09-03 leetcode-0062

这个月又是 DP 专场？

题目

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).

题解

就很简单一个 DP 转移公式

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

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

        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[-1][-1]

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