Analyzing Matrix Traversals and Perfect Squares in Java

Hello, budding programmer! 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 towards 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(int[][] matrix) should implement this traversal and return a list containing the 0-indexed positions of perfect square numbers in the traversed sequence.

Take a 3x4 matrix for instance:

{
    {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 0th, 5th, and 8th positions in the list. Thus, our function returns: {0, 5, 8}.

First, let's put on our Java hats and scrutinize the dimensions of the matrix. To map the landscape of our matrix, we'll use matrix.length to determine the number of rows and matrix[0].length to determine the number of columns. Next, we initialize two ArrayList<Integer>: traversal and results. The traversal list will be responsible for keeping the cell values that we will obtain from the matrix based on our unique diagonal zigzag traversal. The results list will be populated later with the positions of perfect square numbers that can be found in the traversal list.

import java.util.ArrayList;
import java.util.List;

public class DiagonalMatrixTraversal {

    public static List<Integer> diagonalTraverseAndSquares(int[][] matrix) {
        int rows = matrix.length, cols = matrix[0].length;
        List<Integer> traversal = new ArrayList<>();
        List<Integer> results = new ArrayList<>();