30-Day Coding Sprint: Time Needed to Buy Tickets Optimization

Day 29 of 30-day Coding Sprint Today's problem, Time Needed to Buy Tickets, is a perfect example of how you can move from a "literal" simulation to a "mathematical" observation. Approach 1: Simulation Using a Queue - The Logic: We treat the problem exactly as described. We use a queue to store pairs of [tickets_needed, original_index]. - The Flow: 1. Take the person from the front. 2. Subtract 1 from their ticket count and increment time. 3. If they still need tickets, push them back to the end of the queue. 4. Stop as soon as the person at original_index === k has 0 tickets left. - Pros: Very easy to visualize and "act out" the problem. - Cons: Higher time complexity O(n * max_tickets). Approach 2: The Optimized One-Pass The Logic: Instead of simulating every second, we calculate how many tickets each person actually buys before the person at index k finishes. The Observation: People at or before index k: They can buy at most tickets[k] tickets. People after index k: They can buy at most tickets[k] - 1 tickets (because once person k buys their last ticket, the clock stops immediately). Result: Clean O(N) time and O(1) space. #30DaysOfCode #DSASprint #LeetCode #JavaScript #Queues #Simulation #Optimization #Consistency

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