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?

大致题意

机器人每次只能向下向右走一步，给予一个mxn大小的方格，共有几种方法可以到达右下角（机器人在左上角）

题解

题目类型：动态规划

dp[i][j]表示到达第i行第j列有几种方法，初始为1。

状态转移：dp[i][j] = dp[i - 1][j] + dp[i][j - 1]

下方为解

class Solution {public:    int uniquePaths(int m, int n) {        vector
    
     
      > path(m, vector
      
       (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];    }};