62. Unique Paths&机器人走方格I

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.

//最简单的动态规划
//http://www.cnblogs.com/remlostime/archive/2012/11/15/2772263.html

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

return f[m-1][n-1];

}
};