Unique path

题目：

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?

解法一：自己写的，比较诡异

    public int uniquePaths(int m, int n) 
    {
        int [][] grids = new int [m+1][n+1];
        grids[m][n-1]=1;
        for (int i=m-1;i>=0;i--)
        {
            for (int j=n-1;j>=0;j--)
            {
                grids[i][j]=grids[i+1][j]+grids[i][j+1];
        
                
            }
        }
        return grids[0][0];
    }

解法二：九章算法，好理解

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

reference：http://www.jiuzhang.com/solutions/unique-paths/