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 matrix, for instance:
