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

The provided PHP code defines a function called ZigZagMatrix that generates a 2D square matrix with numbers arranged in a zigzag pattern. Here's how the code works:

• It initializes a 2D array $matrix with dimensions $num x $num, where $num represents the size of the square matrix.

• It starts with $i and $j both set to 1 to represent the top-left corner of the matrix.

• It enters a loop that iterates from 0 to $num * $num - 1, which is the total number of elements in the matrix.

• Inside the loop, it assigns the current element number ($e) to the cell in the matrix at position ($i - 1, $j - 1). This means it fills the cells from left to right and top to bottom.

• After assigning the element, it checks if the sum of $i and $j is even or odd using the modulo operator (%). This check determines the direction of the zigzag pattern.

• If ($i + $j) is even, it means the next move should go right or down. It first checks if $j is less than $num. If it is, it increments $j by 1 to move right. If $j is already at the rightmost edge of the matrix, it increments $i by 2 to move down two rows and starts moving left from the next column. However, if $i is already at the top row, it decrements $i by 1 to stay within the matrix boundaries.

• If ($i + $j) is odd, it means the next move should go down or left. It first checks if $i is less than $num. If it is, it increments $i by 1 to move down. If $i is already at the bottom row of the matrix, it increments $j by 2 to move right two columns and starts moving up from the next row. However, if $j is already at the leftmost edge of the matrix, it decrements $j by 1 to stay within the matrix boundaries.

• The loop continues until all elements of the ZigZag matrix are filled.

• Finally, the function returns the generated $matrix.

This code essentially creates a matrix where the numbers are arranged in a zigzag pattern, alternating between moving right and down (when ($i + $j) is even) and moving down and left (when ($i + $j) is odd).

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;
}