Video narration
Trying every pair of prices is the slow way to solve Two Sum with a budget: compare one price with every other, then repeat. Instead, when you see a price, ask: what amount is missing to reach the target? That amount is target minus the current value. Use a hash map-a memory of prices seen and their indices. Take prices 2, 7, 11, 15; target 9. Start with 2. You need 7. Is 7 in the map? No, so store 2 with index 0. Next, 7 needs 2. The map has 2, so return its index, 0, and current index, 1. Check before storing the current value. That keeps you from using the same item twice. Each lookup is usually constant time, so one scan takes O(n) time and O(n) extra space. Like shopping with a budget: remember each price, check its missing amount, and find the pair in one pass.