62. Unique Paths

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?

思路：动态规划的典型题，每个位置都只有两种可能走到它，从上往下或者从左往右，这样可以定义状态方程。

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