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?

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

Note: m and n will be at most 100.

解题思路：

动态规划，每个dp[i][j]代表有几种到达他的路径。注意一下二维vector的初始赋值。

　　

class Solution {
public:
    int uniquePaths(int m, int n) {
        if(m==0&&n==0) return 0;
        vector<vector<int>> dp(m+1, vector<int> (n+1, 1));


        dp[1][1]=1;
        for(int i=1;i<=m;i++)
            for(int j=1;j<=n;j++){
            if(i-1>0&&j-1>0) dp[i][j] = dp[i-1][j]+dp[i][j-1];
            else if(i-1>0&&j-1==0)  dp[i][j] = dp[i-1][j];
            else if(i-1==0&&j-1>0)  dp[i][j] = dp[i][j-1];
            }

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