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Problem

Design a system that manages the reservation state of n seats that are numbered from 1 to n.

Implement the SeatManager class:

SeatManager(int n) Initializes a SeatManager object that will manage n seats numbered from 1 to n. All seats are initially available.
int reserve() Fetches the smallest-numbered unreserved seat, reserves it, and returns its number.
void unreserve(int seatNumber) Unreserves the seat with the given seatNumber.

Examples

Example 1:

**Input**
["SeatManager", "reserve", "reserve", "unreserve", "reserve", "reserve", "reserve", "reserve", "unreserve"]
[[5], [], [], [2], [], [], [], [], [5]]
**Output**
[null, 1, 2, null, 2, 3, 4, 5, null]

**Explanation**
SeatManager seatManager = new SeatManager(5); // Initializes a SeatManager with 5 seats.
seatManager.reserve();    // All seats are available, so return the lowest numbered seat, which is 1.
seatManager.reserve();    // The available seats are [2,3,4,5], so return the lowest of them, which is 2.
seatManager.unreserve(2); // Unreserve seat 2, so now the available seats are [2,3,4,5].
seatManager.reserve();    // The available seats are [2,3,4,5], so return the lowest of them, which is 2.
seatManager.reserve();    // The available seats are [3,4,5], so return the lowest of them, which is 3.
seatManager.reserve();    // The available seats are [4,5], so return the lowest of them, which is 4.
seatManager.reserve();    // The only available seat is seat 5, so return 5.
seatManager.unreserve(5); // Unreserve seat 5, so now the available seats are [5].

Solution

Method 1 – MinHeap with Lazy Initialization

Intuition

To efficiently manage seat reservations, we use a min-heap to keep track of seats that have been unreserved. Instead of initializing the heap with all seat numbers, we maintain a counter for the next available seat. This way, we only add seats to the heap when they are unreserved, saving both time and space.

Approach

Use a min-heap to store seat numbers that have been unreserved.
Maintain a counter to track the next seat to reserve.
On reserve, return the smallest seat number from the heap if available; otherwise, use the counter and increment it.
On unreserve, add the seat number back to the heap.

Complexity

⏰ Time complexity: O(log n) for reserve and unreserve due to heap operations.
🧺 Space complexity: O(n), for storing unreserved seat numbers in the heap.

Code

[{"language":"C++","code":"#include <queue>\nclass SeatManager {\n    priority_queue<int, vector<int>, greater<int>> pq;\n    int next;\npublic:\n    SeatManager(int n) : next(1) {}\n    int reserve() {\n        if (!pq.empty()) {\n            int seat = pq.top(); pq.pop();\n            return seat;\n        }\n        return next++;\n    }\n    void unreserve(int seatNumber) {\n        pq.push(seatNumber);\n    }\n};","lang":"cpp"},{"language":"Java","code":"import java.util.PriorityQueue;\nclass SeatMana

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