LeetCode-in-All

62. Unique Paths

Medium

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:

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:

Solution

#include <vector>

class Solution {
public:
    int uniquePaths(int m, int n) {
        std::vector<std::vector<int>> dp(m, std::vector<int>(n, 0));
        
        // Initialize the first column to 1
        for (int i = 0; i < m; ++i) {
            dp[i][0] = 1;
        }
        
        // Initialize the first row to 1
        for (int j = 0; j < n; ++j) {
            dp[0][j] = 1;
        }
        
        // Fill the rest of the dp array
        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];
    }
};