[LeetCode] Unique Paths

Problem: A robot is located at the top-left corner(0, 0) of a m x n grid.

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?

Example:

Input: m = 3, n = 7
Output: 28

Input: m = 3, n = 2
Output: 3
Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

Approach: It's a simple DP problem. Just look at the implemetation to understand the approach.

Implementation in C#:

    public int UniquePaths(int m, int n)

    {

        int[,] table = new int[m, n];

        for (int i = 0; i < m; ++i)

        {

            table[i, 0] = 1;

        }

        for (int i = 0; i < n; ++i)

        {

            table[0, i] = 1;

        }

        for (int i = 1; i < m; ++i)

        {

            for (int j = 1; j < n; ++j)

            {

                table[i, j] = table[i - 1, j] + table[i, j - 1];

            }

        }

        return table[m - 1, n - 1];

    }

Complexity: O(m * n)