62. Unique Paths

Problem：

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?

给定一个m x n的网格，统计从（0，0）到（m-1，n-1）的不同路径，每次只能向右或向下走。

解决思路：从（0，0）到（i，j）的路径总数等于从（0，0）到（i-1，j）和从（0，0）到（i，j-1）路径数之和。

　　　　　可以用动态规划，即dp[i][j]=dp[i-1][j]+dp[i][j-1]

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int>> dp(m+1, vector<int>(n+1));
        dp[1][1] = 1;
        for (int i=0; i<m; ++i)
            for(int j=0; j<n; ++j) {
                if (i==0 && j==0)
                    continue;
                dp[i+1][j+1] = dp[i][j+1] + dp[i+1][j];
            }
                
        return dp[m][n];
    }
};