[leetcode]62. Unique Paths

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?

Note: m and n will be at most 100.

分析：动态规划，到某一格子的路线总数等于到达左边格子的路线总数加上到达上方格子的路线总数之和。

代码：

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];
    }
};