LeetCode-62-Unique Paths

算法描述：

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 7 x 3 grid. 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

解题思路：动态规划，dp[i][j] = dp[i-1][j] +dp[i][j-1];

    int uniquePaths(int m, int n) {
        vector<vector<int>> dp(m,vector<int>(n,0));
        for(int i=0; i < m; i++) dp[i][0] = 1;
        for(int j =0; j < n; j++) dp[0][j] = 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];
    }