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?

 

 

 

 

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

解1:

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];
            }
        }
     return dp[m - 1][n - 1];   
    }
};

解2:

https://leetcode.com/problems/unique-paths/discuss/22954/C%2B%2B-DP

暂时无法理解，待后续继续学习。