Two-sum: find two numbers in an array that add to a target

Framework

1. Clarify: can elements repeat? are there always two answers? sorted input?
2. Brute force: O(n²) double loop — mention it, then optimize
3. Optimal: hash map of {value → index}; for each x, check if (target - x) is in the map
4. Time: O(n). Space: O(n).
5. Walk through one example end-to-end out loud

Sample answer

```ts
function twoSum(nums: number[], target: number): [number, number] | null {
  const seen = new Map<number, number>(); // value → index
  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);
  }
  return null;
}
```

Talk through it: "I keep a map of values I've seen and their indices. For
each new number, I check if its complement is already in the map. Single
pass, constant-time lookup, linear time overall."

Common pitfalls

• Coding silently — interviewer wants to hear you think
• Forgetting to handle 'no solution' case
• Not stating Big-O until prompted