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 seatsn.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 seatpwill leave the room. It is guaranteed that there will be a student sitting at seatp.
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
104calls will be made toseatandleave.
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.
Python3
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)
Java
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);
*/
C++
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);
*/
Go
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);
*/
TypeScript
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)
*/