LeetCode 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.

简单dp；

• 建立dp数组，dp[i][j]代表到达(i,j)位置的方法。
• 那么dp[i][j] = dp[i-1][j] + dp[i][j-1]， 就很显而易见了。

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