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