Python Coding challenge - Day 525| What is the output of the following Python Code?

 

Code Explanation:

1. Function Definition

def count_paths(m, n):

Defines a function count_paths that takes two arguments m (rows) and n (columns), representing the size of the grid.

2. Initialize the DP Table

    dp = [[1]*n for _ in range(m)]

Creates a 2D list (matrix) dp with m rows and n columns.

Each cell is initialized to 1 because:

There is only 1 way to reach any cell in the first row (move right only).

There is only 1 way to reach any cell in the first column (move down only).

3. Calculate Paths for Remaining Cells

    for i in range(1, m):

        for j in range(1, n):

            dp[i][j] = dp[i-1][j] + dp[i][j-1]

Loops through all cells starting from row 1 and column 1 (skipping the first row and first column).

Updates each cell dp[i][j] with the sum of:

dp[i-1][j]: number of ways to reach the cell above.

dp[i][j-1]: number of ways to reach the cell to the left.

This works because you can only move right or down, so the total ways to reach dp[i][j] is the sum of ways to reach from above and from the left.

4. Return the Result

    return dp[-1][-1]

Returns the value in the bottom-right cell of the matrix (dp[m-1][n-1]), which is the total number of unique paths to reach the bottom-right corner.

5. Function Call and Output

print(count_paths(3, 4))

Calls count_paths with a 3x4 grid.

Output is 10, meaning there are 10 unique paths from the top-left to the bottom-right corner moving only right or down.

Final Output:

10