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1845. Seat Reservation Manager

SourceBiweekly Contest 51 Q2DifficultyMediumRating1428

Description

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.

 

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].

 

Constraints:

  • 1 <= n <= 105
  • 1 <= seatNumber <= n
  • For each call to reserve, it is guaranteed that there will be at least one unreserved seat.
  • For each call to unreserve, it is guaranteed that seatNumber will be reserved.
  • At most 105 calls in total will be made to reserve and unreserve.

Solutions

Solution 1: Priority Queue (Min-Heap)

Thinking

We must always reserve the smallest free seat and later release seats. Scanning a boolean array for the minimum free index is \(O(n)\) per call.

Store free seat numbers in a min-heap: \(\textit{reserve}\) pops the top, \(\textit{unreserve}\) pushes the number back. Both updates are logarithmic.

We define a priority queue (min-heap) \(q\) to store all the available seat numbers. Initially, we add all seat numbers from \(1\) to \(n\) into \(q\).

When calling the \(\textit{reserve}\) method, we pop the top element from \(q\), which is the smallest available seat number.

When calling the \(\textit{unreserve}\) method, we add the seat number back into \(q\).

In terms of time complexity, the initialization time complexity is \(O(n)\) or \(O(n \log n)\), and the time complexity of the \(\textit{reserve}\) and \(\textit{unreserve}\) methods is both \(O(\log n)\). The space complexity is \(O(n)\).

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class SeatManager:
    def __init__(self, n: int):
        self.q = list(range(1, n + 1))

    def reserve(self) -> int:
        return heappop(self.q)

    def unreserve(self, seatNumber: int) -> None:
        heappush(self.q, seatNumber)


# Your SeatManager object will be instantiated and called as such:
# obj = SeatManager(n)
# param_1 = obj.reserve()
# obj.unreserve(seatNumber)

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class SeatManager {
    private PriorityQueue<Integer> q = new PriorityQueue<>();

    public SeatManager(int n) {
        for (int i = 1; i <= n; ++i) {
            q.offer(i);
        }
    }

    public int reserve() {
        return q.poll();
    }

    public void unreserve(int seatNumber) {
        q.offer(seatNumber);
    }
}

/**
 * Your SeatManager object will be instantiated and called as such:
 * SeatManager obj = new SeatManager(n);
 * int param_1 = obj.reserve();
 * obj.unreserve(seatNumber);
 */

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class SeatManager {
public:
    SeatManager(int n) {
        for (int i = 1; i <= n; ++i) {
            q.push(i);
        }
    }

    int reserve() {
        int seat = q.top();
        q.pop();
        return seat;
    }

    void unreserve(int seatNumber) {
        q.push(seatNumber);
    }

private:
    priority_queue<int, vector<int>, greater<int>> q;
};

/**
 * Your SeatManager object will be instantiated and called as such:
 * SeatManager* obj = new SeatManager(n);
 * int param_1 = obj->reserve();
 * obj->unreserve(seatNumber);
 */

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type SeatManager struct {
    q hp
}

func Constructor(n int) SeatManager {
    q := hp{}
    for i := 1; i <= n; i++ {
        heap.Push(&q, i)
    }
    return SeatManager{q}
}

func (this *SeatManager) Reserve() int {
    return heap.Pop(&this.q).(int)
}

func (this *SeatManager) Unreserve(seatNumber int) {
    heap.Push(&this.q, seatNumber)
}

type hp struct{ sort.IntSlice }

func (h hp) Less(i, j int) bool { return h.IntSlice[i] < h.IntSlice[j] }
func (h *hp) Push(v any)        { h.IntSlice = append(h.IntSlice, v.(int)) }
func (h *hp) Pop() any {
    a := h.IntSlice
    v := a[len(a)-1]
    h.IntSlice = a[:len(a)-1]
    return v
}

/**
 * Your SeatManager object will be instantiated and called as such:
 * obj := Constructor(n);
 * param_1 := obj.Reserve();
 * obj.Unreserve(seatNumber);
 */

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class SeatManager {
    private q = new MinPriorityQueue<number>();
    constructor(n: number) {
        for (let i = 1; i <= n; i++) {
            this.q.enqueue(i);
        }
    }

    reserve(): number {
        return this.q.dequeue();
    }

    unreserve(seatNumber: number): void {
        this.q.enqueue(seatNumber);
    }
}

/**
 * Your SeatManager object will be instantiated and called as such:
 * var obj = new SeatManager(n)
 * var param_1 = obj.reserve()
 * obj.unreserve(seatNumber)
 */

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public class SeatManager {
    private PriorityQueue<int, int> q = new PriorityQueue<int, int>();

    public SeatManager(int n) {
        for (int i = 1; i <= n; ++i) {
            q.Enqueue(i, i);
        }
    }

    public int Reserve() {
        return q.Dequeue();
    }

    public void Unreserve(int seatNumber) {
        q.Enqueue(seatNumber, seatNumber);
    }
}

/**
 * Your SeatManager object will be instantiated and called as such:
 * SeatManager obj = new SeatManager(n);
 * int param_1 = obj.Reserve();
 * obj.Unreserve(seatNumber);
 */

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