62. Unique Paths 类别：动态规划 难度：medium

题目：

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?

思路：

对于格点(i,j)。由于只能从上格点(i-1,j)或左格点(i,j-1)到达，并且两者路径是不重复的，因此path[i][j] = path[i-1][j]+path[i][j-1]。

程序：

class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int> > res(m + 1, vector<int>(n + 1, 1));
for(int i = 2;i <= m;i++)
{
for(int j = 2;j <= n;j++)
res[i][j] = res[i - 1][j] + res[i][j - 1];
}
return res[m]
;
}
};