最大兼容性评分和

/*
题目思路：
利用Java Stream API来处理数据流，计算学生和导师之间的兼容性评分。通过构建掩码和递归函数来跟踪最佳分配和评分。
*/

import java.util.stream.IntStream;

public class Solution {
    public int maxCompatibilitySum(int[][] students, int[][] mentors) {
        return maxCompatibilitySumHelper(students, mentors, 0, 0, new int[students.length][1 << students.length]);
    }

    private int maxCompatibilitySumHelper(int[][] students, int[][] mentors, int studentIdx, int mask, int[][] dp) {
        if (studentIdx == students.length) return 0;
        if (dp[studentIdx][mask] != 0) return dp[studentIdx][mask];

        dp[studentIdx][mask] = IntStream.range(0, mentors.length)
            .filter(j -> (mask & (1 << j)) == 0)
            .map(j -> {
                int score = (int) IntStream.range(0, students[studentIdx].length)
                    .filter(k -> students[studentIdx][k] == mentors[j][k])
                    .count();
                return score + maxCompatibilitySumHelper(students, mentors, studentIdx + 1, mask | (1 << j), dp);
            }).max().orElse(0);
        return dp[studentIdx][mask];
    }
}