Java基础 - 节点自平衡树（Size Balanced Tree，简称SBT）
package com.yc.tree;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;
import java.util.List;
public class SizeBalancedTree >{
public class Node{
//data域：存放数据项
T data;
//size域：存放树的大小（节点数目）
int size;
Node parent;
Node left;
Node right;
public Node(T data, int size, Node parent, Node left, Node right){
this.data = data;
this.size = size;
this.parent = parent;
this.left = left;
this.right = right;
}
public String toString(){
return "[data="+data+",size="+size+"]";
}
}
//根节点
private Node root;
public Node root(){
return root;
}
public SizeBalancedTree(){
root = null;
}
public SizeBalancedTree(T data){
root = new Node(data, 1, null, null, null);
}
/**
* 往根为root的树中插入data
* @param data
* @param root
*/
public void insert(T data){
if(root == null){ //如果根为空
root = new Node(data, 1, null, null, null);
}else{
Node current = root;
Node parent = null;
int result = 0;
while(current != null){
parent = current;
result = data.compareTo(current.data);
if(result > 0){
current = current.right;
}else{
current = current.left;
}
}
Node newNode = new Node(data, 1, parent, null, null);
if(result > 0){
parent.right = newNode;
}else{
parent.left = newNode;
}
ancestorAdd1(newNode);
maintain(newNode);
}
}
private void ancestorAdd1(Node node){
Node current = node;
while(current.parent != null){
current.parent.size += 1;
current = current.parent;
}
}
private void ancestorminu1(Node node){
Node current = node;
while(current.parent != null){
current.parent.size -= 1;
current = current.parent;
}
}
private boolean trueOrFalse(Node node){
Node current = node;
while(current != null){
if(current == root.left){
return false;
}else if(current == root.right){
return true;
}
current = current.parent;
}
return false;
}
private void maintain(Node node) { //node为新添加的节点
if(root == node.parent){
return;
}else{
maintainHelp(root, trueOrFalse(node));
}
}
private void maintainHelp(Node node, boolean flag){ //传过来的node为新添加的节点
if(node != null){
/*Node t = node;
Node l = t.left;
Node r = t.right;*/
if(!flag && node.left != null){ //左边
if((node.right == null && node.left.left != null ) || (node.left.left != null && node.left.left.size > node.right.size)){ //case1
right_rot(node);
}
else if((node.right == null && node.left.right != null ) || (node.left.right != null && node.left.right.size > node.right.size)){//case2
left_rot(node.left);
right_rot(node);
}else{
return;
}
maintainHelp(node.left, false);
maintainHelp(node.right, true);
maintainHelp(node, false);
maintainHelp(node, true);
}else if(flag && node.right != null){ //右边
if((node.left == null && node.right.left != null ) || (node.right.left != null && node.right.left.size > node.left.size)){ //case2*
right_rot(node.right);
left_rot(node);
}
else if((node.left == null && node.right.right != null ) || (node.right.right != null && node.right.right.size > node.left.size)){//case1*
left_rot(node);
}else{
return;
}
maintainHelp(node.left, false);
maintainHelp(node.right, true);
maintainHelp(node, false);
maintainHelp(node, true);
}
}
}
/**
* 从根为node的树中删除数据元素为data的节点
* @param node
* @param data
*/
public void remove(Node node, T data){
Node del = find(data);
if(del != null){
boolean what = trueOrFalse(del);
if(del.left == null && del.right == null){
if(del == root){
root = null;
}else{
ancestorminu1(del);
if(del == del.parent.left){
del.parent.left = null;
}else{
del.parent.right = null;
}
del.parent = null;
maintainHelp(root, what);
}
}else if(del.right != null && del.left == null){
//因为已经平衡，所以要删除的节点del有且仅有一个右子节点
if(root == del){
root = del.right;
del.right.parent = null;
del.right = null;
}else{
ancestorminu1(del);
if(del == del.parent.left){
del.parent.left = del.right;
}else{
del.parent.right = del.right;
}
del.right.parent = del.parent;
del.parent = del.right = null;
maintainHelp(root, what);
}
}else if(del.left != null && del.right == null){
//因为已经平衡，所以要删除的节点del有且仅有一个左子节点
if(root == del){
root = del.left;
del.left.parent = null;
del.left = null;
}else{
ancestorminu1(del);
if(del == del.parent.left){
del.parent.left = del.left;
}else{
del.parent.right = del.left;
}
del.left.parent = del.parent;
del.parent = del.left = null;
maintainHelp(root, what);
}
}else{ //左右子树都不为空
Node preOfDel = pre(del, data);
del.data = preOfDel.data;
ancestorminu1(preOfDel);
preOfDel.parent.left = preOfDel.left;
if(preOfDel.left != null){
preOfDel.left.parent = preOfDel.parent;
}
preOfDel.parent = preOfDel.left = null;
maintainHelp(root, what);
}
}else{
return;
}
}
/**
* 在树中查找键值为data的结点
* @param data
* @return
*/
public Node find(T data){
Node current = root;
if(root == null){
return null;
}else{
int result;
while(current != null){
result = data.compareTo(current.data);
if(result > 0){
current = current.right;
}else if(result < 0){
current = current.left;
}else{
return current;
}
}
}
return null;
}
/**
* 在树中查找排名为k的节点(其实为了更好地操作，我觉得可以在每个节点中存放两个域
* lsize和rsize，分别存放该节点的左子树节点数量和右子树节点数量，但更耗内存)
* @param node
* @param k
* @return
*/
public Node select(Node node, int k){
if(root == null){
try {
throw new Exception("该树为空");
} catch (Exception e) {
e.printStackTrace();
}
}else if(root.size < k){
try {
throw new Exception("该节点不存在一个排名为"+k+"的节点，但存在一个最大排名为"+root.size+"的节点");
} catch (Exception e) {
e.printStackTrace();
}
}else{
if(node != null){
int result;
if(node.left != null){
result = node.left.size + 1;
if(result == k){
return node;
}else if(result < k){
return select(node.right, k - result);
}else{
return select(node.left, k);
}
}else if(node.right != null){
if(k == 1){
return node;
}else{
return select(node.right, k - 1);
}
}else{
return node;
}
}
}
return null;
}
//最大值
public T minData(){
return select(root, 1).data;
}
//最小值
public T maxData(){
return select(root, this.root().size).data;
}
//这里考虑到了要查看排名的数据元素不在树中
public int rank(Node node, T data){
Node p = find(data);
T m = minData();
return data.compareTo(m) < 0 ? 1 : (p == null ? cRank(node, data) + 1 : cRank(node, data));
}
//返回以node为根的树中元素值为data的排名
private int cRank(Node node, T data){
if(node != null){
int result = data.compareTo(node.data);
if(node.left != null && node.right != null){
if(result < 0){
return cRank(node.left, data);
}else if(result > 0){
return cRank(node.left, data) + cRank(node.right, data) + 1;
}
return node.left.size + 1;
}else if(node.right != null && node.left == null){
if(result < 0){
return 0;
}else if(result > 0){
return cRank(node.right, data) + 1;
}
return 1;
}else if(node.left != null && node.right == null){
if(result < 0){
return cRank(node.left, data);
}else if(result > 0){
return cRank(node.left, data) + 1;
}
return cRank(node.left, data) + 1;
}else{
if(result < 0){
return 0;
}else if(result > 0){
return 1;
}
return 1;
}
}
return 0;
}
//以node节点为根某数据元素的前驱
public Node pre(Node node, T data){
Node current = node;
Node preNode = null;
int result;
while(current != null){
result = data.compareTo(current.data);
/*if(result == 0){
return current;
}else*/ if(result > 0){
preNode = current;
current = current.right;
}else{
current = current.left;
}
}
return preNode;
}
//以node节点为根某数据元素的后继
public Node succ(Node node, T data){
Node current = node;
Node preNode = null;
int result;
while(current != null){
result = data.compareTo(current.data);
/*if(result == 0){
return current;
}else */if(result < 0){
preNode = current;
current = current.left;
}else{
current = current.right;
}
}
return preNode;
}
/**
* 右旋(x/y才是关键)
* @param x
* │ │
* x y
* ││ -> ││
* y──┘└─γ α──┘└─x
* ││ ││
* α─┘└─β β─┘└─γ
*
*/
private void right_rot(Node x){
Node y = x.left;
y.parent = x.parent;
if(x.parent != null){
if(x == x.parent.left){
x.parent.left = y;
}else{
x.parent.right = y;
}
}
x.left = y.right;
if(y.right != null){
y.right.parent = x;
}
y.right = x;
x.parent = y;
y.size = x.size;
x.size = (y.left == null ? y.size - 0 - 1 : y.size - y.left.size - 1);
if(root == x){
root = y;
}
}
/**
* 左旋(x/y才是关键)
* @param x
* │ │
* x y
* ││ -> ││
* α──┘└─y x──┘└─γ
* ││ ││
* β─┘└─γ α─┘└─β
*/
private void left_rot(Node x){
Node y = x.right;
y.parent = x.parent;
if(x.parent != null){
if(x == x.parent.left){
x.parent.left = y;
}else{
x.parent.right = y;
}
}
x.right = y.left;
if(y.left != null){
y.left.parent = x;
}
y.left = x;
x.parent = y;
y.size = x.size;
x.size = (y.right == null ? y.size - 0 - 1 : y.size - y.right.size - 1);
if(root == x){
root = y;
}
}
//广度优先遍历
public List breadthFirstSearch(){
return cBreadthFirstSearch(root);
}
private List cBreadthFirstSearch(Node node) {
List nodes = new ArrayList();
Deque deque = new ArrayDeque();
if(node != null){
deque.offer(node);
}
while(!deque.isEmpty()){
Node tmp = deque.poll();
nodes.add(tmp);
if(tmp.left != null){
deque.offer(tmp.left);
}
if(tmp.right != null){
deque.offer(tmp.right);
}
}
return nodes;
}
public static void main(String[] args) {
SizeBalancedTree tree = new SizeBalancedTree();
tree.insert(30);
tree.insert(20);
System.out.println( tree.select(tree.root(), 1) );
tree.insert(40);
tree.insert(10);
tree.insert(26);
tree.insert(35);
tree.insert(45);
tree.insert(8);
tree.insert(15);
tree.insert(23);
tree.insert(32);
tree.insert(27);
tree.insert(37);
tree.insert(21);
tree.insert(24);
System.out.println( tree.breadthFirstSearch());
tree.insert(29);
System.out.println( tree.breadthFirstSearch());
System.out.println( "树中排名第14的元素为："+tree.select(tree.root(), 14) );
System.out.println();
System.out.println( "37的排名为："+tree.rank(tree.root(),37));
System.out.println();
System.out.println( "37的前驱为："+tree.pre(tree.root(), 37));
System.out.println( "36的后继为："+tree.succ(tree.root(), 36));
tree.remove(tree.root(), 26);
System.out.println( tree.breadthFirstSearch());
}
}
测试结果为：
[data=20,size=1]
[[data=30,size=15], [data=20,size=9], [data=40,size=5], [data=10,size=3], [data=26,size=5], [data=35,size=3], [data=45,size=1], [data=8,size=1], [data=15,size=1], [data=23,size=3], [data=27,size=1], [data=32,size=1], [data=37,size=1], [data=21,size=1], [data=24,size=1]]
[[data=26,size=16], [data=20,size=7], [data=35,size=8], [data=10,size=3], [data=23,size=3], [data=30,size=4], [data=40,size=3], [data=8,size=1], [data=15,size=1], [data=21,size=1], [data=24,size=1], [data=27,size=2], [data=32,size=1], [data=37,size=1], [data=45,size=1], [data=29,size=1]]
树中排名第14的元素为：[data=37,size=1]
37的排名为：14
37的前驱为：[data=35,size=8]
36的后继为：[data=37,size=1]
[[data=24,size=15], [data=20,size=6], [data=35,size=8], [data=10,size=3], [data=23,size=2], [data=30,size=4], [data=40,size=3], [data=8,size=1], [data=15,size=1], [data=24,size=1], [data=27,size=2], [data=32,size=1], [data=37,size=1], [data=45,size=1], [data=29,size=1]]
Size Balanced Tree(SBT树)整理
【平衡二叉树】SBT学习笔记
这里有C++和Python源码地址：