Taxi Booking

Summary

The Taxi Booking problem involves booking a taxi service. The algorithm should take an array of requests and their respective durations, and return the minimum number of taxis needed to fulfill all requests without overlapping.

This problem requires a greedy approach, as we need to minimize the number of taxis by minimizing the overlapping time slots.

Detailed Explanation

The solution to this problem involves iterating through the array of requests and their durations. We maintain a variable taxis which keeps track of the minimum number of taxis needed at any given point in time.

We start by initializing taxis to 1, as we need at least one taxi initially. Then, for each request in the array:

• If the current request starts after the previous one ended (i.e., there's no overlap), we can reuse the same taxi, so we don't increment taxis.
• If the current request overlaps with the previous one, we need to use a new taxi to fulfill this request. In this case, we increment taxis.

Finally, we return the value of taxis, which represents the minimum number of taxis needed.

Here's a step-by-step breakdown of the solution:

1. Initialize taxis to 1.
2. Iterate through the array of requests and their durations.
3. For each request:
   • If the current request starts after the previous one ended, do nothing (reuse the same taxi).
   • If the current request overlaps with the previous one, increment taxis.
4. Return the value of taxis.

Time complexity: O(n), where n is the number of requests in the array. Space complexity: O(1), as we only use a constant amount of space to store the taxis variable.

Optimized Solutions

Java