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题目链接：https://leetcode.com/problems/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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

很基本的一道动态规划题目。可以将问题划分为子问题看待，到终点有多少种走法是由到终点左边方格有多少种走法 + 到终点上边有多少种走法，因此很容易得出状态转移方程为：dp[i][j] = dp[i][j-1] + dp[i-1][j]。其中初始化第一列和第一行都为1，因为只有一种走法。时间复杂度为O(M*N), 空间复杂度为O(M*N)。

代码如下：

class Solution {public:    int uniquePaths(int m, int n) {        if(m <=0 || n <=0) return 0;        vector
   
    
     > dp(m, vector
     
      (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];        return dp[m-1][n-1];    }};
     
    
   

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