How to resolve the algorithm Zig-zag matrix step by step in the AutoHotkey programming language

Published on 12 May 2024 09:40 PM
#Autohotkey

How to resolve the algorithm Zig-zag matrix step by step in the AutoHotkey programming language

Table of Contents

Problem Statement

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:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Zig-zag matrix step by step in the AutoHotkey programming language

Source code in the autohotkey programming language

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

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