Python Coding challenge - Day 515| What is the output of the following Python Code?

 

Code Explanation:

Step 1: Base Case

if m == 1 or n == 1:

    return 1

If either m == 1 or n == 1, there's only one way to reach the destination: go straight down or straight right, respectively.

So, return 1 in this case.

Step 2: Recursive Case

return count_paths(m - 1, n) + count_paths(m, n - 1)

If you're not at the edge of the grid, the total paths are the sum of:

All paths by going down (reduce m by 1),

All paths by going right (reduce n by 1).

Step 3: Trace count_paths(3, 3)

Let’s calculate count_paths(3, 3) recursively:

count_paths(3, 3)

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

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

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

= (1 + (1 + 1)) + ((1 + 1) + 1)

= (1 + 2) + (2 + 1)

= 3 + 3 = 6

Final Answer:

print(count_paths(3, 3))  # Output: 6

There are 6 unique paths in a 3×3 grid from top-left to bottom-right moving only right or down.

Final Output:

6