What is the time complexity of Two Out of Three?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Two Out of Three?

This problem uses Array, Hash Table, Bit Manipulation. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Two Out of Three?

Insight 1: Using sets to efficiently check for the presence of a number in an array. Sets provide O(1) lookup time, improving the overall efficiency compared to linear search in arrays. Insight 2: Leveraging the properties of sets to automatically handle duplicates within each input array. Sets only store unique elements.

Which companies ask LeetCode 2032. Two Out of Three in interviews?

This problem is frequently asked at Booking.com, Info Edge.

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Two Out of Three - LeetCode 2032 Solution

Two Out of Three - Complete Solution Guide

Two Out of Three is LeetCode problem 2032, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given three integer arrays nums1 , nums2 , and nums3 , return a distinct array containing all the values that are present in at least two out of the three arrays. You may return the values in any order . Example 1: Input: nums1 = [1,1,3,2], nums2 = [2,3], nums3 = [3] Output: [3,2] Explanation: The values that are present in at least two arrays are: - 3, in all three arrays. - 2, in nums1 and nums2. Example 2: Input: nums1 = [3,1], nums2 = [2,3], nums3 = [1,2] Output: [2,3,1] Explanation: The val

Detailed Explanation

The problem asks you to find all the unique numbers that appear in at least two out of three input integer arrays. The input consists of three arrays (`nums1`, `nums2`, `nums3`), and the output is a distinct array containing the numbers that meet the criteria. The order of numbers in the output array doesn't matter. The numbers in the input arrays are all positive integers within a specified range (1 to 100).

Solution Approach

The provided solutions use sets to efficiently solve the problem. Each input array is converted into a set. Then, the code iterates through each set and checks if elements of that set are present in at least one of the other sets. If a number is found in at least two sets, it's added to the result set. Finally, the result set is converted to a list (or vector) and returned.

Step-by-Step Algorithm

Step 1: Convert each input array (`nums1`, `nums2`, `nums3`) into a set to eliminate duplicate numbers and enable efficient lookups.
Step 2: Iterate through the elements of the first set (`s1`). For each element, check if it exists in either the second or third set. If it does, add it to a result set.
Step 3: Repeat Step 2 for the elements of the second set (`s2`).
Step 4: Repeat Step 2 for the elements of the third set (`s3`).
Step 5: Convert the result set into a list (or array or vector) and return it.

Key Insights

Insight 1: Using sets to efficiently check for the presence of a number in an array. Sets provide O(1) lookup time, improving the overall efficiency compared to linear search in arrays.
Insight 2: Leveraging the properties of sets to automatically handle duplicates within each input array. Sets only store unique elements.
Insight 3: The constraint that numbers are within the range 1-100 allows for alternative space-optimized solutions using a boolean array or a bit vector.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table, Bit Manipulation.

Companies

Asked at: Booking.com, Info Edge.

Two Out of Three | LeetCode 2032

Easy

Array Hash Table Bit Manipulation

Time: O(n)Space: O(n)

Solution Code

Available in:

import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Set;

class Solution {
    public List<Integer> twoOutOfThree(int[] nums1, int[] nums2, int[] nums3) {
        Set<Integer> set1 = new HashSet<>();
        Set<Integer> set2 = new HashSet<>();
        Set<Integer> set3 = new HashSet<>();

        for (int num : nums1) {
            set1.add(num);
        }
        for (int num : nums2) {
            set2.add(num);
        }
        for (int num : nums3) {
            set3.add(num);
        }

        Set<Integer> result = new HashSet<>();

        for (int num : set1) {
            if (set2.contains(num) || set3.contains(num)) {
                result.add(num);
            }
        }

        for (int num : set2) {
            if (set1.contains(num) || set3.contains(num)) {
                result.add(num);
            }
        }

        List<Integer> list = new ArrayList<>(result);
        return list;
    }
}

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Problem Info

Description

Problem 2032: Two Out of Three - Detailed explanation and solution approaches.

Topics

Array Hash Table Bit Manipulation

Companies

Booking.comInfo Edge

Stats

Difficulty:Easy

Languages:4

Companies:2

Problem #:2032

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

5 steps

1
Step 1: Convert each input array (`nums1`, `nums2`, `nums3`) into a set to eliminate duplicate numbers and enable efficient lookups.
2
Step 2: Iterate through the elements of the first set (`s1`). For each element, check if it exists in either the second or third set. If it does, add it to a result set.
3
Step 3: Repeat Step 2 for the elements of the second set (`s2`).
4
Step 4: Repeat Step 2 for the elements of the third set (`s3`).
5
Step 5: Convert the result set into a list (or array or vector) and return it.

💡

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(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is O(n) because converting arrays to sets takes O(n) time in the worst case, and iterating through the sets and checking for membership also takes O(n) time, where n is the total number of unique elements across all three input arrays. The space complexity is O(n) because the sets and the result set can store up to n elements in the worst case.

📖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

Counting occurrences using an array

Create a count array of size 101 (to accommodate numbers from 1 to 100). Iterate through each input array and increment the count for each number. Then, iterate through the count array and add numbers with a count of 2 or more to the result list.

Time: O(n)Space: O(1)

Trade-offs: This approach is faster in terms of space complexity because it uses constant space regardless of the size of the input arrays, but the space is fixed. It is only applicable because the input numbers are constrained to a small range (1-100).

Bit manipulation

Represent the presence of each number (1-100) using bits in three integers. Then perform bitwise operations to efficiently find numbers present in at least two integers.

Time: O(n)Space: O(1)

Trade-offs: This approach is very space-efficient as it utilizes only three integers. However, it's less intuitive than set-based solutions and may be harder to understand and maintain.

✨

Key Insights

1Insight 1: Using sets to efficiently check for the presence of a number in an array. Sets provide O(1) lookup time, improving the overall efficiency compared to linear search in arrays.
2Insight 2: Leveraging the properties of sets to automatically handle duplicates within each input array. Sets only store unique elements.
3Insight 3: The constraint that numbers are within the range 1-100 allows for alternative space-optimized solutions using a boolean array or a bit vector.

📚

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!

Edge Cases

Edge case 1: One or more input arrays are empty. The solution correctly handles this; the result will be an empty list if no numbers appear in at least two arrays.
Edge case 2: All three arrays contain the same numbers. The solution will return a list containing these common numbers (duplicates will be removed thanks to the set).

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle duplicate numbers within each array. Failing to use sets (or equivalent mechanisms) leads to incorrect results.

✗Common mistake 2: Not checking all combinations of pairs of arrays. Only checking one array against the others would result in an incomplete solution.

✅

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: Identifying common features or properties among different datasets. For example, finding common genes expressed in different tissue samples.

🏦Real-world scenario 2: Network analysis – identifying nodes (numbers) that connect to at least two other nodes within a graph (represented by the three arrays).

💡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

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ 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: July 23, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 13

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

@CodeNinjaJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Two Out of Three"?

For this easy-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?