LeetCode 62. Unique Paths

题目描述

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.

解题思路

基础动态规划题目，递归方程为:
$$dp[i][j]=dp[i-1][j]+dp[i][j-1]$$
其中 dp 含义为走到该坐标的独一无二的路径数目。

代码

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