Lesson 2

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:

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

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:

Python`1def column_traverse(matrix): 2 rows = len(matrix) 3 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:

Python`1def column_traverse(matrix): 2 rows, cols = len(matrix), len(matrix[0]) 3 direction = 'up' 4 row, col = rows - 1, cols - 1 5 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.

Python`1def column_traverse(matrix): 2 rows, cols = len(matrix), len(matrix[0]) 3 direction = 'up' 4 row, col = rows - 1, cols - 1 5 output = [] 6 7 while len(output) < rows * cols: 8 output.append(matrix[row][col]) 9 10 if direction == 'up': 11 if row - 1 < 0: 12 direction = 'down' 13 col -= 1 14 else: 15 row -= 1 16 else: 17 if row + 1 == rows: 18 direction = 'up' 19 col -= 1 20 else: 21 row += 1 22 23 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.

Let's explore one more way of traversal. We can leverage the utility of Python's `range()`

function to traverse a 2D matrix in reverse order. This function, known for its flexibility, can also create a sequence that decrements.

To achieve this, we use `range()`

with three arguments - `start`

, `stop`

, and `step`

. By setting `step`

to `-1`

, we generate a decreasing sequence.

Consider our familiar $3 \times 4$ matrix:

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

Using a decrementing `range()`

, the reverse traverse pattern would produce this list: `[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]`

.

Here's how we can implement this reverse traversal:

Python`1def reverse_traverse(matrix): 2 rows, cols = len(matrix), len(matrix[0]) 3 output = [] 4 5 for row in range(rows - 1, -1, -1): 6 for col in range(cols - 1, -1, -1): 7 output.append(matrix[row][col]) 8 9 return output`

In this function, we start the `range()`

for `row`

from `rows - 1`

and run it till `-1`

(which is excluded), decrementing at each step. Similarly, our nested `range()`

for `col`

starts from `cols - 1`

and goes till `-1`

. This allows us to start from the bottom-right corner and traverse leftwards, then upwards, covering the entire matrix in reverse order.

As you gain proficiency in matrix traversal in Python, you'll discover the many creative ways to utilize Python's flexible syntax. The more you experiment with different traversal methods, the better you become! Happy practicing!

Congratulations! You have made it through a challenging task in which you maneuvered your way through a complex matrix traversal patterns. The functions you've designed not only tests your Python coding skills but also your ability to visualize spatial patterns.

It's time to put your new knowledge to the test! The next step is to tackle similar challenges on your own. I encourage you to use this lesson as your guide and don't forget to experiment with different matrix sizes and cell values. With plenty of practice, you'll soon master these traversing patterns!