Two Sum

Finds two indices in an array whose values sum to a target

Problem Overview

The Classic Two Sum Challenge

Find two numbers in an array that add up to a target sum and return their indices. This foundational problem appears in virtually every coding interview!

🔍 Problem Breakdown:

Given: [2, 7, 11, 15] and target 9
Find: Indices where numbers sum to target
Return: [0, 1] (because 2 + 7 = 9)
Two Solution Strategies:
Brute Force: Check every pair → O(n²) time, O(1) space
Hash Map: Single pass with lookups → O(n) time, O(n) space

🧠 Key Learning Concepts:

Time vs Space complexity trade-offs
Hash table optimization patterns
Array indexing and iteration strategies
Interview problem-solving methodology
Why This Matters:
Foundation for more complex sum problems (3Sum, 4Sum)
Demonstrates hash map optimization techniques
Tests ability to recognize algorithmic improvements
Common technical interview screening question

Concepts

array iterationhash mapsbrute-force

Complexity Analysis

Time:O(n) for hash map, O(n²) for brute-force

Space:O(n) for hash map, O(1) for brute-force

Solutions

twoSum

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

export function twoSum(nums: number[], target: number): number[] {
  if (!Array.isArray(nums) || nums.length < 2) throw new Error("Input must be an array with at least two numbers");
  const numToIndex: { [key: number]: number } = {};
  for (let i = 0; i < nums.length; i++) {
    const complement = target - nums[i];
    if (numToIndex[complement] !== undefined) return [numToIndex[complement], i];
    numToIndex[nums[i]] = i;
  }
  throw new Error("No two numbers sum to the target");
}

Examples & Test Cases

#1Basic

Input:

Output:

[
  0,
  1
]

#2Not at start

Input:

Output:

[
  1,
  2
]

#3Duplicates

Input:

[
  [
    3,
    3
  ],
  6
]

Output:

[
  0,
  1
]

#4No solution

Input:

Output:{}

#5Too short

Input:

[
  [
    1
  ],
  2
]

Output:{}

#6Invalid

Input:

[
  null,
  5
]

Output:{}