基本概念
二叉树：树的每个节点最多只能有两个子节点
如果我们给二叉树加一个额外的条件，就可以得到一种被称作二叉搜索树(binary search tree)的特殊二叉树。
二叉搜索树要求：若它的左子树不空，则左子树上所有结点的值均小于它的根结点的值； 若它的右子树不空，则右子树上所有结点的值均大于它的根结点的值； 它的左、右子树也分别为二叉排序树。
完整的BinaryTree代码
Node.java
package com.lwl.tree;
public class Node {
int data; //节点数据
Node leftChild; //左子节点的引用
Node rightChild; //右子节点的引用
boolean isDelete;//表示节点是否被删除
public Node(int data){
this.data = data;
}
//打印节点内容
public void display(){
System.out.println(data);
}
}
Tree.java
package com.lwl.tree;
/**
* @author liuweilong
*
*/
public interface Tree {
//查找节点
public Node find(int key);
//插入新节点
public boolean insert(int data);
//中序遍历
public void infixOrder(Node current);
//前序遍历
public void preOrder(Node current);
//后序遍历
public void postOrder(Node current);
//查找最大值
public Node findMax();
//查找最小值
public Node findMin();
//删除节点
public boolean delete(int key);
//Other Method......
}
BinaryTree.java
package com.lwl.tree;
/**
* @author liuweilong
*
*/
public class BinaryTree implements Tree {
//表示根节点
private Node root;
//查找节点
public Node find(int key) {
Node current = root;
while(current != null){
if(current.data > key){//当前值比查找值大，搜索左子树
current = current.leftChild;
}else if(current.data < key){//当前值比查找值小，搜索右子树
current = current.rightChild;
}else{
return current;
}
}
return null;//遍历完整个树没找到，返回null
}
//插入节点
public boolean insert(int data) {
Node newNode = new Node(data);
if(root == null){//当前树为空树，没有任何节点
root = newNode;
return true;
}else{
Node current = root;
Node parentNode = null;
while(current != null){
parentNode = current;
if(current.data > data){//当前值比插入值大，搜索左子节点
current = current.leftChild;
if(current == null){//左子节点为空，直接将新值插入到该节点
parentNode.leftChild = newNode;
return true;
}
}else{
current = current.rightChild;
if(current == null){//右子节点为空，直接将新值插入到该节点
parentNode.rightChild = newNode;
return true;
}
}
}
}
return false;
}
//中序遍历
public void infixOrder(Node current){
if(current != null){
infixOrder(current.leftChild);
System.out.print(current.data+" ");
infixOrder(current.rightChild);
}
}
//前序遍历
public void preOrder(Node current){
if(current != null){
System.out.print(current.data+" ");
infixOrder(current.leftChild);
infixOrder(current.rightChild);
}
}
//后序遍历
public void postOrder(Node current){
if(current != null){
infixOrder(current.leftChild);
infixOrder(current.rightChild);
System.out.print(current.data+" ");
}
}
//找到最大值
public Node findMax(){
Node current = root;
Node maxNode = current;
while(current != null){
maxNode = current;
current = current.rightChild;
}
return maxNode;
}
//找到最小值
public Node findMin(){
Node current = root;
Node minNode = current;
while(current != null){
minNode = current;
current = current.leftChild;
}
return minNode;
}
@Override
public boolean delete(int key) {
Node current = root;
Node parent = root;
boolean isLeftChild = false;
//查找删除值，找不到直接返回false
while(current.data != key){
parent = current;
if(current.data > key){
isLeftChild = true;
current = current.leftChild;
}else{
isLeftChild = false;
current = current.rightChild;
}
if(current == null){
return false;
}
}
//如果当前节点没有子节点
if(current.leftChild == null && current.rightChild == null){
if(current == root){
root = null;
}else if(isLeftChild){
parent.leftChild = null;
}else{
parent.rightChild = null;
}
return true;
//当前节点有一个子节点，右子节点
}else if(current.leftChild == null && current.rightChild != null){
if(current == root){
root = current.rightChild;
}else if(isLeftChild){
parent.leftChild = current.rightChild;
}else{
parent.rightChild = current.rightChild;
}
return true;
//当前节点有一个子节点，左子节点
}else if(current.leftChild != null && current.rightChild == null){
if(current == root){
root = current.leftChild;
}else if(isLeftChild){
parent.leftChild = current.leftChild;
}else{
parent.rightChild = current.leftChild;
}
return true;
}else{
//当前节点存在两个子节点
Node successor = getSuccessor(current);
if(current == root){
successor = root;
}else if(isLeftChild){
parent.leftChild = successor;
}else{
parent.rightChild = successor;
}
successor.leftChild = current.leftChild;
}
return false;
}
public Node getSuccessor(Node delNode){
Node successorParent = delNode;
Node successor = delNode;
Node current = delNode.rightChild;
while(current != null){
successorParent = successor;
successor = current;
current = current.leftChild;
}
//后继节点不是删除节点的右子节点，将后继节点替换删除节点
if(successor != delNode.rightChild){
successorParent.leftChild = successor.rightChild;
successor.rightChild = delNode.rightChild;
}
return successor;
}
public static void main(String[] args) {
BinaryTree bt = new BinaryTree();
bt.insert(50);
bt.insert(20);
bt.insert(80);
bt.insert(10);
bt.insert(30);
bt.insert(60);
bt.insert(90);
bt.insert(25);
bt.insert(85);
bt.insert(100);
bt.delete(10);//删除没有子节点的节点
bt.delete(30);//删除有一个子节点的节点
bt.delete(80);//删除有两个子节点的节点
System.out.println(bt.findMax().data);
System.out.println(bt.findMin().data);
System.out.println(bt.find(100));
System.out.println(bt.find(200));
}
}