Formatted question description: https://leetcode.ca/all/1733.html
1733. Minimum Number of People to Teach
Level
Medium
Description
On a social network consisting of m
users and some friendships between users, two users can communicate with each other if they know a common language.
You are given an integer n
, an array languages
, and an array friendships
where:
- There are
n
languages numbered1
throughn
, languages[i]
is the set of languages thei-th
user knows, andfriendships[i] = [u_i, v_i]
denotes a friendship between the usersu_i
andv_i
.
You can choose one language and teach it to some users so that all friends can communicate with each other. Return the minimum number of users you need to teach.
Note that friendships are not transitive, meaning if x
is a friend of y
and y
is a friend of z
, this doesn’t guarantee that x
is a friend of z
.
Example 1:
Input: n = 2, languages = [[1],[2],[1,2]], friendships = [[1,2],[1,3],[2,3]]
Output: 1
Explanation: You can either teach user 1 the second language or user 2 the first language.
Example 2:
Input: n = 3, languages = [[2],[1,3],[1,2],[3]], friendships = [[1,4],[1,2],[3,4],[2,3]]
Output: 2
Explanation: Teach the third language to users 1 and 3, yielding two users to teach.
Constraints:
2 <= n <= 500
languages.length == m
1 <= m <= 500
1 <= languages[i].length <= n
1 <= languages[i][j] <= n
1 <= u_i < v_i <= languages.length
1 <= friendships.length <= 500
- All tuples
(u_i, v_i)
are unique languages[i]
contains only unique values
Solution
First, obtain each user’s languages. Then for each friendship, check whether the friends can communicate with each other. Only consider the friends that cannot communicate with each other. For such friendships, loop over all languages and find the language such that the minimum number of people need to be taught.
class Solution {
public int minimumTeachings(int n, int[][] languages, int[][] friendships) {
Map<Integer, Set<Integer>> languagesMap = new HashMap<Integer, Set<Integer>>();
int m = languages.length;
for (int i = 0; i < m; i++) {
int index = i + 1;
int[] language = languages[i];
Set<Integer> set = new HashSet<Integer>();
for (int num : language)
set.add(num);
languagesMap.put(index, set);
}
List<int[]> friendshipsList = new ArrayList<int[]>();
int pairs = friendships.length;
for (int i = 0; i < pairs; i++) {
int[] friendship = friendships[i];
int user1 = friendship[0], user2 = friendship[1];
Set<Integer> set1 = new HashSet<Integer>(languagesMap.getOrDefault(user1, new HashSet<Integer>()));
Set<Integer> set2 = new HashSet<Integer>(languagesMap.getOrDefault(user2, new HashSet<Integer>()));
set1.retainAll(set2);
if (set1.size() == 0)
friendshipsList.add(friendship);
}
Set<Integer> candidates = new HashSet<Integer>();
Set<Integer> usersSet = new HashSet<Integer>();
for (int[] friendship : friendshipsList) {
int user1 = friendship[0], user2 = friendship[1];
Set<Integer> set1 = languagesMap.getOrDefault(user1, new HashSet<Integer>());
Set<Integer> set2 = languagesMap.getOrDefault(user2, new HashSet<Integer>());
candidates.addAll(set1);
candidates.addAll(set2);
usersSet.add(user1);
usersSet.add(user2);
}
if (candidates.isEmpty())
return 0;
int minTeach = Integer.MAX_VALUE;
for (int candidate : candidates) {
int teach = 0;
for (int user : usersSet) {
if (!languagesMap.getOrDefault(user, new HashSet<Integer>()).contains(candidate))
teach++;
}
minTeach = Math.min(minTeach, teach);
}
return minTeach;
}
}