不同路径

1、题目

图1

2、题解

动态规划

设置状态数组dp，对于\(dp[i][0]\)和\(dp[0][j]\)都只有一条路径可走，对于\(dp[i][j]=dp[i-1][j]+dp[i][j-1]\)

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

优化空间：按行遍历

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