这是BinarySearchTree类的完整实现-
class BinarySearchTree {
constructor() {
//将根元素初始化为null。
this.root = null;
}
insertIter(data) {
let node = new this.Node(data);
//检查树是否为空
if (this.root === null) {
//插入为第一个元素
this.root = node;
return;
}
let currNode = this.root;
while (true) {
if (data < currNode.data) {
//到达叶节点后，在此处设置值
if (currNode.left === null) {
currNode.left = node;
break;
} else {
currNode = currNode.left;
}
} else {
//到达叶节点后，在此处设置值
if (currNode.right === null) {
currNode.right = node;
break;
} else {
currNode = currNode.right;
}
}
}
}
insertRec(data) {
let node = new this.Node(data);
//检查树是否为空
if (this.root === null) {
//插入为第一个元素
this.root = node;
} else {
insertRecHelper(this.root, node);
}
}
searchIter(data) {
let currNode = this.root;
while (currNode !== null) {
if (currNode.data === data) {
//找到了元素！
return true;
} else if (data < currNode.data) {
//向左移动，因为数据小于父级
currNode = currNode.left;
} else {
//向右移动，因为数据大于父级
currNode = currNode.right;
}
}
return false;
}
searchRec(data) {
return searchRecHelper(data, this.root);
}
getMinVal() {
if (this.root === null) {
throw "空树！";
}
let currNode = this.root;
while (currNode.left !== null) {
currNode = currNode.left;
}
return currNode.data;
}
getMaxVal() {
if (this.root === null) {
throw "空树！";
}
let currNode = this.root;
while (currNode.right !== null) {
currNode = currNode.right;
}
return currNode.data;
}
deleteNode(key) {
return !(deleteNodeHelper(this.root, key) === false);
}
inOrder() {
inOrderHelper(this.root);
}
preOrder() {
preOrderHelper(this.root);
}
postOrder() {
postOrderHelper(this.root);
}
}
BinarySearchTree.prototype.Node = class {
constructor(data, left = null, right = null) {
this.data = data;
this.left = left;
this.right = right;
}
};
//帮助方法
function preOrderHelper(root) {
if (root !== null) {
console.log(root.data);
preOrderHelper(root.left);
preOrderHelper(root.right);
}
}
function inOrderHelper(root) {
if (root !== null) {
inOrderHelper(root.left);
console.log(root.data);
inOrderHelper(root.right);
}
}
function postOrderHelper(root) {
if (root !== null) {
postOrderHelper(root.left);
postOrderHelper(root.right);
console.log(root.data);
}
}
function insertRecHelper(root, node) {
if (node.data < root.data) {
//到达叶节点后，在此处设置值
if (root.left === null) {
root.left = node;
} else {
insertRecHelper(root.left, node);
}
} else {
//到达叶节点后，在此处设置值
if (root.right === null) {
root.right = node;
} else {
insertRecHelper(root.right, node);
}
}
}
function searchRecHelper(data, root) {
if (root === null) {
//到达叶子但没有找到它。
return false;
}
if (data < root.data) {
return searchRecHelper(data, root.left);
} else if (data > root.data) {
return searchRecHelper(data, root.right);
}
//这意味着找到的元素返回true；否则，返回true。
}
/**
* Takes root and key and recursively searches for the key.
* If it finds the key, there could be 3 cases:
*
* 1. This node is a leaf node. *
* Example: Removing F
* A
* / \
* B C
* / / \
* D E F
*
* To remove it, we can simply remove its parent's connection to it.
*
* A
* / \
* B C
* / /
* D E
*
* 2. This node is in between the tree somewhere with one child.
*
* Example: Removing B
* A
* / \
* B C
* / / \
* D E F
*
* To remove it, we can simply make the child node replace the parent node in the above connection
* A
* / \
* D C
* / \
* E F
*
* 3. This node has both children. This is a tricky case.
*
* Example: Removing C *
* A
* / \
* B C
* / / \
* D E F
* / / \
* G H I
*
* In this case, we need to find either a successor or a predecessor of the node and replace this node with
* that. For example, If we go with the successor, its successor will be the element just greater than it,
* ie, the min element in the right subtree. So after deletion, the tree would look like:
*
* A
* / \
* B H
* / / \
* D E F
* / \
* G I
*
* To remove this element, we need to find the parent of the successor, break their link, make successor's left
* and right point to current node's left and right. The easier way is to just replace the data from node to be
* deleted with successor and delete the sucessor.
*/
function deleteNodeHelper(root, key) {
if (root === null) {
//空树返回false；
}
if (key < root.data) {
root.left = deleteNodeHelper(root.left, key);
return root;
} else if (key > root.data) {
root.right = deleteNodeHelper(root.right, key);
return root;
} else {
//没有孩子
//情况1-叶子节点
if (root.left === null && root.right === null) {
root = null;
return root;
}
//独生子女案件
if (root.left === null) return root.right;
if (root.right === null) return root.left;
//两个孩子，所以需要找到继任者
let currNode = root.right;
while (currNode.left !== null) {
currNode = currNode.left;
} root.data = currNode.data;
//从右子树中删除该值。
root.right = deleteNodeHelper(root.right, currNode.data);
return root;
}
}