Unique Matrix Traversal and Perfect Squares in PHP

Hello, Space Explorer! Are you ready to embark on a journey into the land of matrices? In this unit, we're in for a thrilling ride into the world of unique matrix traversal. We'll be navigating through the realm of 2D arrays, following a distinctive order that oozes intrigue. Stay seated, and let's dive right in!

Suppose we have a matrix where each cell represents a distinct symbol or integer. Our task is to decode this matrix by reading the cells in a particular order.

The decoding begins from the top-left cell of the matrix. We move in a bottom-left downward diagonal direction until we hit the left boundary. Upon hitting the left boundary, we move one cell down (unless we're at the bottom-left corner already, in which case we move one cell to the right) and start moving in an upward diagonal direction toward the upper-right.

While moving diagonally up-right, if we hit the top boundary, we move one cell to the right and start moving in a downward diagonal direction towards the bottom-left. However, if we hit the right boundary while moving diagonally upwards, we move one cell down and start moving in a bottom-left direction. In other words, we keep zigzagging diagonally across the matrix until every cell in the matrix is visited.

Upon completing this zigzag traversal, we will have a list of traversed cell values. Next, we process this list to uncover the indices of the perfect square numbers. The function diagonalTraverseAndSquares($matrix) should implement this traversal and return an array containing the positions of perfect square numbers in the traversed sequence.

Take a $3 \times 4$ matrix, for instance:

$matrix = [
    [1, 2, 3, 4],
    [5, 6, 7, 8],
    [9, 10, 11, 12]
];

Upon completing the diagonal traversal, we'll get the list: {1, 5, 2, 3, 6, 9, 10, 7, 4, 8, 11, 12}. From this list, we see that 1, 9, and 4 are perfect squares and are located at the 1st, 6th, and 9th positions in the list. Thus, our function returns: [0, 5, 8].

First, let's examine the dimensions of the matrix. To map the landscape of our matrix, we'll use count($matrix) to determine the number of rows and count($matrix[0]) to determine the number of columns. Next, we initialize two arrays: $traversal and $results. The $traversal array will keep the cell values that we will obtain from the matrix based on our unique diagonal zigzag traversal. The $results array will later be populated with the positions of perfect square numbers that can be found in the $traversal array.

<?php

function diagonalTraverseAndSquares($matrix) {
    $rows = count($matrix);
    $cols = count($matrix[0]);
    $traversal = [];
    $results = [];