Minimum Number of People to Teach
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
nlanguages numbered1throughn. languages[i]is the set of languages thei^thuser knows.friendships[i] = [u_i, v_i]denotes a friendship between the usersu_iandv_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 does not 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
1You 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
2Teach 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
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