#1733

Medium

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Minimum Number of People to Teach

Minimize the number of users to teach a language that ensures all friends can communicate in a social network.

Problem Statement

In a social network of m users, users can communicate if they share a common language. You are given an integer n, an array of languages, and a list of friendships. Each friendship is represented as a pair of users who need a common language to communicate. Your task is to determine the minimum number of users that need to be taught a new language to ensure all friendships can communicate.

The friendships and languages are provided in such a way that each user speaks one or more languages, and the goal is to find the fewest number of users to teach a new language. You can choose one language to teach, and teaching it to a minimal number of users will ensure all connected users can communicate with each other.

Examples

Example 1

Input: n = 2, languages = [[1],[2],[1,2]], friendships = [[1,2],[1,3],[2,3]]

Output: 1

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

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 <= ui < vi <= languages.length
1 <= friendships.length <= 500
All tuples (ui, vi) are unique
languages[i] contains only unique values

Solution Approach

Brute Force Method

A straightforward solution involves scanning each language, checking how many users need to be taught it to connect all friends. This approach is based on brute force but guarantees accuracy by evaluating all possible language choices.

Greedy Language Selection

Instead of evaluating all languages, prioritize languages that connect the most number of users initially. This greedy approach reduces the number of users you need to teach by focusing on the most interconnected groups first.

Hash Table Lookup for Efficiency

Use hash tables to track which users speak each language. This allows efficient lookups when checking how to minimize the number of users that need to be taught, cutting down the time complexity of the brute force approach.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity varies depending on the approach, but for brute force, it is O(n * m) where n is the number of users and m is the number of languages. Using hash tables can optimize the lookup time, improving the efficiency to O(m * log n) for selecting the best language.

What Interviewers Usually Probe

Candidates should be able to identify the need for efficient lookups, especially with hash tables.
A good candidate will propose either the brute force or greedy approach and discuss trade-offs.
Look for understanding of greedy algorithms and optimization strategies when candidates discuss minimizing the number of users.

Common Pitfalls or Variants

Common pitfalls

Focusing only on one approach without considering the trade-offs in terms of time complexity.
Neglecting to handle users who already speak a common language, leading to over-counting the number of users to teach.
Forgetting to account for edge cases, such as users who are isolated in the network and don't need any teaching.

Follow-up variants

Extend the problem to handle larger networks, requiring more advanced algorithms to scale efficiently.
Consider constraints where users can speak multiple languages and need to be taught multiple languages.
Add additional constraints, such as fixed language choices or a limited number of languages that can be taught.

FAQ

How can I optimize my solution for the Minimum Number of People to Teach problem?

Optimize by combining greedy strategies with hash table lookups for efficient language selection.

What is the best way to solve the Minimum Number of People to Teach problem?

A brute force approach works, but leveraging greedy algorithms and hash tables can significantly improve efficiency.

What is the time complexity of solving the Minimum Number of People to Teach problem?

The time complexity is typically O(n * m) for brute force, but using hash tables can reduce it to O(m * log n).

What strategies can I use to minimize the number of people to teach in the network?

Use a greedy approach to teach languages that connect the most users initially, then refine with hash table lookups.

How does GhostInterview help with the Minimum Number of People to Teach problem?

GhostInterview offers guidance on solving this problem using optimal strategies, making sure you address all aspects of the algorithm.

terminal

Solution

Solution 1: Simulation + Statistics

For each friendship, if the sets of languages known by the two people do not intersect, we need to teach one language so that they can communicate. We add these people to a hash set $s$.

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class Solution:
    def minimumTeachings(
        self, n: int, languages: List[List[int]], friendships: List[List[int]]
    ) -> int:
        def check(u: int, v: int) -> bool:
            for x in languages[u - 1]:
                for y in languages[v - 1]:
                    if x == y:
                        return True
            return False

        s = set()
        for u, v in friendships:
            if not check(u, v):
                s.add(u)
                s.add(v)
        cnt = Counter()
        for u in s:
            for l in languages[u - 1]:
                cnt[l] += 1
        return len(s) - max(cnt.values(), default=0)

Continue Practicing

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