What is the time complexity of Two Sum?

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

What data structures are used to solve Two Sum?

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

What are the key insights for solving Two Sum?

Insight 1: Using a hash map (dictionary in Python) allows for efficient lookups of the complement (target - num). Insight 2: The hash map stores each number and its index, enabling quick identification of the pair that sums to the target.

Which companies ask LeetCode 1. Two Sum in interviews?

This problem is frequently asked at AMD, Accenture, Accolite, Adobe, Agoda and 109 more companies.

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Two Sum - LeetCode 1 Solution

Two Sum - Complete Solution Guide

Two Sum is LeetCode problem 1, 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 an array of integers nums and an integer target , return indices of the two numbers such that they add up to target . You may assume that each input would have exactly one solution , and you may not use the same element twice. You can return the answer in any order. Example 1: Input: nums = [2,7,11,15], target = 9 Output: [0,1] Explanation: Because nums[0] + nums[1] == 9, we return [0, 1]. Example 2: Input: nums = [3,2,4], target = 6 Output: [1,2] Example 3: Input: nums = [3,3], target = 6

Detailed Explanation

The Two Sum problem asks you to find two numbers within a given array that add up to a specified target value. The input consists of an array of integers (`nums`) and the target integer (`target`). The output should be the indices (positions) of the two numbers in the array that sum to the target. You are guaranteed that there will be exactly one solution, and you cannot use the same element twice. The indices can be returned in any order.

Solution Approach

The provided solutions use a hash map (or unordered_map in C++) to solve the problem efficiently. The algorithm iterates through the input array. For each number, it calculates the complement needed to reach the target. It then checks if the complement exists as a key in the hash map. If it does, it means the complement (and hence the pair) has already been encountered, and the indices are returned. If not, the current number and its index are added to the hash map for future checks. This approach avoids redundant checks and significantly improves the performance.

Step-by-Step Algorithm

Step 1: Initialize an empty hash map (dictionary in Python).
Step 2: Iterate through the input array `nums` using a loop.
Step 3: For each number `num` in `nums`, calculate the `complement` as `target - num`.
Step 4: Check if the `complement` exists as a key in the hash map.
Step 5: If the `complement` exists, return the index of the `complement` (stored in the hash map) and the current index `i`.
Step 6: If the `complement` does not exist, add the current number `num` and its index `i` to the hash map.
Step 7: If the loop completes without finding a pair, return an empty array (or handle accordingly based on language).

Key Insights

Insight 1: Using a hash map (dictionary in Python) allows for efficient lookups of the complement (target - num).
Insight 2: The hash map stores each number and its index, enabling quick identification of the pair that sums to the target.
Insight 3: A brute-force approach (nested loops) would have O(n^2) time complexity, while the hash map approach achieves O(n) time complexity.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table.

Companies

Asked at: AMD, Accenture, Accolite, Adobe, Agoda, Airbnb, Airbus SE, Akamai, Altimetrik, Amadeus, Amazon, American Express, Apple, Atlassian, Avito, BNY Mellon, Barclays, BlackStone, Bloomberg, Bolt, Braze, ByteDance, Cadence, Capgemini, Careem, Chewy, Cisco, Cognizant, Comcast, Criteo, Deloitte, Deutsche Bank, Devsinc, Docusign, DoorDash, Dropbox, EPAM Systems, EY, EarnIn, Epic Systems, Expedia, FPT, Fidelity, Flipkart, FreshWorks, Garmin, Goldman Sachs, Google, Grab, HCL, Honeywell, Huawei, Hubspot, IBM, Infosys, Intel, Intuit, J.P. Morgan, KLA, Karat, LinkedIn, Luxoft, Mastercard, Meta, Microsoft, MindTree, Morgan Stanley, Myntra, Nagarro, Nielsen, Nutanix, Nvidia, Oracle, Ozon, Palo Alto Networks, PayPal, Paytm, Publicis Sapient, Pwc, Qualcomm, Roblox, SAP, Samsung, ServiceNow, Shopee, Siemens, Slice, Snowflake, SoFi, Spotify, Tech Mahindra, Tekion, TikTok, Tinkoff, UKG, Uber, VMware, Visa, Walmart Labs, Western Digital, Wipro, Wise, Wissen Technology, Wix, Yahoo, Yandex, Yelp, ZScaler, Zoho, athenahealth, eBay, jio, persistent systems, tcs.

Two Sum | LeetCode 1

Easy

Array Hash Table

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

Solution Code

Available in:

import java.util.HashMap;
import java.util.Map;

class Solution {
    public int[] twoSum(int[] nums, int target) {
        Map<Integer, Integer> numMap = new HashMap<>();
        for (int i = 0; i < nums.length; i++) {
            int complement = target - nums[i];
            if (numMap.containsKey(complement)) {
                return new int[] {numMap.get(complement), i};
            }
            numMap.put(nums[i], i);
        }
        return new int[]{};
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 1: Two Sum - Detailed explanation and solution approaches.

Topics

Array Hash Table

Companies

AMDAccentureAccoliteAdobeAgodaAirbnbAirbus SEAkamai

Stats

Difficulty:Easy

Languages:4

Companies:114

Problem #:1

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: Initialize an empty hash map (dictionary in Python).
2
Step 2: Iterate through the input array `nums` using a loop.
3
Step 3: For each number `num` in `nums`, calculate the `complement` as `target - num`.
4
Step 4: Check if the `complement` exists as a key in the hash map.
5
Step 5: If the `complement` exists, return the index of the `complement` (stored in the hash map) and the current index `i`.
6
Step 6: If the `complement` does not exist, add the current number `num` and its index `i` to the hash map.
7
Step 7: If the loop completes without finding a pair, return an empty array (or handle accordingly based on language).

💡

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 algorithm iterates through the array once (O(n)). Hash map operations (insertion and lookup) take constant time on average, O(1). Therefore, the overall time complexity is O(n). The space complexity is O(n) because, in the worst case, the hash map could store all the numbers from the input array.

📖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

Solution Approaches

Brute Force

Check every pair of numbers

Time: O(n²)Space: O(1)

Hash Table

Store numbers and their indices for O(1) lookup

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

Alternative Approaches

Brute Force

Nested loops iterate through all possible pairs of numbers in the array to check if their sum equals the target.

Time: O(n^2)Space: O(1)

Trade-offs: Simple to implement but inefficient for large arrays. Prefer the hash map approach for better performance unless the array is very small.

✨

Key Insights

1Insight 1: Using a hash map (dictionary in Python) allows for efficient lookups of the complement (target - num).
2Insight 2: The hash map stores each number and its index, enabling quick identification of the pair that sums to the target.
3Insight 3: A brute-force approach (nested loops) would have O(n^2) time complexity, while the hash map approach achieves O(n) time complexity.

📚

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: The array might contain duplicate numbers. The solution correctly handles this as long as there's only one valid pair that sums to the target.
Edge case 2: The target value might not be found. The solution handles this by returning an empty array or a suitable alternative as shown in the provided code snippets.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle the case where the target sum is not found in the array.

✗Common mistake 2: Incorrectly managing indices when returning the result, leading to off-by-one errors or returning incorrect indices.

✅

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: Finding pairs of transactions that total a specific amount in financial data analysis.

🏦Real-world scenario 2: Identifying pairs of data points with a specific combined value in scientific simulations or data mining.

💡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: June 2, 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

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

@AlgoMasterMay 29

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

@InterviewProMay 22

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

@CodeNinjaMay 15

❓

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 "Two Sum"?

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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