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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Analysis:

This is a DP problem. We use 1D array to store the state.

Solution:

 1 public class Solution {
 2     public int uniquePaths(int m, int n) {
 3         if (m==0 || n==0) return 0;
 4   
 5         int[] path = new int[n];
 6         Arrays.fill(path,1);
 7 
 8         for (int i=1;i<m;i++){
 9             path[0] = 1;
10             for (int j=1;j<n;j++)
11                 path[j] = path[j] + path[j-1];
12         }
13 
14         return path[n-1];        
15         
16     }
17 }

Leetcode-Unique Paths

原文：http://www.cnblogs.com/lishiblog/p/4102789.html