62. Unique Paths

Problem Statement

Medium

There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.

Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The test cases are generated so that the answer will be less than or equal to 2 * 10⁹.

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

Constraints:

1 <= m, n <= 100

C++

Source file

class Solution {
public:
    #define mp make_pair
    map <pair<int, int>, int> memo;
    int uniquePaths(int m, int n) {
        if(!m || !n) return 0;
        if (m==1 && n==1){
            return 1;
        }
        if(!memo[mp(m-1, n)])
            memo[mp(m-1, n)] = uniquePaths(m-1, n);
        if(!memo[mp(m, n-1)])
            memo[mp(m, n-1)] = uniquePaths(m, n-1);
        return memo[mp(m-1, n)] + memo[mp(m, n-1)];
    }
};