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Unique Paths

Problem Statement​

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.

Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The test cases are generated so that the answer will be less than or equal to 2 * 10^9.

Leetcode link

Examples​

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

Code​

Python3 Code

class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        dp = [[1] * m for _ in range(n)]
        for i in reversed(range(n - 1)):
            for j in reversed(range(m - 1)):
                dp[i][j] = dp[i + 1][j] + dp[i][j + 1]
        return dp[0][0]