Introduction

In this blog post, we will explore how to solve the LeetCode problem "1947" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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.

Explanation

Here's the breakdown of the solution:

• Calculate Compatibility Scores: Precompute the compatibility score for every possible student-mentor pair and store it in a matrix. This avoids redundant calculations.
• Optimal Assignment using Permutations: Since the constraints state m <= 8, we can efficiently generate all possible permutations of mentor assignments to students.

• Maximize Sum: Iterate through each permutation, calculate the total compatibility score for that assignment, and keep track of the maximum score found so far.

• Runtime Complexity: O(m! m n), where m is the number of students/mentors and n is the number of questions. O(m!) to generate permutations, O(m * n) to calculate the compatibility scores for each permutation.

• Storage Complexity: O(m^2) for the compatibility score matrix.

Code

    from itertools import permutations

def maxCompatibilitySum(students, mentors):
    """
    Calculates the maximum compatibility score sum for student-mentor pairings.

    Args:
        students: A 2D list of student answers.
        mentors: A 2D list of mentor answers.

    Returns:
        The maximum compatibility score sum.
    """

    m = len(students)
    n = len(students[0])

    # Calculate compatibility scores for all student-mentor pairs
    compatibility_scores = [[0] * m for _ in range(m)]
    for i in range(m):
        for j in range(m):
            score = 0
            for k in range(n):
                if students[i][k] == mentors[j][k]:
                    score += 1
            compatibility_scores[i][j] = score

    # Find the optimal assignment using permutations
    max_score = 0
    for permutation in permutations(range(m)):
        current_score = 0
        for i in range(m):
            current_score += compatibility_scores[i][permutation[i]]
        max_score = max(max_score, current_score)

    return max_score