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2274. Maximum Consecutive Floors Without Special Floors

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.

 

Example 1:

Input: bottom = 2, top = 9, special = [4,6]
Output: 3
Explanation: The following are the ranges (inclusive) of consecutive floors without a special floor:
- (2, 3) with a total amount of 2 floors.
- (5, 5) with a total amount of 1 floor.
- (7, 9) with a total amount of 3 floors.
Therefore, we return the maximum number which is 3 floors.

Example 2:

Input: bottom = 6, top = 8, special = [7,6,8]
Output: 0
Explanation: Every floor rented is a special floor, so we return 0.

 

Constraints:

  • 1 <= special.length <= 105
  • 1 <= bottom <= special[i] <= top <= 109
  • All the values of special are unique.

Solutions

Solution 1: Sorting

We can sort the special floors in ascending order, then calculate the number of floors between each pair of adjacent special floors. Finally, we calculate the number of floors between the first special floor and $\textit{bottom}$, as well as the number of floors between the last special floor and $\textit{top}$. The maximum of these floor counts is the answer.

The time complexity is $O(n \times \log n)$, and the space complexity is $O(\log n)$. Here, $n$ is the length of the array $\textit{special}$.

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class Solution:
    def maxConsecutive(self, bottom: int, top: int, special: List[int]) -> int:
        special.sort()
        ans = max(special[0] - bottom, top - special[-1])
        for x, y in pairwise(special):
            ans = max(ans, y - x - 1)
        return ans

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class Solution {
    public int maxConsecutive(int bottom, int top, int[] special) {
        Arrays.sort(special);
        int n = special.length;
        int ans = Math.max(special[0] - bottom, top - special[n - 1]);
        for (int i = 1; i < n; ++i) {
            ans = Math.max(ans, special[i] - special[i - 1] - 1);
        }
        return ans;
    }
}

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class Solution {
public:
    int maxConsecutive(int bottom, int top, vector<int>& special) {
        ranges::sort(special);
        int ans = max(special[0] - bottom, top - special.back());
        for (int i = 1; i < special.size(); ++i) {
            ans = max(ans, special[i] - special[i - 1] - 1);
        }
        return ans;
    }
};

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func maxConsecutive(bottom int, top int, special []int) int {
    sort.Ints(special)
    ans := max(special[0]-bottom, top-special[len(special)-1])
    for i, x := range special[1:] {
        ans = max(ans, x-special[i]-1)
    }
    return ans
}

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function maxConsecutive(bottom: number, top: number, special: number[]): number {
    special.sort((a, b) => a - b);
    const n = special.length;
    let ans = Math.max(special[0] - bottom, top - special[n - 1]);
    for (let i = 1; i < n; ++i) {
        ans = Math.max(ans, special[i] - special[i - 1] - 1);
    }
    return ans;
}

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