Python Coding challenge - Day 523| What is the output of the following Python Code?

 

Code Explanation:

1. DP Table Initialization

dp = [[1]*c for _ in range(r)]

Creates a 2D list (dp) with r rows and c columns.

Every cell is initialized to 1.

Why 1? Because:

The first row and first column can only be reached in one way (all right or all down).

After this line, the DP table (dp) looks like this for r=4, c=3:

[

 [1, 1, 1],

 [1, 1, 1],

 [1, 1, 1],

 [1, 1, 1]

]

2. Filling the DP Table

for i in range(1, r):

    for j in range(1, c):

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

Starts from cell (1,1), since row 0 and column 0 are already known (only 1 path).

For each cell (i, j), the number of paths is:

dp[i-1][j]: from the cell above

dp[i][j-1]: from the cell to the left

Adds both to get total paths to current cell.

 Table gets filled like this step by step:

[

 [1, 1, 1],        # row 0 (base row)

 [1, 2, 3],        # row 1

 [1, 3, 6],        # row 2

 [1, 4, 10]        # row 3

]

3. Return Final Answer

return dp[-1][-1]

dp[-1][-1] gives value at bottom-right corner.

Here: dp[3][2] = 10, which is the number of unique paths in a 4 x 3 grid.

4. Function Call

print(count_paths(4, 3))

This prints the result of the function — which is:

Final Output: 10

There are 10 unique paths in a 4×3 grid moving only right or down.