62. Unique Paths

There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time

Example 1:

Input: m = 3, n = 7
Output: 28

Example 2:

Input: m = 3, n = 2
Output: 3
Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner: 1. Right -> Down -> Down 2. Down -> Down -> Right 3. Down -> Right -> Down

Constraints:

1 <= m, n <= 100

Solution

class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        dp = [[0 for _ in range(n)] for _ in range(m)]

        for c in range(n):
            dp[0][c] = 1

        for r in range(m):
            dp[r][0] = 1

        for r in range(1, m):
            for c in range(1, n):
                dp[r][c] = dp[r - 1][c] + dp[r][c - 1]

        return dp[-1][-1]