Stack 栈

  • 线性结构, 仅能够在栈顶进行操作
  • 先进后出 First In Last Out
  • 实现方式: 数组、链表
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class Stack {
  constructor() {
    this.stack = []
  }
  // 进栈
  push(item) {
    this.stack.push(item)
  }
  // 出栈
  pop() {
    return this.stack.pop()
  }
  // 栈顶元素
  top() {
    return this.stack[this.size() - 1]
  }
  // 栈尾元素
  end() {
    return this.stack[0]
  }
  // 栈的大小
  size() {
    return this.stack.length
  }
  // 清空栈
  clear() {
    this.stack = []
  }
  // 栈是否为空
  isEmpty() {
    return this.size() === 0
  }
}

括号合法性

编辑器代码检测 Vue模板解析

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function isLegalBracket(str) {
  let stack = new Stack()
  for (const item of str) {
    if (item === '(') {
      stack.push(item)
    } else if (item === ')') {
      if (stack.isEmpty()) {
        return '不合法'
      }
      stack.pop()
    }
  }
  return stack.isEmpty() ? '合法' : '不合法'
}

function isLegalBrackets(str) {
  const map = {
    '(': -1,
    ')': 1,
    '[': -2,
    ']': 2,
    '{': -3,
    '}': 3
  }
  let stack = new Stack()
  for (const item of str) {
    if (map[item] < 0) {
      stack.push(item)
    } else {
      if (stack.pop() + map[item] !== 0) return false
    }
  }
  return stack.isEmpty()
}

两个队列实现一个栈

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class QueueStack {

  constructor() {
    this.dataQueue = new Queue()
    this.emptyQueue = new Queue()
  }

  push(item) {
    this.dataQueue.enqueue(item)
  }

  pop() {
    while (this.dataQueue.size() > 1) {
      this.emptyQueue.enqueue(this.dataQueue.dequeue())
    }
    let item = this.dataQueue.dequeue()
    [this.dataQueue, this.emptyQueue] = [this.emptyQueue, this.dataQueue]
    return item
  }

  top() {
    return this.dataQueue.tail()
  }

  end() {
    return this.dataQueue.head()
  }
}

Queue 队列

  • 线性结构, 队头删除元素, 队尾添加元素
  • 先进先出 First In First Out
  • 实现方式: 数组、链表
  • 常应用于: Kafka RabbitMQ Socket

单链队列

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class Queue {
  constructor() {
    this.queue = []
  }
  // 队尾添加元素
  enqueue(item) {
    this.queue.push(item)
  }
  // 队头删除元素
  dequeue() {
    return this.queue.shift()
  }
  // 头部元素
  head() {
    return this.queue[0]
  }
  // 尾部元素
  tail() {
    return this.queue[this.size() - 1]
  }
  // 队列大小
  size() {
    return this.queue.length
  }
  // 清空队列
  clear() {
    this.queue = []
  }
  // 队列是否为空
  isEmpty() {
    return this.size() === 0
  }
}

出队 时间复杂度 O(n)

斐波那契数列

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function fibonacci(n) {
  if (n === 1 || n === 2) return 1
  let queue = new Queue()

  let index = 2
  queue.enqueue(1)
  queue.enqueue(1)
  while (index < n) {
    let delItem = queue.dequeue()
    let headItem = queue.head()

    queue.enqueue(delItem + headItem)

    ++index
  }
  queue.dequeue()
  return queue.head()
}

两个栈实现一个队列

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function StackQueue() {

  constructor() {
    this.dataStack = new Stack()
    this.emptyStack = new Stack()
  }

  enqueue(item) {
    this.dataStack.push(item)
  }

  dequeue() {
    while (this.dataStack.size() > 1) {
      this.emptyStack.push(this.dataStack.pop())
    }
    let item = this.dataStack.pop()
    while (!this.emptyStack.isEmpty()) {
      this.dataStack.push(this.emptyStack.pop())
    }
    return item
  }

  head() {
    return this.dataStack.end()
  }

  tail() {
    return this.dataStack.top()
  }
}

function StackQueueOptimize() {

  constructor() {
    this.enqueueStack = new Stack()
    this.dequeueStack = new Stack()
  }

  initStack() {
    if (this.dequeueStack.isEmpty()) {
      while (!this.enqueueStack.isEmpty()) {
        this.dequeueStack.push(this.enqueueStack.pop())
      }
    }
  }

  enqueue(item) {
    this.enqueueStack.push(item)
  }

  dequeue() {
    this.initStack()
    return this.dequeueStack.pop()
  }

  head() {
    this.initStack()
    return this.dequeueStack.top()
  }

  tail() {
    if (this.enqueueStack.isEmpty()) {
      while (!this.dequeueStack.isEmpty()) {
        this.enqueueStack.push(this.dequeueStack.pop())
      }
    }
    return this.enqueueStack.top()
  }
}

循环队列

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class SqQueue {
  constructor(length) {
    this.queue = new Array(length + 1)
  }
  ...
}

出队 时间复杂度 O(1)

  • 线性结构 单链表、双向链表、循环链表
  • 递归结构

单向链表

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class Node {
  constructor(data, next = null) {
    this.data = data
    this.next = next
  }
}
class LinkList {
  constructor() {
    this.length = 0
    this.head = null
    this.tail = null
  }

  append(data) {
    let newNode = new Node(data)
    if (this.head === null ) {
      this.head = newNode
      this.tail = newNode
    } else {
      this.tail.next = newNode
      this.tail = newNode
    }
    this.length += 1
    return newNode
  }

  print() {
    let currNode = this.head
    while (currNode) {
      console.log(currNode.data)
      currNode = currNode.next
    }
  }

  get(index) {
    let node = this.getNode(index)
    return node && node.data
  }

  getNode(index) {
    if (index < 0 || index >= length) return null
    let currNode = this.head
    while (index-- > 0) {
      currNode = currNode.next
    }
    return currNode
  }

  insert(index, data) {
    if (index < 0 || index > length) return null
    if (index === this.length) {
      return this.append(data)
    } else {
      let newNode = new Node(data)
      if (index === 0) {
        newNode.next = this.head
        this.head = newNode
      } else {
        let prevNode = this.getNode(index - 1)
        newNode.next = prevNode.next
        prevNode.next = newNode
      }
      this.length += 1
      return newNode
    }
  }

  remove(index) {
    if (index < 0 || index >= length) return null
    let delNode = null
    if (index === 0) {
      delNode = this.head
      this.head = this.head.next
      if (this.head === null) {
        this.tail = null
      }
    } else {
      let prevNode = this.getNode(index - 1)
      delNode = prevNode.next
      if (delNode.next === null) {
        tail = prevNode
      } else {
        prevNode.next = prevNode.next.next
      }
    }
    this.length -= 1
    delNode.next = null
    return delNode.data
  }

  indexOf(data) {
    let index = -1
    let currNode = this.head
    while (currNode) {
      index += 1
      if (currNode.data === data) {
        return index
      } else {
        currNode = currNode.next
      }
    }
    return -1
  }

  clear() {
    this.length = 0
    this.head = null
    this.tail = null
  }

  isEmpty() {
    return this.length === 0
  }
}

function createLinkList(arr) {
  let head = null
  const length = arr.length
  for (let i = length - 1; i >= 0; i--) {
    const node = new Node(arr[i])
    node.next = head
    head = node
  }
  return head
}

反转链表

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function reverseLinkList(linkNode) {
  let head = linkNode
  let nextNode = linkNode.next

  head.next = null

  while (nextNode) {
    let temp = nextNode.next
    nextNode.next = head
    head = nextNode
    nextNode = temp
  }
  return head
}

function reverseLinkList(linkNode) {
  let prevNode = null
  let currNode = null
  let nextNode = linkNode

  while (nextNode) {
    if (curNode && !prevNode) {
      delete curNode.next
    }

    if (prevNode && currNode) {
      currNode.next = prevNode
    }
    prevNode = currNode
    currNode = nextNode
    nextNode = nextNode.next
  }

  currNode.next = prevNode
  return currNode
}

const arr = [100, 200, 300, 400, 500]
const linkList = createLinkList(arr)
console.log(linkList, reverseLinkList(linkList))

双向链表

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class Node {
  constructor({data, prev = null, next = null}) {
    this.data = data
    this.prev = prev
    this.next = next
  }
}

Tree 树

  • 递归结构

二叉树

  • 完全二叉树
  • 满二叉树
  • 在二叉树的第 i(i >=1 ) 层, 最多有 2^(i - 1) 个节点
  • 深度为 k(k >= 0) 的二叉树, 最少有 k 个节点
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class BinTreeNode {
  constructor(data) {
    this.data = data
    this.leftChild = null
    this.rightChild = null
    this.parentChild = null
  }
}
class BinaryTree {
  constructor(str) {
    this.root = null
  }

  initTree(str) { /* 二叉树的广义表 */
    let stack = new Stack()
    let k = 0
    let newNode = null
    for (const item of str) {
      if (item === '#') {
        break
      }
      switch (item) {
        case '(':
          stack.push(newNode)
          k = 1
          break
        case ',':
          k = 2
          break
        case ')':
          stack.pop()
          break
        default:
          newNode = new BinTreeNode(item)
          if (this.root === null) {
            this.root = newNode
          } else {
            let topItem = stack.top()
            if (k === 1) {
              topItem.leftChild = newNode
            } else if (k === 2) {
              topItem.rightChild = newNode
            }
            newNode.parentNode = topItem
          }
          break
      }
    }
  }

  /* 递归 */
  prevOrderRecursion(node = this.root) {
    if (node === null) return
    console.log(node.data)
    this.prevOrderRecursion(node.leftChild)
    this.prevOrderRecursion(node.rightChild)
  }
  // 前序遍历
  preOrder(node = this.root) {
    let stack = new Stack()
    let currNode = node
    while (currNode) {
      console.log(currNode.data)
      if (currNode.rightChild) {
        stack.push(currNode.rightChild)
      }
      if (currNode.leftChild) {
        currNode = currNode.leftChild
      } else {
        currNode = stack.pop()
      }
    }
  }

  /* 递归 */
  inOrderRecursion(node = this.root) {
    if (node === null) return
    this.inOrderRecursion(node.leftChild)
    console.log(node.data)
    this.inOrderRecursion(node.rightChild)
  }
  // 中序遍历
  inOrder(node = this.root) {
    let stack = new Stack()
    let currNode = node
    while (true) {
      while (currNode) {
        stack.push(currNode)
        currNode = currNode.leftChild
      }
      let popItem = stack.pop()
      console.log(popItem.data)
      currNode = popItem.rightChild
      if (!currNode && stack.isEmpty()) break
    }
  }

  /* 递归 */
  postOrderRecursion(node = this.root) {
    if (node === null) return
    this.postOrderRecursion(node.leftChild)
    this.postOrderRecursion(node.rightChild)
    console.log(node.data)
  }
  // 后序遍历
  postOrder(node = this.root) {
    const Tag = function(node, state) {
      this.node = node
      this.state = state
    }
    let stack = new Stack()
    let currNode = node
    while (true) {
      while (currNode) {
        let tag = new Tag(currNode, 0)
        stack.push(tag)
        currNode = currNode.leftChild
      }
      let popItem = stack.pop()
      if (popItem.node.rightChild && popItem.state === 0) {
        popItem.state = 1
        stack.push(popItem)
        currNode = popItem.node.rightChild
      } else {
        console.log(popItem.node.data)
      }
      if (!currNode && stack.isEmpty()) break
    }
  }

  // 树的节点数量
  treeNodeCount(node) {
    if (node === null) return 0
    let leftNodeCount = this.treeNodeCount(node.leftChild)
    let rightNodeCount = this.treeNodeCount(node.rightChild)
    return leftNodeCount + rightNodeCount + 1
  }
  size() {
    return this.treeNodeCount(this.root)
  }

  // 树的高度
  treeHeight(node) {
    if (node === null) return 0
    let leftChildHeight = this.treeHeight(node.leftChild)
    let rightChildHeight = this.treeHeight(node.rightChild)
    return Math.max(leftChildHeight, rightChildHeight) + 1
  }
  height() {
    return this.treeHeight(this.root)
  }

  // 查找节点
  findNode(node, data) {
    if (node === null) return null
    if (node.data === data) return node
    return this.findNode(node.leftChild, data) || this.findNode(node.rightChild, data)
  }
  find(data) {
    this.findNode(this.root, data)
  }

  // 树的镜像
  mirror(node = this.root) {
    this.mirror1(node)
    // this.mirror2(node)
  }
  mirror1(node) {
    if (node === null) return
    [node.leftChild, node.rightChild] = [node.rightChild, node.leftChild]
    this.mirror1(node.leftChild)
    this.mirror1(node.rightChild)
  }
  mirror2(node) {
    if (node === null) return
    let left = this.mirror2(node.leftChild)
    let right = this.mirror2(node.rightChild)
    node.leftChild = right
    node.rightChild = left
  }
}
//           A
//        /     \
//       B       C
//     /   \    /   \
//    D     E  F     G
//         / \  \   /
//        H   I  J K

// 中序遍历 D B H E I A F J C K G
// 前序遍历 A B D E H I C F J G K
// 后序遍历 D H I E B J F K G C A
let bt = new BinaryTree()
bt.initTree('A(B(D,E(H,I)),C(F(,J),G(K)))#')
bt.mirror()
bt.inOrder()

BST 二叉搜索树

  • 左 < 根 < 右

寻找 BST 第 K 小值问题，使用中序遍历，二分算法，正好是按照从小到大排序的

AVL 树

平衡二叉树 BBT
避免二叉树变成链表, 降低效率

  • 左单旋转: 不平衡节点平衡因子为2, 其右孩子平衡因子为1
  • 右单旋转: 不平衡节点平衡因子为-2, 其左孩子平衡因子为-1
  • 先左后右双旋转: 不平衡节点平衡因子为-2, 左孩子平衡因子为1
  • 先右后左双旋转: 不平衡节点平衡因子为2, 右孩子平衡因子为-1

红黑树

一种自动平衡的二叉树

B 树

物理上是多叉树，但逻辑上是一个 BST
用于高效 I/O，关系型数据库

Heap 堆

  • 时间复杂度 O(logn)
  • 节点的值，总是不大于（或不小于）父节点的值
  • 逻辑结构是一颗完全二叉树
  • 物理结构是一个数组 (连续存储 节省空间)
  • 查找比BST慢，增删比BST快

最大堆

最小堆

UFSets 并查集