Problem Description
There are n people in a line queuing to buy tickets. You are given a 0-indexed integer array tickets of length n where the number of tickets that the i-th person would like to buy is tickets[i]. Each person takes exactly 1 second to buy a ticket and has to go back to the end of the line to buy more tickets. If a person does not have any tickets left to buy, they leave the line. Return the time taken for the person initially at position k (0-indexed) to finish buying tickets.
Key Insights
- Each person in line takes 1 second to buy a ticket.
- A person can only buy one ticket at a time and must return to the end of the line for additional tickets.
- The task is to simulate the queue until the k-th person has bought all their tickets.
- The process continues until the tickets for the k-th person reach zero.
Space and Time Complexity
Time Complexity: O(n * max(tickets)), where n is the number of people in line and max(tickets) is the maximum number of tickets any person wants to buy.
Space Complexity: O(n), for the tickets array.
Solution
To solve this problem, we can use a simulation approach with a queue structure. We iterate through the queue, allowing each person to buy one ticket per second. After buying a ticket, if they still want more tickets, they move to the back of the queue. We keep track of the total time until the k-th person has bought all their tickets. This approach effectively simulates the buying process, ensuring we accurately measure the time taken for the specific person.