Question

1172. 餐盘栈

English Version

题目描述

我们把无限数量 ∞ 的栈排成一行，按从左到右的次序从 0 开始编号。每个栈的的最大容量 capacity 都相同。

实现一个叫「餐盘」的类 DinnerPlates：

• DinnerPlates(int capacity) - 给出栈的最大容量 capacity。
• void push(int val) - 将给出的正整数 val 推入 从左往右第一个 没有满的栈。
• int pop() - 返回 从右往左第一个 非空栈顶部的值，并将其从栈中删除；如果所有的栈都是空的，请返回 -1。
• int popAtStack(int index) - 返回编号 index 的栈顶部的值，并将其从栈中删除；如果编号 index 的栈是空的，请返回 -1。

 

示例：

输入： 
["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],[],[],[],[],[]]
输出：
[null,null,null,null,null,null,2,null,null,20,21,5,4,3,1,-1]

解释：
DinnerPlates D = DinnerPlates(2);  // 初始化，栈最大容量 capacity = 2
D.push(1);
D.push(2);
D.push(3);
D.push(4);
D.push(5);     // 栈的现状为：  2  4
                    1  3  5
                  ﹈ ﹈ ﹈
D.popAtStack(0);   // 返回 2。栈的现状为：    4
                      1  3  5
                      ﹈ ﹈ ﹈
D.push(20);    // 栈的现状为：  20  4
                   1  3  5
                   ﹈ ﹈ ﹈
D.push(21);    // 栈的现状为：  20  4 21
                   1  3  5
                   ﹈ ﹈ ﹈
D.popAtStack(0);   // 返回 20。栈的现状为：     4 21
                        1  3  5
                      ﹈ ﹈ ﹈
D.popAtStack(2);   // 返回 21。栈的现状为：     4
                        1  3  5
                      ﹈ ﹈ ﹈ 
D.pop()      // 返回 5。栈的现状为：    4
                        1  3 
                      ﹈ ﹈  
D.pop()      // 返回 4。栈的现状为：  1  3 
                       ﹈ ﹈   
D.pop()      // 返回 3。栈的现状为：  1 
                       ﹈   
D.pop()      // 返回 1。现在没有栈。
D.pop()      // 返回 -1。仍然没有栈。

 

提示：

• 1 <= capacity <= 20000
• 1 <= val <= 20000
• 0 <= index <= 100000
• 最多会对 push，pop，和 popAtStack 进行 200000 次调用。

解法

方法一：栈数组 + 有序集合

我们定义以下数据结构或变量：

• capacity：每个栈的容量；
• stacks：栈数组，用于存储所有的栈，其中每个栈的最大容量都是 capacity；
• not_full：有序集合，用于存储所有未满的栈在栈数组中的下标。

对于 push(val) 操作：

• 我们首先判断 not_full 是否为空，如果为空，则说明没有未满的栈，需要新建一个栈，然后将 val 压入该栈中，此时判断容量 capacity 是否大于 $1$，如果大于 $1$，则将该栈的下标加入 not_full 中。
• 如果 not_full 不为空，则说明有未满的栈，我们取出 not_full 中最小的下标 index，将 val 压入 stacks[index] 中，此时如果 stacks[index] 的容量等于 capacity，则将 index 从 not_full 中删除。

对于 popAtStack(index) 操作：

• 我们首先判断 index 是否在 stacks 的下标范围内，如果不在，则直接返回 $-1$。如果 stacks[index] 为空，同样直接返回 $-1$。
• 如果 stacks[index] 不为空，则弹出 stacks[index] 的栈顶元素 val。如果 index 等于 stacks 的长度减 $1$，则说明 stacks[index] 是最后一个栈，如果为空，我们循环将最后一个栈的下标从 not_full 中移出，并且在栈数组 stacks 中移除最后一个栈，直到最后一个栈不为空、或者栈数组 stacks 为空为止。否则，如果 stacks[index] 不是最后一个栈，我们将 index 加入 not_full 中。
• 最后返回 val。

对于 pop() 操作：

• 我们直接调用 popAtStack(stacks.length - 1) 即可。

时间复杂度 $(n \times \log n)$，空间复杂度 $O(n)$。其中 $n$ 为操作次数。

from sortedcontainers import SortedSet


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)

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);
 */

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);
 */

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);
 */

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)
 */