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1947. Maximum Compatibility Score Sum

Difficulty Topics

Description

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. The answers of the students are represented by a 2D integer array students where students[i] is an integer array that contains the answers of the ith student (0-indexed). The answers of the mentors are represented by a 2D integer array mentors where mentors[j] is an integer array that contains the answers of the jth mentor (0-indexed).

Each student will be assigned to one mentor, and each mentor will have one student assigned to them. The compatibility score of a student-mentor pair is the number of answers that are the same for both the student and the mentor.

  • For example, if the student's answers were [1, 0, 1] and the mentor's answers were [0, 0, 1], then their compatibility score is 2 because only the second and the third answers are the same.

You are tasked with finding the optimal student-mentor pairings to maximize the sum of the compatibility scores.

Given students and mentors, return the maximum compatibility score sum that can be achieved.

 

Example 1:

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:
- student 0 to mentor 2 with a compatibility score of 3.
- student 1 to mentor 0 with a compatibility score of 2.
- student 2 to mentor 1 with a compatibility score of 3.
The compatibility score sum is 3 + 2 + 3 = 8.

Example 2:

Input: students = [[0,0],[0,0],[0,0]], mentors = [[1,1],[1,1],[1,1]]
Output: 0
Explanation: The compatibility score of any student-mentor pair is 0.

 

Constraints:

  • m == students.length == mentors.length
  • n == students[i].length == mentors[j].length
  • 1 <= m, n <= 8
  • students[i][k] is either 0 or 1.
  • mentors[j][k] is either 0 or 1.

Solution

maximum-compatibility-score-sum.py
class Solution:
    def maxCompatibilitySum(self, students: List[List[int]], mentors: List[List[int]]) -> int:
        n = len(students)

        def dfs(i, used, score):
            if i == n: return score

            res = float(-inf)

            for j, mentor in enumerate(mentors):
                if j in used: continue

                ss = sum(int(a == b) for a, b in zip(students[i], mentor))
                used.add(j)
                score += ss

                res = max(res, dfs(i + 1, used, score))

                used.remove(j)
                score -= ss

            return res

        return dfs(0, set(), 0)