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?

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];
    }
}
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