leetcode-62-不同路径

题目描述：

方法一：

class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        return int(math.factorial(m+n-2)/math.factorial(m-1)/math.factorial(n-1))

方法二：动态规划 O(m*n) O(m*n)

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

 

另：空间：O(n)

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]