JavaScript實現二叉搜索樹

// 創建BinarySearchTree
function BinarySerachTree() {
  // 創建節點構造函數
  function Node(key) {
    this.key = key
    this.left = null
    this.right = null
  }

  // 保存根的屬性
  this.root = null

  // 二叉搜索樹相關的操作方法
  // 向樹中插入數據
  BinarySerachTree.prototype.insert = function (key) {
    // 1.根據key創建對應的node
    var newNode = new Node(key)

    // 2.判斷根節點是否有值
    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.準備向左子樹插入數據
      if (node.left === null) { // 1.1.node的左子樹上沒有內容
        node.left = newNode
      } else { // 1.2.node的左子樹上已經有瞭內容
        this.insertNode(node.left, newNode)
      }
    } else { // 2.準備向右子樹插入數據
      if (node.right === null) { // 2.1.node的右子樹上沒有內容
        node.right = newNode
      } else { // 2.2.node的右子樹上有內容
        this.insertNode(node.right, newNode)
      }
    }
  }

  // 獲取最大值和最小值
  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.如果傳入的node為null那麼, 那麼就退出遞歸
    if (node === null) {
      return false
    }

    // 2.判斷node節點的值和傳入的key大小
    if (node.key > key) { // 2.1.傳入的key較小, 向左邊繼續查找
      return this.searchNode(node.left, key)
    } else if (node.key < key) { // 2.2.傳入的key較大, 向右邊繼續查找
      return this.searchNode(node.right, key)
    } else { // 2.3.相同, 說明找到瞭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
  }

  // 刪除節點
  BinarySerachTree.prototype.remove = function (key) {
    // 1.獲取當前的node
    var node = this.root
    var parent = null

    // 2.循環遍歷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.如果傳入的node為null, 直接退出遞歸.
    if (node === null) return null

    // 2.判斷key和對應node.key的大小
    if (node.key > key) {
      node.left = this.removeNode(node.left, key)

    }
  }

  // 刪除結點
  BinarySerachTree.prototype.remove = function (key) {
    // 1.定義臨時保存的變量
    var current = this.root
    var parent = this.root
    var isLeftChild = true

    // 2.開始查找節點
    while (current.key !== key) {
      parent = current
      if (key < current.key) {
        isLeftChild = true
        current = current.left
      } else {
        isLeftChild = false
        current = current.right
      }

      // 如果發現current已經指向null, 那麼說明沒有找到要刪除的數據
      if (current === null) return false
    }

    // 3.刪除的結點是葉結點
    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.刪除有一個子節點的節點
    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.刪除有兩個節點的節點
    else {
      // 1.獲取後繼節點
      var successor = this.getSuccessor(current)

      // 2.判斷是否是根節點
      if (current == this.root) {
        this.root = successor
      } else if (isLeftChild) {
        parent.left = successor
      } else {
        parent.right = successor
      }

      // 3.將刪除節點的左子樹賦值給successor
      successor.left = current.left
    }

    return true
  }

  // 找後繼的方法
  BinarySerachTree.prototype.getSuccessor = function (delNode) {
    // 1.使用變量保存臨時的節點
    var successorParent = delNode
    var successor = delNode
    var current = delNode.right // 要從右子樹開始找

    // 2.尋找節點
    while (current != null) {
      successorParent = successor
      successor = current
      current = current.left
    }

    // 3.如果是刪除圖中15的情況, 還需要如下代碼
    if (successor != delNode.right) {
      successorParent.left = successor.right
      successor.right = delNode.right
    }
  }

  // 遍歷方法
  //handler為回調函數
  // 先序遍歷
  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)
    }
  }

  // 中序遍歷
  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)
    }
  }

  // 後續遍歷
  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)
    }
  }
  
  /*
  // 測試遍歷結果(inOrderTraversal可以替換成別的遍歷方式)
    resultString = ""
    bst.inOrderTraversal(function (key) {
      resultString += key + " "
    })
    alert(resultString) // 3 5 6 7 8 9 10 11 12 13 14 15 18 20 25 
   */
}