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.

 

最简单的动态规划。

class Solution {
public:
    int uniquePaths(int m, int n) {
        if(n == 0)return 0;
        int a[100];
        for(int i = 0 ; i < n ; i++)a[i] = 1;
        for(int i = 1 ; i < m ; i++)
        {
            for(int j = 1 ; j < n ; j++)
            {
                a[j] = a[j - 1] + a[j];
            }
        }
        return a[n-1];
    }
};