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:
public class Solution {
public int uniquePaths(int m, int n) {
int[][] dp = new int[m+1][n+1];
dp[1][0] = 1;
for(int i=1; i<=m; i++){
for(int j=1; j<=n; j++){
dp[i][j] = dp[i-1][j] + dp[i][j-1];
}
}
return dp[m][n];
}
}