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 numbered`1`

through`n`

, `languages[i]`

is the set of languages the`i-th`

user knows, and`friendships[i] = [u_i, v_i]`

denotes a friendship between the users`u_i`

and`v_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;
}
}
```