Description
You have an infinite number of stacks arranged in a row and numbered (left to right) from 0, each of the stacks has the same maximum capacity.
Implement the DinnerPlates class:
DinnerPlates(int capacity) Initializes the object with the maximum capacity of the stacks capacity.void push(int val) Pushes the given integer val into the leftmost stack with a size less than capacity.int pop() Returns the value at the top of the rightmost non-empty stack and removes it from that stack, and returns -1 if all the stacks are empty.int popAtStack(int index) Returns the value at the top of the stack with the given index index and removes it from that stack or returns -1 if the stack with that given index is empty.
Example 1:
Input
["DinnerPlates", "push", "push", "push", "push", "push", "popAtStack", "push", "push", "popAtStack", "popAtStack", "pop", "pop", "pop", "pop", "pop"]
[[2], [1], [2], [3], [4], [5], [0], [20], [21], [0], [2], [], [], [], [], []]
Output
[null, null, null, null, null, null, 2, null, null, 20, 21, 5, 4, 3, 1, -1]
Explanation:
DinnerPlates D = DinnerPlates(2); // Initialize with capacity = 2
D.push(1);
D.push(2);
D.push(3);
D.push(4);
D.push(5); // The stacks are now: 2 4
1 3 5
﹈ ﹈ ﹈
D.popAtStack(0); // Returns 2. The stacks are now: 4
1 3 5
﹈ ﹈ ﹈
D.push(20); // The stacks are now: 20 4
1 3 5
﹈ ﹈ ﹈
D.push(21); // The stacks are now: 20 4 21
1 3 5
﹈ ﹈ ﹈
D.popAtStack(0); // Returns 20. The stacks are now: 4 21
1 3 5
﹈ ﹈ ﹈
D.popAtStack(2); // Returns 21. The stacks are now: 4
1 3 5
﹈ ﹈ ﹈
D.pop() // Returns 5. The stacks are now: 4
1 3
﹈ ﹈
D.pop() // Returns 4. The stacks are now: 1 3
﹈ ﹈
D.pop() // Returns 3. The stacks are now: 1
﹈
D.pop() // Returns 1. There are no stacks.
D.pop() // Returns -1. There are still no stacks.
Constraints:
1 <= capacity <= 2 * 1041 <= val <= 2 * 1040 <= index <= 105- At most
2 * 105 calls will be made to push, pop, and popAtStack.
Solutions
Solution 1: Stack Array + Ordered Set
We define the following data structures or variables:
capacity: The capacity of each stack;stacks: Stack array, used to store all stacks, each with a maximum capacity of capacity;not_full: Ordered set, used to store the indices of all non-full stacks in the stack array.
For the push(val) operation:
- We first check if
not_full is empty. If it is, it means there are no non-full stacks, so we need to create a new stack and push val into it. At this point, we check if the capacity capacity is greater than 1. If it is, we add the index of this stack to not_full.
- If
not_full is not empty, it means there are non-full stacks. We take out the smallest index index from not_full, and push val into stacks[index]. At this point, if the capacity of stacks[index] equals capacity, we remove index from not_full.
For the popAtStack(index) operation:
- We first check if
index is within the index range of stacks. If it is not, we directly return -1. If stacks[index] is empty, we also directly return -1.
- If
stacks[index] is not empty, we pop the top element val from stacks[index]. If index equals the length of stacks minus 1, it means stacks[index] is the last stack. If it is empty, we loop to remove the index of the last stack from not_full, and remove the last stack from the stack array stacks, until the last stack is not empty, or the stack array stacks is empty. Otherwise, if stacks[index] is not the last stack, we add index to not_full.
- Finally, return
val.
For the pop() operation:
- We directly call
popAtStack(stacks.length - 1).
The time complexity is (n × log n), and the space complexity is O(n). Here, n is the number of operations.
PythonJavaC++GoTypeScript
class DinnerPlates:
def __init__(self, capacity: int):
self.capacity = capacity
self.stacks = []
self.not_full = SortedSet()
def push(self, val: int) -> None:
if not self.not_full:
self.stacks.append([val])
if self.capacity > 1:
self.not_full.add(len(self.stacks) - 1)
else:
index = self.not_full[0]
self.stacks[index].append(val)
if len(self.stacks[index]) == self.capacity:
self.not_full.discard(index)
def pop(self) -> int:
return self.popAtStack(len(self.stacks) - 1)
def popAtStack(self, index: int) -> int:
if index < 0 or index >= len(self.stacks) or not self.stacks[index]:
return -1
val = self.stacks[index].pop()
if index == len(self.stacks) - 1 and not self.stacks[-1]:
while self.stacks and not self.stacks[-1]:
self.not_full.discard(len(self.stacks) - 1)
self.stacks.pop()
else:
self.not_full.add(index)
return val
# Your DinnerPlates object will be instantiated and called as such:
# obj = DinnerPlates(capacity)
# obj.push(val)
# param_2 = obj.pop()
# param_3 = obj.popAtStack(index)(code-box)
class DinnerPlates {
private int capacity;
private List<Deque<Integer>> stacks = new ArrayList<>();
private TreeSet<Integer> notFull = new TreeSet<>();
public DinnerPlates(int capacity) {
this.capacity = capacity;
}
public void push(int val) {
if (notFull.isEmpty()) {
stacks.add(new ArrayDeque<>());
stacks.get(stacks.size() - 1).push(val);
if (capacity > 1) {
notFull.add(stacks.size() - 1);
}
} else {
int index = notFull.first();
stacks.get(index).push(val);
if (stacks.get(index).size() == capacity) {
notFull.pollFirst();
}
}
}
public int pop() {
return popAtStack(stacks.size() - 1);
}
public int popAtStack(int index) {
if (index < 0 || index >= stacks.size() || stacks.get(index).isEmpty()) {
return -1;
}
int val = stacks.get(index).pop();
if (index == stacks.size() - 1 && stacks.get(stacks.size() - 1).isEmpty()) {
while (!stacks.isEmpty() && stacks.get(stacks.size() - 1).isEmpty()) {
notFull.remove(stacks.size() - 1);
stacks.remove(stacks.size() - 1);
}
} else {
notFull.add(index);
}
return val;
}
}
/**
* Your DinnerPlates object will be instantiated and called as such:
* DinnerPlates obj = new DinnerPlates(capacity);
* obj.push(val);
* int param_2 = obj.pop();
* int param_3 = obj.popAtStack(index);
*/(code-box)
class DinnerPlates {
public:
DinnerPlates(int capacity) {
this->capacity = capacity;
}
void push(int val) {
if (notFull.empty()) {
stacks.emplace_back(stack<int>());
stacks.back().push(val);
if (capacity > 1) {
notFull.insert(stacks.size() - 1);
}
} else {
int index = *notFull.begin();
stacks[index].push(val);
if (stacks[index].size() == capacity) {
notFull.erase(index);
}
}
}
int pop() {
return popAtStack(stacks.size() - 1);
}
int popAtStack(int index) {
if (index < 0 || index >= stacks.size() || stacks[index].empty()) {
return -1;
}
int val = stacks[index].top();
stacks[index].pop();
if (index == stacks.size() - 1 && stacks[index].empty()) {
while (!stacks.empty() && stacks.back().empty()) {
notFull.erase(stacks.size() - 1);
stacks.pop_back();
}
} else {
notFull.insert(index);
}
return val;
}
private:
int capacity;
vector<stack<int>> stacks;
set<int> notFull;
};
/**
* Your DinnerPlates object will be instantiated and called as such:
* DinnerPlates* obj = new DinnerPlates(capacity);
* obj->push(val);
* int param_2 = obj->pop();
* int param_3 = obj->popAtStack(index);
*/(code-box)
type DinnerPlates struct {
capacity int
stacks [][]int
notFull *redblacktree.Tree
}
func Constructor(capacity int) DinnerPlates {
return DinnerPlates{capacity: capacity, notFull: redblacktree.NewWithIntComparator()}
}
func (this *DinnerPlates) Push(val int) {
if this.notFull.Size() == 0 {
this.stacks = append(this.stacks, []int{val})
if this.capacity > 1 {
this.notFull.Put(len(this.stacks)-1, nil)
}
} else {
index, _ := this.notFull.Left().Key.(int)
this.stacks[index] = append(this.stacks[index], val)
if len(this.stacks[index]) == this.capacity {
this.notFull.Remove(index)
}
}
}
func (this *DinnerPlates) Pop() int {
return this.PopAtStack(len(this.stacks) - 1)
}
func (this *DinnerPlates) PopAtStack(index int) int {
if index < 0 || index >= len(this.stacks) || len(this.stacks[index]) == 0 {
return -1
}
val := this.stacks[index][len(this.stacks[index])-1]
this.stacks[index] = this.stacks[index][:len(this.stacks[index])-1]
if index == len(this.stacks)-1 && len(this.stacks[index]) == 0 {
for len(this.stacks) > 0 && len(this.stacks[len(this.stacks)-1]) == 0 {
this.notFull.Remove(len(this.stacks) - 1)
this.stacks = this.stacks[:len(this.stacks)-1]
}
} else {
this.notFull.Put(index, nil)
}
return val
}
/**
* Your DinnerPlates object will be instantiated and called as such:
* obj := Constructor(capacity);
* obj.Push(val);
* param_2 := obj.Pop();
* param_3 := obj.PopAtStack(index);
*/(code-box)
class DinnerPlates {
capacity: number;
stacks: number[][];
notFull: TreeSet<number>;
constructor(capacity: number) {
this.capacity = capacity;
this.stacks = [];
this.notFull = new TreeSet<number>();
}
push(val: number): void {
if (this.notFull.size() === 0) {
this.stacks.push([val]);
if (this.capacity > 1) {
this.notFull.add(this.stacks.length - 1);
}
} else {
const index = this.notFull.first()!;
this.stacks[index].push(val);
if (this.stacks[index].length === this.capacity) {
this.notFull.delete(index);
}
}
}
pop(): number {
return this.popAtStack(this.stacks.length - 1);
}
popAtStack(index: number): number {
if (index < 0 || index >= this.stacks.length || this.stacks[index].length === 0) {
return -1;
}
const val = this.stacks[index].pop()!;
if (index === this.stacks.length - 1 && this.stacks[index].length === 0) {
while (this.stacks.length > 0 && this.stacks[this.stacks.length - 1].length === 0) {
this.notFull.delete(this.stacks.length - 1);
this.stacks.pop();
}
} else {
this.notFull.add(index);
}
return val;
}
}
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 DinnerPlates object will be instantiated and called as such:
* var obj = new DinnerPlates(capacity)
* obj.push(val)
* var param_2 = obj.pop()
* var param_3 = obj.popAtStack(index)
*/(code-box)
