【leetcode】 Unique Path(easy)

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?

思路：可能是因为已经知道要用动态规划了，做起来特别顺，一次AC。

设m=5,n=4, 在二维格子里，最上面一行和最左边一行的可以到达的方式都只有1. 其他格子里的只要把它上边和左边的次数加起来就好了。

0  1  1  1

1  2  3  4

1  3  6  10

1  4  10 20

1  5  15 35

如上，那么5*4的格子有35种走法。

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int>> ways(m, vector<int>(n,1));
        for(int i = 1; i < m; i++)
        {
            for(int j = 1; j < n; j++)
            {
                ways[i][j] = ways[i - 1][j] + ways[i][j - 1];
            }
        }
        return ways[m - 1][n - 1];
    }
};