
fn zigzag(n: usize) -> Vec<Vec<usize>> {
let mut l: Vec<SortIndex> = (0..n * n).map(|i| SortIndex::new(i % n, i / n)).collect();
l.sort();
let init_vec = vec![0; n];
let mut result: Vec<Vec<usize>> = repeat(init_vec).take(n).collect();
for (i, &SortIndex { x, y }) in l.iter().enumerate() {
result[y][x] = i
}
result
}
fn main() {
println!("{:?}", 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
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
write(num lpad 4);
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
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
Standard ML
fun rowprint r = (List.app (fn i => print (StringCvt.padLeft #" " 3 (Int.toString i))) r;
print "\n");
fun zig lst M = List.app rowprint (lst M);
fun sign t = if t mod 2 = 0 then ~1 else 1;
fun zag n = List.tabulate (n,
fn i=> rev ( List.tabulate (n,
fn j =>
let val t = n-j+i and u = n+j-i in
if i <= j
then t*t div 2 + sign t * ( t div 2 - i )
else n*n - 1 - ( u*u div 2 + sign u * ( u div 2 - n + 1 + i) )
end
)));
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 val it = () : unit
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
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
adapted from the J solution
#import std
#import nat
zigzag = ~&mlPK2xnSS+ num+ ==+sum~~|=xK9xSL@iiK0+ iotatest 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
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
Wren
import "./fmt" for Conv, Fmt
var zigzag = Fn.new { |n|
var r = List.filled(n*n, 0)
var i = 0
var n2 = n * 2
for (d in 1..n2) {
var x = d - n
if (x < 0) x = 0
var y = d - 1
if (y > n - 1) y = n - 1
var j = n2 - d
if (j > d) j = d
for (k in 0...j) {
if (d&1 == 0) {
r[(x+k)*n+y-k] = i
} else {
r[(y-k)*n+x+k] = i
}
i = i + 1
}
}
return r
}
var n = 5
var w = Conv.itoa(n*n - 1).count
var i = 0
for (e in zigzag.call(n)) {
Fmt.write("$*d ", w, e)
if (i%n == n - 1) System.print()
i = i + 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
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 rowzkl
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())});
}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(); }]];
s.pump(String,T(Void.Read,m-1), ("%3s"*m+"\n").fmt);
}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)
.pump(String,T(Void.Read,m-1), ("%3s"*m+"\n").fmt);
}- Output:
The results are the same
zz(5).println(); 0 1 5 6 14 2 4 7 13 15 3 8 12 16 21 9 11 17 20 22 10 18 19 23 24
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