[Leetcode 62]: Unique Paths

Problem link: https://leetcode.com/problems/unique-paths/?envType=problem-list-v2&envId=dynamic-programming

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 * 109.

Solution:

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

        for i in range(n):
            dp[0][i] = 1
        
        for j in range(m):
            dp[j][0] = 1

        for i in range(1, m):
            for j in range(1, n):
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1]
        
        return dp[m - 1][n - 1]