Maximum Consecutive Floors Without Special Floors

Problem Description

Alice manages a company and has rented some floors of a building as office space. Alice has decided some of these floors should be special floors, used for relaxation only. You are given two integers bottom and top, which denote that Alice has rented all the floors from bottom to top (inclusive). You are also given the integer array special, where special[i] denotes a special floor that Alice has designated for relaxation. Return the maximum number of consecutive floors without a special floor.

Key Insights

• The problem requires finding the longest segment of consecutive non-special floors between the bottom and top range.
• Special floors can be stored in a data structure that allows quick lookups (like a set).
• The segments of non-special floors can be calculated by analyzing the gaps between consecutive special floors.

Space and Time Complexity

Time Complexity: O(n log n) - where n is the number of special floors, due to sorting. Space Complexity: O(n) - for storing the special floors.

Solution

To solve the problem, we can follow these steps:

1. Sort the list of special floors.
2. Calculate the gaps between the bottom and the first special floor, between consecutive special floors, and between the last special floor and top.
3. The maximum of these gaps will give us the maximum number of consecutive floors without a special floor.

We will utilize a sorted array to keep track of the special floors, and then iterate through the sorted list to find the maximum gap.

Code Solutions