Leetcode 62: 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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

 

public class Solution {
    public int UniquePaths(int m, int n) {
        var dp = new int[m, n];
        
        for (int i = m - 1; i >= 0; i--)
        {
            for (int j = n - 1; j >= 0; j--)
            {
                if (i == m - 1 || j == n - 1)
                {
                    dp[i, j] = 1;
                }
                else
                {
                    dp[i, j] = dp[i + 1, j] + dp[i, j + 1];
                }
            }
        }
        
        return dp[0, 0];
    }
}