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1. Two Sum

easyAsked at Duolingo

Given an array of integers and a target, return indices of two numbers that sum to target.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given an array of integers nums and an integer target, return the indices of the two numbers such that they add up to target. You may assume each input has exactly one solution and you cannot use the same element twice.

Constraints

  • 2 <= nums.length <= 10^4
  • -10^9 <= nums[i] <= 10^9
  • Exactly one valid answer exists

Examples

Example 1

Input
nums = [2,7,11,15], target = 9
Output
[0,1]

Example 2

Input
nums = [3,2,4], target = 6
Output
[1,2]

Approaches

1. Brute force

Check every pair of indices.

Time
O(n^2)
Space
O(1)
for (let i=0;i<nums.length;i++)
  for (let j=i+1;j<nums.length;j++)
    if (nums[i]+nums[j]===target) return [i,j];

Tradeoff:

2. Hash map one-pass

Store seen numbers in a map; for each value check if complement exists. One pass, constant lookup.

Time
O(n)
Space
O(n)
function twoSum(nums, target) {
  const seen = new Map();
  for (let i = 0; i < nums.length; i++) {
    const need = target - nums[i];
    if (seen.has(need)) return [seen.get(need), i];
    seen.set(nums[i], i);
  }
}

Tradeoff:

Duolingo-specific tips

Duolingo values readable solutions that you could imagine running inside a spaced-repetition scheduler or lesson scorer—name variables clearly and explain the hash-map invariant as you write.

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