Question

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?

Solution

The key to the solution is to create 2D array to record ways.

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