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：

 1 public int uniquePaths(int m, int n) {
 2     if(m<=0 || n<=0)
 3         return 0;
 4     int[] res = new int[n];
 5     res[0] = 1;
 6     for(int i=0;i<m;i++)
 7     {
 8         for(int j=1;j<n;j++)
 9         {
10            res[j] += res[j-1];
11         }
12     }
13     return res[n-1];
14 }

一维DP方法2：

 1 public class Solution {
 2     public int uniquePaths(int m, int n) {
 3         if (m == 0 || n == 0) return 0;
 4         int[] res = new int[n];
 5         for (int k=0; k<n; k++) {
 6             res[k] = 1;
 7         }
 8         for (int i=1; i<m; i++) {
 9             for (int j=1; j<n; j++) {
10                 res[j] = res[j-1] + res[j];
11             }
12         }
13         return res[n-1];
14     }
15 }

 

转载于:https://www.cnblogs.com/EdwardLiu/p/3726907.html