什么叫二叉查找树
一个节点最多只有左子树和右子树。而且左子树中的节点都小于节点,右子树中的所有节点都大于根节点。
什么叫满二叉树
除了叶子节点外所有节点都有左子树和右子树。而且叶子节点个数满足。假设高度h，则叶子节点个数是2的
（h-1）次方。
如下图：
image.png
什么叫完全二叉树
就是把满二叉树，从上到下从左到右编号1~n。然后完全二叉树有k个节点，k小于n，则1到k的每个节点和满二叉树一一对应。就是完全二叉树
如下图：
image.png
深度遍历（3种）
1 前序遍历
按照满二叉树的编号，1,2,3 1--->2--->3
2 中序遍历，还是按照满二叉树的编号 2--->1--->3
3 后序遍历 2---3---1
如果遇到的是一颗树，那就按照基本的在走一遍。比如前序遍历
image.png
前序遍历：1 2 4 5 7 8 3 6 (优先遍历左子树，然后到叶子节点之后，再回过来遍历，最上层的右子树)
中序遍历：4 2 7 5 8 1 3 6
后序遍历：4 7 8 5 2 6 3 1
层次遍历：1 2 3 4 5 6 7 8
最后上代码，说明BST（二叉查找树）如何进行增删查找。
import java.util.HashMap;
import java.util.Map;
import java.util.Stack;
public class BSTreeComparable<T extends Comparable> {
private transient Node root;
private static final String SUCCESSOR="successor";
private static final String SUCCESSOR_PARENT="parent";
private static final Node EMPTY_NODE = new Node(null,null,null,"empty node");
public BSTreeComparable() { //初始化为一个空树
root = null;
}
/**ConcurrentHashMap
* 查询数据方法
* @param key
* @return
*/
public Node get(T key){
if(root ==null) return null;
Node node = getRecursive(root,key);
if(node ==null) return EMPTY_NODE;
return node;
}
/**
* 递归比较大小，如果小于该节点，则拿左节点继续比较
* 如果大于该节点，就拿右节点继续比较
* @param tree
* @param key
* @return
*/
private Node getRecursive(Node tree,T key){
if(tree==null) return null;
if(key.compareTo(tree.key)<0){
return getRecursive(tree.leftNode,key);
}else if(key.compareTo(tree.key)>0){
return getRecursive(tree.rightNode,key);
}else{
return tree;
}
}
/**
* 往BST中插入数据
* @param key
* @param value
*/
public void put(T key,Object value){
if (root == null){
root = new Node(null,null,key,value);
}else{
putRecursive(root,key,value);
}
}
private Node putRecursive(Node tree,T key,Object value){
if(tree==null) return new Node(null,null,key,value);
if(key.compareTo(tree.key)<0){
tree.leftNode = putRecursive(tree.leftNode,key,value);
}else if(key.compareTo(tree.key)>0){
tree.rightNode = putRecursive(tree.rightNode,key,value);
}else{
tree.content = value;
}
return tree;
}
public void remove(T key){
Node newTree = remove(root,key);
root = newTree;
}
/**
* 从tree中找到这个节点，然后干掉，然后返回一颗新的树
* @param tree
* @param key
* @return
*/
private Node remove(Node tree ,T key){
if(tree==null) return null;
//先递归去找到这个节点
if (key.compareTo(tree.key) < 0) {
tree.leftNode = remove(tree.leftNode, key);
return tree;
}
else if (key.compareTo(tree.key) > 0) {
tree.rightNode = remove(tree.rightNode, key);
return tree;
}// 相等说明已经找到这个节点了
else{
//case 1 假如这个节点左子树为空，则右子树顶包
if (tree.leftNode == null && tree.rightNode!=null) {
Node rightTree = tree.rightNode;
tree=null;
return rightTree;
}
//case 2 假如这个节点右子树为空，则左子树顶包
else if (tree.rightNode == null&& tree.leftNode!=null){
Node leftTree = tree.leftNode;
tree=null;
return leftTree;
//case 3 是叶子节点
}else if(tree.rightNode == null&& tree.leftNode==null){
tree=null; return null;
}
//case 4 假如这个节点左右子树都不为空，则找到右子树种的最小值顶包
else{
Node toBeDeleted = tree;
Map map = getSuccessor(tree.rightNode,null);
Node successor = (Node) map.get(SUCCESSOR);
Node successorParent = (Node) map.get(SUCCESSOR_PARENT);
//如果successorParent是null的话，说明successor就是右节点
if(successorParent==null){
successor.leftNode = toBeDeleted.leftNode;
tree=null;
toBeDeleted =null;
return successor;
}else{
successor.leftNode = toBeDeleted.leftNode;
successor.rightNode = toBeDeleted.rightNode;
successorParent.leftNode =null;
tree=null;
toBeDeleted =null;
return successor;
}
}
}
}
/**
* 返回顶包的节点，右子树的最小值就是继承者
* @param tree
* @param map
* @return
*/
private Map<String,Node> getSuccessor(Node tree,Map<String,Node> map) {
if (map == null) {
map = new HashMap<>();
}
if (tree.leftNode == null){
map.put(SUCCESSOR,tree);
return map;
}
map.put(SUCCESSOR_PARENT,tree);
Map<String,Node> map2 = getSuccessor(tree.leftNode,map);
return map2;
}
public static int getHeight(Node root) {
if (root == null) {
return 0;
}
int leftHeight = 0;//记录左子树的树高
int rightHeight = 0;//记录右子树树高
if (root.leftNode != null) {//左子树不为空
leftHeight += getHeight(root.leftNode) + 1;//实际就是左子树树高的累计，加上root节点，如果不加1，得到的就是最大子树的树高，不好root节点
}
if (root.rightNode != null) {
rightHeight += getHeight(root.rightNode) + 1;
}
return leftHeight >= rightHeight ? leftHeight : rightHeight;
}
public void displayTree(){
Stack globalStack = new Stack();
globalStack.push(root);
int treeHeight = getHeight(root);
int nBlanks = (int) Math.pow(2d,(double)treeHeight);
boolean isRowEmpty = false;
System.out.println("=========================================================================");
while(!isRowEmpty) {
Stack localStack = new Stack();
isRowEmpty = true;
for (int j =0;j<nBlanks;j++) {
System.out.print(" ");
}
while (!globalStack.isEmpty()) {
Node temp = (Node)globalStack.pop();
if (temp!=null) {
System.out.print(temp.key);
localStack.push(temp.leftNode);
localStack.push(temp.rightNode);
if (temp.leftNode != null || temp.rightNode !=null) {
isRowEmpty = false;
}
}
else {
System.out.print("--");
localStack.push(null);
localStack.push(null);
}
for (int j = 0;j<nBlanks*2-2;j++) {
System.out.print(" ");
}
}
System.out.println();
nBlanks /= 2;
while (!localStack.isEmpty()) {
globalStack.push(localStack.pop());
}
}
System.out.println("=========================================================================");
}
static final class Node<T>{
public Node leftNode;
public Node rightNode;
public T key;
public Object content;
public Node(Node leftNode, Node rightNode, T key, Object content) {
this.leftNode = leftNode;
this.rightNode = rightNode;
this.key = key;
this.content = content;
}
}
}
测试类如下图：
public class BSTreeComparableTest {
public static void main(String[] args) {
BSTreeComparable tree = new BSTreeComparable();
tree.put(20,"20");
tree.put(10,"10");
tree.put(7,"7");
tree.put(4,"4");
tree.put(30,"30");
tree.put(40,"40");
tree.put(14,"14");
tree.put(12,"12");
tree.put(15,"15");
//tree.remove(12); //删除叶子节点
//tree.remove(30); //删除有右子树的节点
//tree.remove(7); //删除有左子树的节点
//tree.remove(1); //删除不存在的节点
//tree.remove(10); //删除有左子树和右子树的节点
tree.displayTree();
}
}
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