62.寻找路径

Unique Paths

问题描述：

A robot is located at the top-left corner of a m x n grid (marked ‘Start’ in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked ‘Finish’ in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

测试代码(c++):

class Solution {public:    int uniquePaths(int m, int n) {        vector<vector<int> > dp(m+1,vector<int>(n+1,0));        dp[0][1] = 1;        for(int i=1;i<=m;i++)        {            for(int j=1;j<=n;j++)            {                dp[i][j] = dp[i-1][j]+dp[i][j-1];            }        }        return dp[m][n];    }};

性能：

参考答案：

class Solution {public:    int uniquePaths(int m, int n) {        if (m < 1 || n < 1) return 0;        vector<int> T(n, 1);        for (int i = 1; i < m; i++) {            for (int j = 1; j < n; j++) {                T[j] = T[j-1] + T[j];            }        }        return T[n-1];    }};

参考答案（python）：

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

性能：