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

The optimal solution has a time complexity of O(M + K + L).

What is the space complexity of Minimum Number of People to Teach?

The space complexity is O(M + N).

What data structures are used to solve Minimum Number of People to Teach?

This problem uses Array, Hash Table, Greedy. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Minimum Number of People to Teach?

Insight 1: The core idea is to identify pairs of friends who cannot communicate with each other initially (disjoint language sets). Insight 2: Teaching a single language to some users is equivalent to finding the language that would 'cover' the most number of uncommunicative users.

Which companies ask LeetCode 1733. Minimum Number of People to Teach in interviews?

This problem is frequently asked at Duolingo.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Minimum Number of People to Teach - LeetCode 1733 Solution

Minimum Number of People to Teach - Complete Solution Guide

Minimum Number of People to Teach is LeetCode problem 1733, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

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

Detailed Explanation

The problem describes a social network where users can communicate if they share a common language. You're given a number of languages, a list of languages each user knows, and a list of friendships between users. The goal is to find the minimum number of users you need to teach a single language to, so that all friends can communicate. Friendships are *not* transitive, meaning only direct friends need to be able to communicate.

Solution Approach

The solution first identifies pairs of friends who cannot communicate. Then, it iterates through the identified uncommunicative users, counting how many of them know each language. Finally, it finds the language known by the most uncommunicative users and calculates the number of users that *would* still need to be taught after teaching everyone this most common language.

Step-by-Step Algorithm

Step 1: Create a list of sets, where each set represents the languages known by a user. This allows for efficient disjoint checks.
Step 2: Iterate through the friendship list and check if each pair of friends can communicate (i.e., their language sets are not disjoint). If they cannot, add both users to a set of 'uncommunicative users'.
Step 3: If there are no uncommunicative users, return 0, as no teaching is needed.
Step 4: Create a language count array to store the frequency of each language among the uncommunicative users.
Step 5: Iterate through the uncommunicative users and, for each user, increment the count of each language they know in the language count array.
Step 6: Find the language with the maximum count in the language count array. This represents the language that, if taught to the uncommunicative users who *don't* already know it, would minimize the total number of users taught.
Step 7: Calculate the minimum number of teachings needed by subtracting the maximum language count from the total number of uncommunicative users.

Key Insights

Insight 1: The core idea is to identify pairs of friends who cannot communicate with each other initially (disjoint language sets).
Insight 2: Teaching a single language to some users is equivalent to finding the language that would 'cover' the most number of uncommunicative users.
Insight 3: Creating sets to store languages for each user allows efficient disjoint checks.

Complexity Analysis

Time Complexity: O(M + K + L)

Space Complexity: O(M + N)

Topics

This problem involves: Array, Hash Table, Greedy.

Companies

Asked at: Duolingo.

Minimum Number of People to Teach | LeetCode 1733

Medium

Array Hash Table Greedy

Time: O(M + K + L)Space: O(M + N)

Solution Code

Available in:

import java.util.*;

class Solution {
    public int minimumTeachings(int n, int[][] languages, int[][] friendships) {
        List<Set<Integer>> languageSets = new ArrayList<>();
        for (int[] language : languages) {
            Set<Integer> languageSet = new HashSet<>();
            for (int lang : language) {
                languageSet.add(lang);
            }
            languageSets.add(languageSet);
        }

        Set<Integer> uncommunicativeUsers = new HashSet<>();
        for (int[] friendship : friendships) {
            int u = friendship[0];
            int v = friendship[1];
            int uIdx = u - 1;
            int vIdx = v - 1;
            if (Collections.disjoint(languageSets.get(uIdx), languageSets.get(vIdx))) {
                uncommunicativeUsers.add(uIdx);
                uncommunicativeUsers.add(vIdx);
            }
        }

        if (uncommunicativeUsers.isEmpty()) {
            return 0;
        }

        int[] langCounts = new int[n + 1];
        for (int userIdx : uncommunicativeUsers) {
            for (int lang : languageSets.get(userIdx)) {
                langCounts[lang]++;
            }
        }

        int maxCoverage = 0;
        if (langCounts.length > 1) {
            for(int i = 0; i < langCounts.length; i++){
                maxCoverage = Math.max(maxCoverage, langCounts[i]);
            }
        }

        return uncommunicativeUsers.size() - maxCoverage;
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 1733: Minimum Number of People to Teach - Detailed explanation and solution approaches.

Topics

Array Hash Table Greedy

Companies

Duolingo

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:1733

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

7 steps

1
Step 1: Create a list of sets, where each set represents the languages known by a user. This allows for efficient disjoint checks.
2
Step 2: Iterate through the friendship list and check if each pair of friends can communicate (i.e., their language sets are not disjoint). If they cannot, add both users to a set of 'uncommunicative users'.
3
Step 3: If there are no uncommunicative users, return 0, as no teaching is needed.
4
Step 4: Create a language count array to store the frequency of each language among the uncommunicative users.
5
Step 5: Iterate through the uncommunicative users and, for each user, increment the count of each language they know in the language count array.
6
Step 6: Find the language with the maximum count in the language count array. This represents the language that, if taught to the uncommunicative users who *don't* already know it, would minimize the total number of users taught.
7
Step 7: Calculate the minimum number of teachings needed by subtracting the maximum language count from the total number of uncommunicative users.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(M + K + L)

💾

Space Complexity

O(M + N)

📝

Why?

The time complexity is determined by the dominant operations, which are iterating through the friendships, and counting the languages of uncommunicative users. The space complexity is determined by the data structures used to store the language sets, the set of uncommunicative users, and the language counts.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Graph approach using connected components

Represent the social network as a graph. Users are nodes and friendships are edges. Use connected components to find groups of users that can communicate with each other. For each connected component, find the minimum number of people to teach to allow everyone in the component to communicate. Then, sum these values across all components.

Time: O(M + K)Space: O(M + N)

Trade-offs: Potentially more complex to implement, might be useful if we wanted to find the minimum number of languages we need to teach overall to all users.

✨

Key Insights

1Insight 1: The core idea is to identify pairs of friends who cannot communicate with each other initially (disjoint language sets).
2Insight 2: Teaching a single language to some users is equivalent to finding the language that would 'cover' the most number of uncommunicative users.
3Insight 3: Creating sets to store languages for each user allows efficient disjoint checks.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Greedy Algorithm

Making the best choice at each step without looking ahead.

Edge Cases

Edge case 1: When friendships exist, but all friends can already communicate. The solution correctly returns 0 in this case because the set of uncommunicative users is empty.
Edge case 2: When the friendship list is empty. The code will also work correctly in this case as the `uncommunicative_users` set remains empty. The time and space complexity will depend on how the inputs for `languages` are structured in that case.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Failing to account for the case where all friends can already communicate, resulting in incorrect output or runtime errors.

✗Common mistake 2: Incorrectly identifying uncommunicative users due to not properly checking for common languages using sets/maps.

✗Common mistake 3: Overlooking the fact that you can only teach *one* language, and focusing on teaching the minimum number of languages in total to all the uncommunicative users, which is not the question.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Designing a training program in a company. You have teams of employees working together. You want to teach a language (e.g., a programming language or a foreign language) to the minimum number of employees so that everyone on each team can effectively communicate with each other.

🏦Real-world scenario 2: Minimizing translation costs in international collaborations. Different researchers from different countries are collaborating on a project, and you want to minimize the number of researchers who need to learn a common language to facilitate communication within teams.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: September 22, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 14

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 7

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Minimum Number of People to Teach"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether hash table techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?