【leetcode】unique paths

问题：

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.

分析：

1、采用DFS，时间复杂度O(n^4)，大集合会超时；采用DFS+缓冲（即“备忘录”法）时间O(n^2)。

2、用动规，时间O(n^2)，空间O(n^2)；可以优化，后续补上。

3、还可以用数学公式，后续补上。

代码：

class Solution {public:    int uniquePaths(int m, int n) {        vector<vector<int>> p(m,vector<int>(n,1));        //边界        for(int i=0;i<m;i++) p[i][0]=1;        for(int j=0;j<n;j++) p[0][j]=1;        for(int i=1;i<m;i++)            for(int j=1;j<n;j++){                //动规：自底向上                p[i][j]=p[i-1][j]+p[i][j-1];            }        return p[m-1][n-1];    }};