Formatted question description: https://leetcode.ca/all/1947.html
1947. Maximum Compatibility Score Sum
Level
Medium
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 i-th
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 j-th
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 either0
or1
.mentors[j][k]
is either0
or1
.
Solution
Since both m
and n
do not exceed 8, each row in students
and mentors
can be considered as a binary representation and can be converted into an integer that does not exceed 255. After converting into integers, calculate the permutations of the m
rows. For each permutation, calculate the compatibility score sum using bitwise operation, and return the maximum compatibility score sum.
class Solution {
public int maxCompatibilitySum(int[][] students, int[][] mentors) {
int m = students.length, n = students[0].length;
int[] studentsNums = new int[m];
int[] mentorsNums = new int[m];
for (int i = 0; i < m; i++) {
studentsNums[i] = convertToNum(students[i]);
mentorsNums[i] = convertToNum(mentors[i]);
}
int[] nums = new int[m];
for (int i = 0; i < m; i++)
nums[i] = i;
int maxSum = 0;
List<List<Integer>> permutations = permute(nums);
for (List<Integer> permutation : permutations) {
int sum = 0;
for (int i = 0; i < m; i++)
sum += n - Integer.bitCount(studentsNums[i] ^ mentorsNums[permutation.get(i)]);
maxSum = Math.max(maxSum, sum);
}
return maxSum;
}
public int convertToNum(int[] arr) {
int num = 0;
int length = arr.length;
for (int i = 0; i < length; i++)
num += arr[i] << i;
return num;
}
public List<List<Integer>> permute(int[] nums) {
int length = nums.length;
List<List<Integer>> permutations = new ArrayList<List<Integer>>();
List<Integer> permutation = new ArrayList<Integer>();
for (int i = 0; i < length; i++)
permutation.add(nums[i]);
backtrack(length, permutations, 0, permutation);
return permutations;
}
public void backtrack(int length, List<List<Integer>> permutations, int start, List<Integer> permutation) {
if (start == length)
permutations.add(new ArrayList<Integer>(permutation));
else {
for (int i = start; i < length; i++) {
Collections.swap(permutation, start, i);
backtrack(length, permutations, start + 1, permutation);
Collections.swap(permutation, start, i);
}
}
}
}