# Unique Paths Problem

## Description

LeetCode Problem 62.

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?

Example 1:

 1 2 Input: m = 3, n = 7 Output: 28

Example 2:

 1 2 3 4 5 6 7 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

Example 3:

 1 2 Input: m = 7, n = 3 Output: 28

Example 4:

 1 2 Input: m = 3, n = 3 Output: 6

Constraints:

• 1 <= m, n <= 100
• It’s guaranteed that the answer will be less than or equal to 2 * 10^9.

## Sample C++ Code

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