855. Exam Room

Description

There is an exam room with n seats in a single row labeled from 0 to n - 1.

When a student enters the room, they must sit in the seat that maximizes the distance to the closest person. If there are multiple such seats, they sit in the seat with the lowest number. If no one is in the room, then the student sits at seat number 0.

Design a class that simulates the mentioned exam room.

Implement the ExamRoom class:

ExamRoom(int n) Initializes the object of the exam room with the number of the seats n.
int seat() Returns the label of the seat at which the next student will set.
void leave(int p) Indicates that the student sitting at seat p will leave the room. It is guaranteed that there will be a student sitting at seat p.

Example 1:

Input
["ExamRoom", "seat", "seat", "seat", "seat", "leave", "seat"]
[[10], [], [], [], [], [4], []]
Output
[null, 0, 9, 4, 2, null, 5]

Explanation
ExamRoom examRoom = new ExamRoom(10);
examRoom.seat(); // return 0, no one is in the room, then the student sits at seat number 0.
examRoom.seat(); // return 9, the student sits at the last seat number 9.
examRoom.seat(); // return 4, the student sits at the last seat number 4.
examRoom.seat(); // return 2, the student sits at the last seat number 2.
examRoom.leave(4);
examRoom.seat(); // return 5, the student sits at the last seat number 5.

Constraints:

1 <= n <= 10⁹
It is guaranteed that there is a student sitting at seat p.
At most 10⁴ calls will be made to seat and leave.

Solutions

Solution 1: Ordered Set + Hash Table

Considering that each time we call $\text{seat}()$, we need to find the seat with the maximum distance, we can use an ordered set to store seat intervals. Each element of the ordered set is a tuple $(l, r)$, indicating that the seats between $l$ and $r$ (excluding $l$ and $r$) can be occupied by a student. Initially, the ordered set contains only one element $(-1, n)$, indicating that the seats between $(-1, n)$ can be occupied by a student.

Additionally, we use two hash tables $\textit{left}$ and $\textit{right}$ to maintain the left and right neighbors of each occupied seat, making it easier to merge two seat intervals when calling $\text{leave}(p)$.

The time complexity is $O(\log n)$, and the space complexity is $O(n)$. Here, $n$ is the number of seats in the exam room.

Python3JavaC++GoTypeScript

class ExamRoom:
    def __init__(self, n: int):
        def dist(x):
            l, r = x
            return r - l - 1 if l == -1 or r == n else (r - l) >> 1

        self.n = n
        self.ts = SortedList(key=lambda x: (-dist(x), x[0]))
        self.left = {}
        self.right = {}
        self.add((-1, n))

    def seat(self) -> int:
        s = self.ts[0]
        p = (s[0] + s[1]) >> 1
        if s[0] == -1:
            p = 0
        elif s[1] == self.n:
            p = self.n - 1
        self.delete(s)
        self.add((s[0], p))
        self.add((p, s[1]))
        return p

    def leave(self, p: int) -> None:
        l, r = self.left[p], self.right[p]
        self.delete((l, p))
        self.delete((p, r))
        self.add((l, r))

    def add(self, s):
        self.ts.add(s)
        self.left[s[1]] = s[0]
        self.right[s[0]] = s[1]

    def delete(self, s):
        self.ts.remove(s)
        self.left.pop(s[1])
        self.right.pop(s[0])


# Your ExamRoom object will be instantiated and called as such:
# obj = ExamRoom(n)
# param_1 = obj.seat()
# obj.leave(p)

class ExamRoom {
    private TreeSet<int[]> ts = new TreeSet<>((a, b) -> {
        int d1 = dist(a), d2 = dist(b);
        return d1 == d2 ? a[0] - b[0] : d2 - d1;
    });
    private Map<Integer, Integer> left = new HashMap<>();
    private Map<Integer, Integer> right = new HashMap<>();
    private int n;

    public ExamRoom(int n) {
        this.n = n;
        add(new int[] {-1, n});
    }

    public int seat() {
        int[] s = ts.first();
        int p = (s[0] + s[1]) >> 1;
        if (s[0] == -1) {
            p = 0;
        } else if (s[1] == n) {
            p = n - 1;
        }
        del(s);
        add(new int[] {s[0], p});
        add(new int[] {p, s[1]});
        return p;
    }

    public void leave(int p) {
        int l = left.get(p), r = right.get(p);
        del(new int[] {l, p});
        del(new int[] {p, r});
        add(new int[] {l, r});
    }

    private int dist(int[] s) {
        int l = s[0], r = s[1];
        return l == -1 || r == n ? r - l - 1 : (r - l) >> 1;
    }

    private void add(int[] s) {
        ts.add(s);
        left.put(s[1], s[0]);
        right.put(s[0], s[1]);
    }

    private void del(int[] s) {
        ts.remove(s);
        left.remove(s[1]);
        right.remove(s[0]);
    }
}

/**
 * Your ExamRoom object will be instantiated and called as such:
 * ExamRoom obj = new ExamRoom(n);
 * int param_1 = obj.seat();
 * obj.leave(p);
 */

int N;

int dist(const pair<int, int>& p) {
    auto [l, r] = p;
    if (l == -1 || r == N) return r - l - 1;
    return (r - l) >> 1;
}

struct cmp {
    bool operator()(const pair<int, int>& a, const pair<int, int>& b) const {
        int d1 = dist(a), d2 = dist(b);
        return d1 == d2 ? a.first < b.first : d1 > d2;
    };
};

class ExamRoom {
public:
    ExamRoom(int n) {
        N = n;
        this->n = n;
        add({-1, n});
    }

    int seat() {
        auto s = *ts.begin();
        int p = (s.first + s.second) >> 1;
        if (s.first == -1) {
            p = 0;
        } else if (s.second == n) {
            p = n - 1;
        }
        del(s);
        add({s.first, p});
        add({p, s.second});
        return p;
    }

    void leave(int p) {
        int l = left[p], r = right[p];
        del({l, p});
        del({p, r});
        add({l, r});
    }

private:
    set<pair<int, int>, cmp> ts;
    unordered_map<int, int> left;
    unordered_map<int, int> right;
    int n;

    void add(pair<int, int> s) {
        ts.insert(s);
        left[s.second] = s.first;
        right[s.first] = s.second;
    }

    void del(pair<int, int> s) {
        ts.erase(s);
        left.erase(s.second);
        right.erase(s.first);
    }
};

/**
 * Your ExamRoom object will be instantiated and called as such:
 * ExamRoom* obj = new ExamRoom(n);
 * int param_1 = obj->seat();
 * obj->leave(p);
 */

type ExamRoom struct {
    rbt   *redblacktree.Tree
    left  map[int]int
    right map[int]int
    n     int
}

func Constructor(n int) ExamRoom {
    dist := func(s []int) int {
        if s[0] == -1 || s[1] == n {
            return s[1] - s[0] - 1
        }
        return (s[1] - s[0]) >> 1
    }
    cmp := func(a, b any) int {
        x, y := a.([]int), b.([]int)
        d1, d2 := dist(x), dist(y)
        if d1 == d2 {
            return x[0] - y[0]
        }
        return d2 - d1
    }
    this := ExamRoom{redblacktree.NewWith(cmp), map[int]int{}, map[int]int{}, n}
    this.add([]int{-1, n})
    return this
}

func (this *ExamRoom) Seat() int {
    s := this.rbt.Left().Key.([]int)
    p := (s[0] + s[1]) >> 1
    if s[0] == -1 {
        p = 0
    } else if s[1] == this.n {
        p = this.n - 1
    }
    this.del(s)
    this.add([]int{s[0], p})
    this.add([]int{p, s[1]})
    return p
}

func (this *ExamRoom) Leave(p int) {
    l, _ := this.left[p]
    r, _ := this.right[p]
    this.del([]int{l, p})
    this.del([]int{p, r})
    this.add([]int{l, r})
}

func (this *ExamRoom) add(s []int) {
    this.rbt.Put(s, struct{}{})
    this.left[s[1]] = s[0]
    this.right[s[0]] = s[1]
}

func (this *ExamRoom) del(s []int) {
    this.rbt.Remove(s)
    delete(this.left, s[1])
    delete(this.right, s[0])
}

/**
 * Your ExamRoom object will be instantiated and called as such:
 * obj := Constructor(n);
 * param_1 := obj.Seat();
 * obj.Leave(p);
 */

class ExamRoom {
    private ts: TreeSet<number[]> = new TreeSet<number[]>((a, b) => {
        const d1 = this.dist(a),
            d2 = this.dist(b);
        return d1 === d2 ? a[0] - b[0] : d2 - d1;
    });
    private left: Map<number, number> = new Map();
    private right: Map<number, number> = new Map();
    private n: number;

    constructor(n: number) {
        this.n = n;
        this.add([-1, n]);
    }

    seat(): number {
        const s = this.ts.first();
        let p = Math.floor((s[0] + s[1]) / 2);
        if (s[0] === -1) {
            p = 0;
        } else if (s[1] === this.n) {
            p = this.n - 1;
        }
        this.del(s);
        this.add([s[0], p]);
        this.add([p, s[1]]);
        return p;
    }

    leave(p: number): void {
        const l = this.left.get(p)!;
        const r = this.right.get(p)!;
        this.del([l, p]);
        this.del([p, r]);
        this.add([l, r]);
    }

    private dist(s: number[]): number {
        const [l, r] = s;
        return l === -1 || r === this.n ? r - l - 1 : Math.floor((r - l) / 2);
    }

    private add(s: number[]): void {
        this.ts.add(s);
        this.left.set(s[1], s[0]);
        this.right.set(s[0], s[1]);
    }

    private del(s: number[]): void {
        this.ts.delete(s);
        this.left.delete(s[1]);
        this.right.delete(s[0]);
    }
}

type Compare<T> = (lhs: T, rhs: T) => number;

class RBTreeNode<T = number> {
    data: T;
    count: number;
    left: RBTreeNode<T> | null;
    right: RBTreeNode<T> | null;
    parent: RBTreeNode<T> | null;
    color: number;
    constructor(data: T) {
        this.data = data;
        this.left = this.right = this.parent = null;
        this.color = 0;
        this.count = 1;
    }

    sibling(): RBTreeNode<T> | null {
        if (!this.parent) return null; // sibling null if no parent
        return this.isOnLeft() ? this.parent.right : this.parent.left;
    }

    isOnLeft(): boolean {
        return this === this.parent!.left;
    }

    hasRedChild(): boolean {
        return (
            Boolean(this.left && this.left.color === 0) ||
            Boolean(this.right && this.right.color === 0)
        );
    }
}

class RBTree<T> {
    root: RBTreeNode<T> | null;
    lt: (l: T, r: T) => boolean;
    constructor(compare: Compare<T> = (l: T, r: T) => (l < r ? -1 : l > r ? 1 : 0)) {
        this.root = null;
        this.lt = (l: T, r: T) => compare(l, r) < 0;
    }

    rotateLeft(pt: RBTreeNode<T>): void {
        const right = pt.right!;
        pt.right = right.left;

        if (pt.right) pt.right.parent = pt;
        right.parent = pt.parent;

        if (!pt.parent) this.root = right;
        else if (pt === pt.parent.left) pt.parent.left = right;
        else pt.parent.right = right;

        right.left = pt;
        pt.parent = right;
    }

    rotateRight(pt: RBTreeNode<T>): void {
        const left = pt.left!;
        pt.left = left.right;

        if (pt.left) pt.left.parent = pt;
        left.parent = pt.parent;

        if (!pt.parent) this.root = left;
        else if (pt === pt.parent.left) pt.parent.left = left;
        else pt.parent.right = left;

        left.right = pt;
        pt.parent = left;
    }

    swapColor(p1: RBTreeNode<T>, p2: RBTreeNode<T>): void {
        const tmp = p1.color;
        p1.color = p2.color;
        p2.color = tmp;
    }

    swapData(p1: RBTreeNode<T>, p2: RBTreeNode<T>): void {
        const tmp = p1.data;
        p1.data = p2.data;
        p2.data = tmp;
    }

    fixAfterInsert(pt: RBTreeNode<T>): void {
        let parent = null;
        let grandParent = null;

        while (pt !== this.root && pt.color !== 1 && pt.parent?.color === 0) {
            parent = pt.parent;
            grandParent = pt.parent.parent;

            /*  Case : A
                Parent of pt is left child of Grand-parent of pt */
            if (parent === grandParent?.left) {
                const uncle = grandParent.right;

                /* Case : 1
                   The uncle of pt is also red
                   Only Recoloring required */
                if (uncle && uncle.color === 0) {
                    grandParent.color = 0;
                    parent.color = 1;
                    uncle.color = 1;
                    pt = grandParent;
                } else {
                    /* Case : 2
                       pt is right child of its parent
                       Left-rotation required */
                    if (pt === parent.right) {
                        this.rotateLeft(parent);
                        pt = parent;
                        parent = pt.parent;
                    }

                    /* Case : 3
                       pt is left child of its parent
                       Right-rotation required */
                    this.rotateRight(grandParent);
                    this.swapColor(parent!, grandParent);
                    pt = parent!;
                }
            } else {
                /* Case : B
               Parent of pt is right child of Grand-parent of pt */
                const uncle = grandParent!.left;

                /*  Case : 1
                    The uncle of pt is also red
                    Only Recoloring required */
                if (uncle != null && uncle.color === 0) {
                    grandParent!.color = 0;
                    parent.color = 1;
                    uncle.color = 1;
                    pt = grandParent!;
                } else {
                    /* Case : 2
                       pt is left child of its parent
                       Right-rotation required */
                    if (pt === parent.left) {
                        this.rotateRight(parent);
                        pt = parent;
                        parent = pt.parent;
                    }

                    /* Case : 3
                       pt is right child of its parent
                       Left-rotation required */
                    this.rotateLeft(grandParent!);
                    this.swapColor(parent!, grandParent!);
                    pt = parent!;
                }
            }
        }
        this.root!.color = 1;
    }

    delete(val: T): boolean {
        const node = this.find(val);
        if (!node) return false;
        node.count--;
        if (!node.count) this.deleteNode(node);
        return true;
    }

    deleteAll(val: T): boolean {
        const node = this.find(val);
        if (!node) return false;
        this.deleteNode(node);
        return true;
    }

    deleteNode(v: RBTreeNode<T>): void {
        const u = BSTreplace(v);

        // True when u and v are both black
        const uvBlack = (u === null || u.color === 1) && v.color === 1;
        const parent = v.parent!;

        if (!u) {
            // u is null therefore v is leaf
            if (v === this.root) this.root = null;
            // v is root, making root null
            else {
                if (uvBlack) {
                    // u and v both black
                    // v is leaf, fix double black at v
                    this.fixDoubleBlack(v);
                } else {
                    // u or v is red
                    if (v.sibling()) {
                        // sibling is not null, make it red"
                        v.sibling()!.color = 0;
                    }
                }
                // delete v from the tree
                if (v.isOnLeft()) parent.left = null;
                else parent.right = null;
            }
            return;
        }

        if (!v.left || !v.right) {
            // v has 1 child
            if (v === this.root) {
                // v is root, assign the value of u to v, and delete u
                v.data = u.data;
                v.left = v.right = null;
            } else {
                // Detach v from tree and move u up
                if (v.isOnLeft()) parent.left = u;
                else parent.right = u;
                u.parent = parent;
                if (uvBlack) this.fixDoubleBlack(u);
                // u and v both black, fix double black at u
                else u.color = 1; // u or v red, color u black
            }
            return;
        }

        // v has 2 children, swap data with successor and recurse
        this.swapData(u, v);
        this.deleteNode(u);

        // find node that replaces a deleted node in BST
        function BSTreplace(x: RBTreeNode<T>): RBTreeNode<T> | null {
            // when node have 2 children
            if (x.left && x.right) return successor(x.right);
            // when leaf
            if (!x.left && !x.right) return null;
            // when single child
            return x.left ?? x.right;
        }
        // find node that do not have a left child
        // in the subtree of the given node
        function successor(x: RBTreeNode<T>): RBTreeNode<T> {
            let temp = x;
            while (temp.left) temp = temp.left;
            return temp;
        }
    }

    fixDoubleBlack(x: RBTreeNode<T>): void {
        if (x === this.root) return; // Reached root

        const sibling = x.sibling();
        const parent = x.parent!;
        if (!sibling) {
            // No sibiling, double black pushed up
            this.fixDoubleBlack(parent);
        } else {
            if (sibling.color === 0) {
                // Sibling red
                parent.color = 0;
                sibling.color = 1;
                if (sibling.isOnLeft()) this.rotateRight(parent);
                // left case
                else this.rotateLeft(parent); // right case
                this.fixDoubleBlack(x);
            } else {
                // Sibling black
                if (sibling.hasRedChild()) {
                    // at least 1 red children
                    if (sibling.left && sibling.left.color === 0) {
                        if (sibling.isOnLeft()) {
                            // left left
                            sibling.left.color = sibling.color;
                            sibling.color = parent.color;
                            this.rotateRight(parent);
                        } else {
                            // right left
                            sibling.left.color = parent.color;
                            this.rotateRight(sibling);
                            this.rotateLeft(parent);
                        }
                    } else {
                        if (sibling.isOnLeft()) {
                            // left right
                            sibling.right!.color = parent.color;
                            this.rotateLeft(sibling);
                            this.rotateRight(parent);
                        } else {
                            // right right
                            sibling.right!.color = sibling.color;
                            sibling.color = parent.color;
                            this.rotateLeft(parent);
                        }
                    }
                    parent.color = 1;
                } else {
                    // 2 black children
                    sibling.color = 0;
                    if (parent.color === 1) this.fixDoubleBlack(parent);
                    else parent.color = 1;
                }
            }
        }
    }

    insert(data: T): boolean {
        // search for a position to insert
        let parent = this.root;
        while (parent) {
            if (this.lt(data, parent.data)) {
                if (!parent.left) break;
                else parent = parent.left;
            } else if (this.lt(parent.data, data)) {
                if (!parent.right) break;
                else parent = parent.right;
            } else break;
        }

        // insert node into parent
        const node = new RBTreeNode(data);
        if (!parent) this.root = node;
        else if (this.lt(node.data, parent.data)) parent.left = node;
        else if (this.lt(parent.data, node.data)) parent.right = node;
        else {
            parent.count++;
            return false;
        }
        node.parent = parent;
        this.fixAfterInsert(node);
        return true;
    }

    find(data: T): RBTreeNode<T> | null {
        let p = this.root;
        while (p) {
            if (this.lt(data, p.data)) {
                p = p.left;
            } else if (this.lt(p.data, data)) {
                p = p.right;
            } else break;
        }
        return p ?? null;
    }

    *inOrder(root: RBTreeNode<T> = this.root!): Generator<T, undefined, void> {
        if (!root) return;
        for (const v of this.inOrder(root.left!)) yield v;
        yield root.data;
        for (const v of this.inOrder(root.right!)) yield v;
    }

    *reverseInOrder(root: RBTreeNode<T> = this.root!): Generator<T, undefined, void> {
        if (!root) return;
        for (const v of this.reverseInOrder(root.right!)) yield v;
        yield root.data;
        for (const v of this.reverseInOrder(root.left!)) yield v;
    }
}

class TreeSet<T = number> {
    _size: number;
    tree: RBTree<T>;
    compare: Compare<T>;
    constructor(
        collection: T[] | Compare<T> = [],
        compare: Compare<T> = (l: T, r: T) => (l < r ? -1 : l > r ? 1 : 0),
    ) {
        if (typeof collection === 'function') {
            compare = collection;
            collection = [];
        }
        this._size = 0;
        this.compare = compare;
        this.tree = new RBTree(compare);
        for (const val of collection) this.add(val);
    }

    size(): number {
        return this._size;
    }

    has(val: T): boolean {
        return !!this.tree.find(val);
    }

    add(val: T): boolean {
        const successful = this.tree.insert(val);
        this._size += successful ? 1 : 0;
        return successful;
    }

    delete(val: T): boolean {
        const deleted = this.tree.deleteAll(val);
        this._size -= deleted ? 1 : 0;
        return deleted;
    }

    ceil(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(p.data, val) >= 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    floor(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(val, p.data) >= 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    higher(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(val, p.data) < 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    lower(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(p.data, val) < 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    first(): T | undefined {
        return this.tree.inOrder().next().value;
    }

    last(): T | undefined {
        return this.tree.reverseInOrder().next().value;
    }

    shift(): T | undefined {
        const first = this.first();
        if (first === undefined) return undefined;
        this.delete(first);
        return first;
    }

    pop(): T | undefined {
        const last = this.last();
        if (last === undefined) return undefined;
        this.delete(last);
        return last;
    }

    *[Symbol.iterator](): Generator<T, void, void> {
        for (const val of this.values()) yield val;
    }

    *keys(): Generator<T, void, void> {
        for (const val of this.values()) yield val;
    }

    *values(): Generator<T, undefined, void> {
        for (const val of this.tree.inOrder()) yield val;
        return undefined;
    }

    /**
     * Return a generator for reverse order traversing the set
     */
    *rvalues(): Generator<T, undefined, void> {
        for (const val of this.tree.reverseInOrder()) yield val;
        return undefined;
    }
}

/**
 * Your ExamRoom object will be instantiated and called as such:
 * var obj = new ExamRoom(n)
 * var param_1 = obj.seat()
 * obj.leave(p)
 */

855. Exam Room

Description

Solutions

Solution 1: Ordered Set + Hash Table

Comments