What is the time complexity of Intersection of Two Arrays?

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

What is the space complexity of Intersection of Two Arrays?

The space complexity is O(m+n).

What data structures are used to solve Intersection of Two Arrays?

This problem uses Array, Hash Table, Two Pointers, Binary Search, Sorting. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Intersection of Two Arrays?

Insight 1: Using sets (or hash tables) is crucial for efficiently finding the intersection because sets inherently store only unique elements and provide fast lookups (O(1) on average). Insight 2: The optimal approach involves iterating through one array and checking for the presence of each element in a set created from the other array. This avoids nested loops, which would lead to a less efficient solution.

Which companies ask LeetCode 349. Intersection of Two Arrays in interviews?

This problem is frequently asked at CVENT, Criteo, IBM, J.P. Morgan, LinkedIn and 7 more companies.

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Intersection of Two Arrays - LeetCode 349 Solution

Q: How to solve Intersection of Two Arrays?

The provided solutions use sets (or hash sets/unordered sets) to efficiently find the intersection. First, one of the input arrays is converted into a set. This set is then iterated through and checked for the presence of every number in the second array. If a number from the second array is found in the first set it’s added to the result set. Finally, the result set is converted back into an array for output.

Intersection of Two Arrays - Complete Solution Guide

Intersection of Two Arrays is LeetCode problem 349, 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 two integer arrays nums1 and nums2 , return an array of their intersection . Each element in the result must be unique and you may return the result in any order . Example 1: Input: nums1 = [1,2,2,1], nums2 = [2,2] Output: [2] Example 2: Input: nums1 = [4,9,5], nums2 = [9,4,9,8,4] Output: [9,4] Explanation: [4,9] is also accepted. Constraints: 1 <= nums1.length, nums2.length <= 1000 0 <= nums1[i], nums2[i] <= 1000

Detailed Explanation

The problem asks you to find the intersection of two integer arrays, `nums1` and `nums2`. The intersection is the set of elements that are present in both arrays. The output should contain only unique elements, and the order of elements doesn't matter. The input arrays can contain duplicate elements, but the output must not. There are constraints on the size of the input arrays (maximum 1000 elements) and the range of values within the arrays (0 to 1000 inclusive).

Solution Approach

The provided solutions use sets (or hash sets/unordered sets) to efficiently find the intersection. First, one of the input arrays is converted into a set. This set is then iterated through and checked for the presence of every number in the second array. If a number from the second array is found in the first set it’s added to the result set. Finally, the result set is converted back into an array for output.

Step-by-Step Algorithm

Step 1: Create a set from one of the input arrays (e.g., `nums1`). This eliminates duplicate elements.
Step 2: Iterate through the second input array (e.g., `nums2`).
Step 3: For each element in `nums2`, check if it exists in the set created from `nums1`.
Step 4: If the element exists in the set, add it to a new set (or other structure) to store the intersection.
Step 5: Convert the resulting set of unique intersecting elements into an array and return it.

Key Insights

Insight 1: Using sets (or hash tables) is crucial for efficiently finding the intersection because sets inherently store only unique elements and provide fast lookups (O(1) on average).
Insight 2: The optimal approach involves iterating through one array and checking for the presence of each element in a set created from the other array. This avoids nested loops, which would lead to a less efficient solution.
Insight 3: The provided Python solution leverages the built-in set operations for a concise and efficient solution, but understanding the underlying set operations is important for adapting this to other languages.

Complexity Analysis

Time Complexity: O(m+n)

Space Complexity: O(m+n)

Topics

This problem involves: Array, Hash Table, Two Pointers, Binary Search, Sorting.

Companies

Asked at: CVENT, Criteo, IBM, J.P. Morgan, LinkedIn, MongoDB, Nvidia, PayPal, Two Sigma, Wix, Yandex, tcs.

Intersection of Two Arrays | LeetCode 349

Easy

Array Hash Table Two Pointers Binary Search Sorting

Time: O(m+n)Space: O(m+n)

Solution Code

Available in:

class Solution {
    public int[] intersection(int[] nums1, int[] nums2) {
        Set<Integer> set1 = new HashSet<>();
        for (int num : nums1) {
            set1.add(num);
        }
        Set<Integer> set2 = new HashSet<>();
        for (int num : nums2) {
            if (set1.contains(num)) {
                set2.add(num);
            }
        }
        int[] result = new int[set2.size()];
        int i = 0;
        for (int num : set2) {
            result[i++] = num;
        }
        return result;
    }
}

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Problem Info

Description

Problem 349: Intersection of Two Arrays - Detailed explanation and solution approaches.

Topics

Array Hash Table Two Pointers Binary Search Sorting

Companies

CVENTCriteoIBMJ.P. MorganLinkedInMongoDBNvidiaPayPal

Stats

Difficulty:Easy

Languages:4

Companies:12

Problem #:349

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: Create a set from one of the input arrays (e.g., `nums1`). This eliminates duplicate elements.
2
Step 2: Iterate through the second input array (e.g., `nums2`).
3
Step 3: For each element in `nums2`, check if it exists in the set created from `nums1`.
4
Step 4: If the element exists in the set, add it to a new set (or other structure) to store the intersection.
5
Step 5: Convert the resulting set of unique intersecting elements into an array 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(m+n)

💾

Space Complexity

O(m+n)

📝

Why?

Creating a set from an array takes O(n) time, where n is the length of the array. Iterating through the second array and checking for membership in the set takes O(m) time, where m is the length of the second array. The space complexity is dominated by the size of the smaller set, which in the worst case could be O(min(m,n)) if all elements are unique and one array is much shorter than the other.

📖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

Nested Loops

Use nested loops to iterate through each array and compare elements. Track seen elements to avoid duplicates.

Time: O(m*n)Space: O(min(m,n))

Trade-offs: Less efficient than the set-based approach, especially for large arrays. Simpler to understand for beginners but less performant.

Sorting and Two Pointers

Sort both arrays and use two pointers to efficiently find common elements.

Time: O(m log m + n log n)Space: O(1) or O(m+n) (depending on sorting algorithm)

Trade-offs: Can be efficient if sorting is fast (like in-place merge sort). Less efficient in space for the larger arrays (O(m+n) using merge sort).

✨

Key Insights

1Insight 1: Using sets (or hash tables) is crucial for efficiently finding the intersection because sets inherently store only unique elements and provide fast lookups (O(1) on average).
2Insight 2: The optimal approach involves iterating through one array and checking for the presence of each element in a set created from the other array. This avoids nested loops, which would lead to a less efficient solution.
3Insight 3: The provided Python solution leverages the built-in set operations for a concise and efficient solution, but understanding the underlying set operations is important for adapting this to other languages.

📚

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!

Two Pointers

Using two indices to traverse data from different positions simultaneously.

Binary Search

Halving the search space each step. Like finding a word in a dictionary!

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: Empty input arrays. The solutions correctly handle this by returning an empty array.
Edge case 2: Arrays with all duplicate elements. The solutions correctly handle this by only returning unique elements.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling duplicate elements correctly. Failing to use a set (or similar data structure) can lead to duplicates in the output.

✗Common mistake 2: Inefficiently searching for elements. Nested loops without optimization (like using a set for lookups) will result in a time complexity of O(m*n), which is significantly less efficient.

✅

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: Database queries. Finding common records between two datasets is a frequent task in database management.

🏦Real-world scenario 2: Recommender systems. Identifying users with similar preferences by comparing their lists of liked items (movies, products, etc.).

💡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: November 17, 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

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

@TechLeadJul 14

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

@DevExpert92Jul 7

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJun 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.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

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 "Intersection of Two Arrays"?

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.

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