【leetcode】62. Unique Paths

一、题目描述

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.

思路：动态规划问题，dp[i][j]代表到第i, j 位置的空格时的路径条数。状态转换方程为dp[i][j] = dp[i-1][j] + dp[i][j-1]。注意一开始要将dp中所有值初始化为1。

c++代码（3ms，1.89%）

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