How to Explain Two Sum in English

The problem

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

You do not need to invent a new algorithm. Narrate brute force, then a hash map of values you have already seen.

# seen: value → index
seen = {}
for i, n in enumerate(nums):
    need = target - n
    if need in seen:
        return [seen[need], i]
    seen[n] = i

How to explain it

1. 1. Restate

   Say the problem in your own words.

   One or two sentences. Show you understood the input, the output, and the goal — not that you memorised the prompt.

2. 2. Approach

   Name the method before you code.

   Brute force first if you need it, then the structure you will use: hash map, two pointers, stack, binary search.

3. 3. Example

   Walk one concrete input.

   Pick small numbers. Say what you store, what you compare, and what you return. Interviewers follow an example more easily than abstract talk.

4. 4. Time and space

   One sentence each.

   After the example, before you claim you are done. “Time is O(n) because we scan once. Space is O(n) for the map.”

5. 5. Edge cases

   Name at least one unusual input.

   Empty input, duplicates, already sorted, overflow. Invite a follow-up: “I would also check …”

• “Let me restate this.”
• “My first instinct is brute force, then I will optimise.”
• “I will keep a hash map of values I have already seen.”
• “Time is O(n). Space is O(n) for the map.”

Practise out loud

Model spoken script

Let me restate this. I have an array of numbers and a target. I need the two indices that add up to that target, and I cannot reuse the same index. I will assume there is exactly one pair. My first instinct is brute force: check every pair. That is correct but O(n²). I would rather scan once and keep a hash map of values I have already seen. For example, nums are 2, 7, 11, 15 and the target is 9. I see 2, store 2 at index 0. At 7 I need 2, the map has it, so I return 0 and 1. Time is O(n) because I scan once. Space is O(n) for the map. I would also check the empty array and the case where the pair is at the two ends.