Step by Step solution about How to resolve the algorithm Zig-zag matrix step by step in the Mathematica / Wolfram Language programming language

Code Explanation:

The code you provided includes two functions, ZigZag and ZigZag2, to generate matrices with a specific zig-zag pattern. Here's a detailed explanation for each function:

ZigZag Function:

• Purpose: Generates a matrix with a zig-zag pattern using a mathematical formula.
• Parameters:
  • size: An integer representing the size of the square matrix to generate.
• Working:
  • Initializes an empty matrix empty with dimensions size x size.
  • Replaces each element of empty with a value based on its position using the following formula:

    1/2 (i+j)^2-(i+j)/2-i (1-Mod[i+j,2])-j Mod[i+j,2]
    

    where i and j are the row and column indices of the element.
  • Replaces elements where i + j > size + 1 with a value calculated using a temporary matrix tmp:

    size^2 - tmp[[size-i+1,size-j+1]] - 1
    

• Output: Returns the generated matrix.

ZigZag2 Function:

• Purpose: Generates a matrix with a zig-zag pattern using a loop-based approach.
• Parameters:
  • size: An integer representing the size of the square matrix to generate.
• Working:
  • Initializes a matrix data with dimensions size x size.
  • Sets the initial row and column indices (i and j) to 1.
  • Iterates over all elements in the matrix, assigning each element a value in sequence.
  • Based on whether the sum of the current row and column indices is even or odd, the loop follows specific rules to move to the next element in the zig-zag pattern.
• Output: Returns the generated matrix.

Usage Examples:

• ZigZag[5] // MatrixForm: Generates a 5x5 matrix with a zig-zag pattern using the mathematical formula.
• ZigZag2[6] // MatrixForm: Generates a 6x6 matrix with a zig-zag pattern using the loop-based approach.

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]
]


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
 ]


ZigZag[5] // MatrixForm
ZigZag2[6] // MatrixForm