How do you solve the Two Sum problem efficiently? | Interview Question

Q: How do you solve the Two Sum problem efficiently?

**Target Audience:** Beginners preparing for coding interviews — you know basic Python lists and loops; nothing else assumed. **Difficulty:** Easy **Language:** Python 3 > **How to read this doc:** Every idea is explained in plain language first, then tagged with `📌 Interview term:` so you also learn the exact words an interviewer expects. Every output shown was produced by actually running the code with `python3` (3.13); nothing is typed in by hand. ## 1. Why This Even Matters — A Story First You walk into a shop with a gift card worth exactly **9**. It only works if you spend all of it on **exactly two items**. The shelf has items priced 2, 7, 11 and 15. The slow way: pick up the first item, then try it with every other item; put it down, pick up the second item, try it with every item after it, and so on. With 4 items that is 6 tries. With 3,000 items it is about 4.5 million tries. The smart way: carry a small notebook. Walk along the shelf once. At each item, ask one question

The problem

Question presented to candidate: "Given a list of integers and a target, return the indices of the two numbers that add up to the target. You can assume there is exactly one answer and you cannot use the same element twice. Please code it in Python and tell me the time and space complexity."

What a strong answer should cover:

The brute force first (check every pair, O(n²)), then the improvement: for each x, look up its complement target - x.
A one-pass dict mapping value → index, with the lookup done before the insert so an element never pairs with itself.
O(n) average time and O(n) extra space, and why "average": dict lookups are O(1) on average, not in the worst case.
The sorted-input alternative: two pointers, O(n) time and O(1) space, and why sorting loses the original indices.
Python specifics: enumerate for index + value, in on a dict is a hash lookup (on a list it is a linear scan), and Python ints never overflow.

Clarifying questions expected:

Indices or values? Is the input sorted?
What should happen when there is no pair?

Code / implementation expected: Yes — a two_sum(nums, target) function in Python using a dict, run on a few inputs including duplicates and a no-answer case.

arrays
hashing

Try it yourself

Sketch your approach before you read the solution. That is what the interview tests.

Stuck? Get a hint.

A short nudge toward the approach. It will not give the answer away.

Solution

Target Audience: Beginners preparing for coding interviews — you know basic Python lists and loops; nothing else assumed. Difficulty: Easy Language: Python 3

How to read this doc: Every idea is explained in plain language first, then tagged with 📌 Interview term: so you also learn the exact words an interviewer expects. Every output shown was produced by actually running the code with python3 (3.13); nothing is typed in by hand.

1. Why This Even Matters — A Story First

You walk into a shop with a gift card worth exactly 9. It only works if you spend all of it on exactly two items. The shelf has items priced 2, 7, 11 and 15.

The slow way: pick up the first item, then try it with every other item; put it down, pick up the second item, try it with every item after it, and so on. With 4 items that is 6 tries. With 3,000 items it is about 4.5 million trie

The solution is hidden so you can try first

12 min read · 11 sections

Python code

Edit the code and run it here. Each printed line with an expected value becomes a test.

PythonOne-pass hash map Two Sum on six inputs

Practice

PythonBrute force vs sort + two pointers vs hash map: counting the work

Practice

Discussion

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