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 }