Columnar ZigZag and Reverse Traversal of Matrices

Hello, fellow coder! Are you excited to dive into a new, intriguing coding challenge? In this lesson, we're going to explore special traversals of matrices. Using the Python programming language, we'll find our way through a matrix by climbing up and down the columns, zigzagging as we go. Sound exciting? Buckle up, then, and get ready!

Here's the task: you've been given a 2D matrix consisting of individual cells, each holding a unique integer value. Your goal is to create a function that will traverse this matrix, starting at the bottom right cell. From there, you'll travel up to the top of the same column, then move left to the next column, and then continue downwards from the top of this new column. After reaching the bottom of the column, you again move left and start moving upwards. This unique traverse pattern will be performed until all the cells have been visited.

Consider this small $3 \times 4$ matrix as an example:

[
    [1, 2, 3, 4],
    [5, 6, 7, 8],
    [9, 10, 11, 12]
]

With the described traversal pattern, your function should return this list: [12, 8, 4, 3, 7, 11, 10, 6, 2, 1, 5, 9]

The first step towards a solution is understanding the dimensions of the matrix with which we're working. We can do this using Python's built-in len() function. Let's set up our function and identify the matrix size:

def column_traverse(matrix):
    rows = len(matrix)
    cols = len(matrix[0])

Now that we're aware of the matrix dimensions, we should establish the starting point (bottom-right) and the direction of travel (upwards initially). Additionally, we'll need a list to keep track of the cells we've visited in order:

def column_traverse(matrix):
    rows, cols = len(matrix), len(matrix[0])
    direction = 'up'
    row, col = rows - 1, cols - 1
    output = []

It's time to go exploring! We'll now implement a while loop to traverse the matrix. This loop will continue until we have covered all the cells in the matrix. As we "visit" each cell, we'll add the value in the cell to our list.

def column_traverse(matrix):
    rows, cols = len(matrix), len(matrix[0])
    direction = 'up'
    row, col = rows - 1, cols - 1
    output = []
    
    while len(output) < rows * cols:
        output.append(matrix[row][col])
        
        if direction == 'up':
            if row - 1 < 0:
                direction = 'down'
                col -= 1
            else:
                row -= 1
        else:
            if row + 1 == rows:
                direction = 'up'
                col -= 1
            else:
                row += 1

    return output

That's it, we've completed the function! This Python function will return the output list, which gives us the order of traversal through the matrix.