JavaScript实现二叉搜索树（BST）详解

// 创建BinarySearchTree
function BinarySerachTree() {
  // 创建节点构造函数
  function Node(key) {
    this.key = key
    this.left = null
    this.right = null
  }

  // 保存根的属性
  this.root = null

  // 二叉搜索树相关的操作方法
  // 向树中插入数据
  BinarySerachTree.prototype.insert = function (key) {
    // 1.根据key创建对应的node
    var newNode = new Node(key)

    // 2.判断根节点是否有值
    if (this.root === null) {
      this.root = newNode
    } else {
      this.insertNode(this.root, newNode)
    }
  }

  BinarySerachTree.prototype.insertNode = function (node, newNode) {
    if (newNode.key < node.key) { // 1.准备向左子树插入数据
      if (node.left === null) { // 1.1.node的左子树上没有内容
        node.left = newNode
      } else { // 1.2.node的左子树上已经有了内容
        this.insertNode(node.left, newNode)
      }
    } else { // 2.准备向右子树插入数据
      if (node.right === null) { // 2.1.node的右子树上没有内容
        node.right = newNode
      } else { // 2.2.node的右子树上有内容
        this.insertNode(node.right, newNode)
      }
    }
  }

  // 获取最大值和最小值
  BinarySerachTree.prototype.min = function () {
    var node = this.root
    while (node.left !== null) {
      node = node.left
    }
    return node.key
  }

  BinarySerachTree.prototype.max = function () {
    var node = this.root
    while (node.right !== null) {
      node = node.right
    }
    return node.key
  }

  // 搜搜特定的值
  /*
  BinarySerachTree.prototype.search = function (key) {
    return this.searchNode(this.root, key)
  }

  BinarySerachTree.prototype.searchNode = function (node, key) {
    // 1.如果传入的node为null那么, 那么就退出递归
    if (node === null) {
      return false
    }

    // 2.判断node节点的值和传入的key大小
    if (node.key > key) { // 2.1.传入的key较小, 向左边继续查找
      return this.searchNode(node.left, key)
    } else if (node.key < key) { // 2.2.传入的key较大, 向右边继续查找
      return this.searchNode(node.right, key)
    } else { // 2.3.相同, 说明找到了key
      return true
    }
  }
  */
  BinarySerachTree.prototype.search = function (key) {
    var node = this.root
    while (node !== null) {
      if (node.key > key) {
        node = node.left
      } else if (node.key < key) {
        node = node.right
      } else {
        return true
      }
    }
    return false
  }

  // 删除节点
  BinarySerachTree.prototype.remove = function (key) {
    // 1.获取当前的node
    var node = this.root
    var parent = null

    // 2.循环遍历node
    while (node) {
      if (node.key > key) {
        parent = node
        node = node.left
      } else if (node.key < key) {
        parent = node
        node = node.right
      } else {
        if (node.left == null && node.right == null) {

        }
      }
    }
  }

  BinarySerachTree.prototype.removeNode = function (node, key) {
    // 1.如果传入的node为null, 直接退出递归.
    if (node === null) return null

    // 2.判断key和对应node.key的大小
    if (node.key > key) {
      node.left = this.removeNode(node.left, key)

    }
  }

  // 删除结点
  BinarySerachTree.prototype.remove = function (key) {
    // 1.定义临时保存的变量
    var current = this.root
    var parent = this.root
    var isLeftChild = true

    // 2.开始查找节点
    while (current.key !== key) {
      parent = current
      if (key < current.key) {
        isLeftChild = true
        current = current.left
      } else {
        isLeftChild = false
        current = current.right
      }

      // 如果发现current已经指向null, 那么说明没有找到要删除的数据
      if (current === null) return false
    }

    // 3.删除的结点是叶结点
    if (current.left === null && current.right === null) {
      if (current == this.root) {
        this.root == null
      } else if (isLeftChild) {
        parent.left = null
      } else {
        parent.right = null
      }
    }

    // 4.删除有一个子节点的节点
    else if (current.right === null) {
      if (current == this.root) {
        this.root = current.left
      } else if (isLeftChild) {
        parent.left = current.left
      } else {
        parent.right = current.left
      }
    } else if (current.left === null) {
      if (current == this.root) {
        this.root = current.right
      } else if (isLeftChild) {
        parent.left = current.right
      } else {
        parent.right = current.right
      }
    }

    // 5.删除有两个节点的节点
    else {
      // 1.获取后继节点
      var successor = this.getSuccessor(current)

      // 2.判断是否是根节点
      if (current == this.root) {
        this.root = successor
      } else if (isLeftChild) {
        parent.left = successor
      } else {
        parent.right = successor
      }

      // 3.将删除节点的左子树赋值给successor
      successor.left = current.left
    }

    return true
  }

  // 找后继的方法
  BinarySerachTree.prototype.getSuccessor = function (delNode) {
    // 1.使用变量保存临时的节点
    var successorParent = delNode
    var successor = delNode
    var current = delNode.right // 要从右子树开始找

    // 2.寻找节点
    while (current != null) {
      successorParent = successor
      successor = current
      current = current.left
    }

    // 3.如果是删除图中15的情况, 还需要如下代码
    if (successor != delNode.right) {
      successorParent.left = successor.right
      successor.right = delNode.right
    }
  }

  // 遍历方法
  //handler为回调函数
  // 先序遍历
  BinarySerachTree.prototype.preOrderTraversal = function (handler) {
    this.preOrderTranversalNode(this.root, handler)
  }

  BinarySerachTree.prototype.preOrderTranversalNode = function (node, handler) {
    if (node !== null) {
      handler(node.key)
      this.preOrderTranversalNode(node.left, handler)
      this.preOrderTranversalNode(node.right, handler)
    }
  }

  // 中序遍历
  BinarySerachTree.prototype.inOrderTraversal = function (handler) {
    this.inOrderTraversalNode(this.root, handler)
  }

  BinarySerachTree.prototype.inOrderTraversalNode = function (node, handler) {
    if (node !== null) {
      this.inOrderTraversalNode(node.left, handler)
      handler(node.key)
      this.inOrderTraversalNode(node.right, handler)
    }
  }

  // 后续遍历
  BinarySerachTree.prototype.postOrderTraversal = function (handler) {
    this.postOrderTraversalNode(this.root, handler)
  }

  BinarySerachTree.prototype.postOrderTraversalNode = function (node, handler) {
    if (node !== null) {
      this.postOrderTraversalNode(node.left, handler)
      this.postOrderTraversalNode(node.right, handler)
      handler(node.key)
    }
  }
  
  /*
  // 测试遍历结果(inOrderTraversal可以替换成别的遍历方式)
    resultString = ""
    bst.inOrderTraversal(function (key) {
      resultString += key + " "
    })
    alert(resultString) // 3 5 6 7 8 9 10 11 12 13 14 15 18 20 25 
   */
}