Maximum Consecutive Floors Without Special Floors

Maximum Consecutive Floors Without Special Floors

What is this problem about?

The "Maximum Consecutive Floors Without Special Floors" problem is a practical array-based challenge that involves interval calculation. You are given a range of floors in a building, defined by a bottom and a top floor. Within this range, certain floors are designated as "special" (for example, they might be used for maintenance or storage and are not available). Your goal is to find the maximum number of consecutive floors that do not contain any special floors. This requires you to look at the gaps between the special floors, as well as the gaps at the very beginning and end of the floor range.

Why is this asked in interviews?

Companies like Amazon use the Maximum Consecutive Floors Without Special Floors interview question to check a candidate's attention to detail and ability to handle edge cases. While the logic is relatively straightforward, the "boundaries"—the floors between the bottom floor and the first special floor, and between the last special floor and the top floor—are often overlooked by less experienced developers. It tests if you can transform a set of points into a set of intervals and compare their lengths efficiently.

Algorithmic pattern used?

The primary algorithmic pattern used here is Sorting. By sorting the list of special floors, you can iterate through them once and calculate the distance between each adjacent pair. The gaps you need to check are:

1. special[0] - bottom (floors before the first special floor)
2. special[i] - special[i-1] - 1 (floors between two consecutive special floors)
3. top - special[last] (floors after the last special floor) The maximum of all these values gives the final result. Sorting allows you to solve the problem in $O(n \log n)$ time, which is highly efficient.

Example explanation?

Imagine a building with floors from 2 to 10. The special floors are [4, 7].

1. Sort the special floors: [4, 7].
2. Gap before the first special floor: floors 2 and 3. (4 - 2 = 2 floors).
3. Gap between 4 and 7: floors 5 and 6. (7 - 4 - 1 = 2 floors).
4. Gap after the last special floor: floors 8, 9, and 10. (10 - 7 = 3 floors). The maximum consecutive floors without a special floor is 3. This simple logic is the core of the Maximum Consecutive Floors Without Special Floors coding problem.

Common mistakes candidates make?

The most frequent error is neglecting the floors at the boundaries (bottom and top). Many candidates only calculate the gaps between special floors. Another mistake is an "off-by-one" error when calculating the number of floors in a gap—remember that the floors themselves are inclusive, but the special floor itself is not part of the consecutive run. Forgetting to sort the special floors before iterating is also a common blunder that leads to incorrect gap calculations.

Interview preparation tip

Always be mindful of boundary conditions in any interval-related problem. When given a range [A, B] and some points inside it, always check the sub-ranges [A, point1] and [pointN, B]. This pattern appears in many interview questions, from scheduling to memory management simulations.