Python Coding challenge - Day 519| What is the output of the following Python Code?

 

Code Explanation:

 1. Function Definition

def count_paths(r, c):

Defines a function named count_paths with two parameters:

r: number of rows

c: number of columns

2. Base Case: When One Dimension is 1

    if r == 1 or c == 1:

        return 1

If either the number of rows r or the number of columns c is 1:

There is only one path (straight line across the row or down the column).

This condition stops the recursion when we reach the edge of the grid.

3. Recursive Case: Sum of Two Choices

    return count_paths(r - 1, c) + count_paths(r, c - 1)

This line calculates the total number of paths by:

Moving down: reduces rows by 1 (count_paths(r - 1, c))

Moving right: reduces columns by 1 (count_paths(r, c - 1))

It adds the number of paths from both possibilities.

4. Function Call and Output

print(count_paths(3, 3))

This calls the function with a 3×3 grid and prints the result.

Step-by-Step Evaluation

Let's walk through the recursion for count_paths(3, 3):

count_paths(3, 3)

= count_paths(2, 3) + count_paths(3, 2)

count_paths(2, 3) = count_paths(1, 3) + count_paths(2, 2) = 1 + 2 = 3

count_paths(3, 2) = count_paths(2, 2) + count_paths(3, 1) = 2 + 1 = 3

So,

count_paths(3, 3) = 3 + 3 = 6

Final Output

6