Leetcode: 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?

推荐方法：DP矩阵做法其实还可以节省一维：2D矩阵变成一维数组DP：

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

一维DP方法2：

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