Exploring Diagonal Matrix Traversal Techniques

Introduction

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

Task Statement

Suppose we have a 2D 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. From the first cell, we move one cell down. Then, we start moving diagonally in the top-right direction until we hit the top boundary. Hitting the top boundary, we move one cell to the right and start moving diagonally in the bottom-left direction. Hitting the left boundary, we move one cell down (unless it is the last left boundary, in which case we move one cell to the right) and start moving diagonally in the top-right direction. Hitting the right boundary, we move one cell to the right (unless it is the last right boundary, in which case we move one cell down) and start moving diagonally in the bottom-left direction. In other words, we keep zig-zagging 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 diagonal_traverse_and_squares(matrix) should implement this traversal and return a list containing the 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 1st, 6th, and 9th positions in the list. Thus, our function returns: [0, 5, 8] .

Solution Building: Step 1

First, let's put on our Python hats and scrutinize the dimensions of the 2D matrix. To map the landscape of our matrix, we'll use the len() function to determine the number of rows and columns. Next, we initialize two lists: 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. Python import math def diagonal_traverse(matrix): rows, cols = len(matrix), len(matrix[0]) traversal = [] results = []

Join the 1M+ learners on CodeSignal

Be a part of our community of 1M+ users who develop and demonstrate their skills on CodeSignal

Solution Building: Step 2

The next step involves the actual traversal of the 2D matrix. This process is done diagonally in a zigzag pattern. We begin from the top-left corner (cell [0][0]) and make our journey through the matrix using two variables, row and col, to track the cell indices. We also initialize dir with '1' which dictates that the starting direction is the down-left direction.

However, it's not just a simple left-right or up-down movement; as per the rules, we need to ensure we change our direction whenever we hit an edge. Let dir = -1 dictate the up-right direction. To ensure we continue the correct diagonal movement and don't exceed the matrix boundaries, we use conditional checks within the loop.

Python

    row = col = 0
    dir = 1
    for _ in range(rows * cols):  # Loop runs for total number of cells in matrix.
        traversal.append(matrix[row][col])  # Append the current cell value to traversal.
        
        # Logic to control direction based on edges:
        if dir == 1:  # Moving down-left
            if row == rows - 1:
                col += 1
                dir = -1
            elif col == 0:
                row += 1
                dir = -1
            else:
                row += 1
                col -= 1
        else:  # Moving up-right
            if col == cols - 1:
                row += 1
                dir = 1
            elif row == 0:
                col += 1
                dir = 1
            else:
                row -= 1
                col += 1

    row = col = 0
    dir = 1
    for _ in range(rows * cols):  # Loop runs for total number of cells in matrix.
        traversal.append(matrix[row][col])  # Append the current cell value to traversal.
        
        # Logic to control direction based on edges:
        if dir == 1:  # Moving down-left
            if row == rows - 1:
                col += 1
                dir = -1
            elif col == 0:
                row += 1
                dir = -1
            else:
                row += 1
                col -= 1
        else:  # Moving up-right
            if col == cols - 1:
                row += 1
                dir = 1
            elif row == 0:
                col += 1
                dir = 1
            else:
                row -= 1
                col += 1

Introduction

Task Statement

Solution Building: Step 1

Join the 1M+ learners on CodeSignal

Solution Building: Step 2

Solution Building: Step 3

Lesson Summary