Maximum Compatibility Score Sum — LeetCode 1947 Python Solution

The problem

There is a survey that consists of n questions where each question's answer is either 0 (no) or 1 (yes). The survey was given to m students numbered from 0 to m - 1 and m mentors numbered from 0 to m - 1.

Example

Input

students = [[1,1,0],[1,0,1],[0,0,1]], mentors = [[1,0,0],[0,0,1],[1,1,0]]

Output

8

Explanation

We assign students to mentors in the following way:

Python solution

class Solution:
    def maxCompatibilitySum(
        self, students: List[List[int]], mentors: List[List[int]]
    ) -> int:
        def dfs(i: int, s: int):
            if i >= m:
                nonlocal ans
                ans = max(ans, s)
                return
            for j in range(m):
                if not vis[j]:
                    vis[j] = True
                    dfs(i + 1, s + g[i][j])
                    vis[j] = False

        ans = 0
        m = len(students)
        vis = [False] * m
        g = [[0] * m for _ in range(m)]
        for i, x in enumerate(students):
            for j, y in enumerate(mentors):
                g[i][j] = sum(a == b for a, b in zip(x, y))
        dfs(0, 0)
        return ans

Complexity

Pattern: Backtracking

Build candidates one choice at a time and abandon a branch the moment it cannot work. LeetCode 1947. Maximum Compatibility Score Sum is filed here because LeetCode tags it Backtracking, which is the vocabulary this hub collects.

The backtracking guide has the Python template for the pattern and the 105 LeetCode problems that use it.

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