Unique Paths

Problem Statement - link #

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?

Examples #

Example 1:

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

Example 2:

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:

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

Example 4:

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.

Solutions #

class Solution {
public:
    int uniquePaths(int m, int n) {
        
        vector<vector<int>> dp(m,vector<int>(n,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-1][n-1];
    }
};