PPractick

The problem

A gift-card kiosk lets a customer pick exactly two items whose prices add up to the card's value, and it needs to show which two. With thousands of items, checking every pair is O(n²) and noticeably slow. The classic answer uses a hash map: as you walk through the prices, you ask "have I already seen the complement target − price?" If so, you've found the pair; if not, you remember the current price and its position. That's one pass and O(n) time, and it's probably the most frequently asked interview question there is.

Example: prices [2, 7, 11, 15], target 9 → indices [0, 1] (2 + 7).

Function signature

vector<int> twoSum(const vector<int>& nums, int target);  // indices of the two numbers, or {-1, -1}

Test cases

Input (nums, target)	Output	Explanation
([2, 7, 11, 15], 9)	[0, 1]	2 + 7
([3, 2, 4], 6)	[1, 2]	3 + 3 isn't allowed: the same element can't be used twice
([3, 3], 6)	[0, 1]	Two different elements with equal values
([-1, -2, -3, -4, -5], -8)	[2, 4]	Negative numbers
([1, 2, 3], 7)	[-1, -1]	No pair exists

(Confirm: return the indices (smaller first) of two different elements; LeetCode guarantees exactly one answer, and here {-1, -1} signals none.)

How interviewers phrase it

• "Given an array and a target, return the indices of two numbers that add up to the target" (LeetCode 1).
• "Is there a pair with the given sum?" (a yes/no version).
• Follow-ups: the sorted-array version (two pointers), 3Sum, 4Sum, and counting pairs.

Clarifying questions to ask

1. Return indices or values?
2. Is exactly one solution guaranteed? What if there is none?
3. Can the same element be used twice?
4. Is the array sorted?

Follow-ups to expect

1. "Why check the map before inserting the current element?"
2. "What if the array is sorted?"
3. "Can you sort first for an unsorted array?"
4. "How would you count all pairs with the sum?"
5. "Complexity?"

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