伸展树与半伸展树属于自组织的数据结构，能按访问频率调整节点的位置
调整一般通过如下方式：
1）绕根的单旋转，跟AVL的单旋转类似
2）一字型旋转(ZigZig Rotation)
3)之字形旋转(ZigZag Rotation)
旋转操作较简单，有点点繁琐。
半伸展树不做完全的一字型旋转，它只让父节点绕祖父节点做单旋转。
不管怎样，每次访问(插入/查找 ，删除时展开被删除父节点)后把该节点调整到根节点的位置
伸展树代码：
package algorithms.tree;
/**
* @author yovn
*
*/
public class SplayTree<E extends Comparable<E>> extends DefaultBSTree<E> implements BSTree<E> {
static class SplayTreeNode<E extends Comparable<E>> extends BSTNode<E>
{
SplayTreeNode<E> parent;
SplayTreeNode(SplayTreeNode<E> parent,E key) {
super(key);
this.parent=parent;
}
}
@Override
public boolean delete(E ele) {
return _delete((SplayTreeNode<E>)root,ele);
}
private boolean _delete(SplayTreeNode<E> pointer, E ele) {
int cmp=ele.compareTo(pointer.key);
while(cmp!=0)
{
if(cmp<0)
{
pointer=(SplayTreeNode<E>)pointer.left;
}
else
{
pointer=(SplayTreeNode<E>)pointer.right;
}
if(pointer==null)return false;
cmp=ele.compareTo(pointer.key);
}
//okay find it
SplayTreeNode<E> p=pointer.parent;
if(pointer.left==null)
{
if(p!=null)
{
keep_right(pointer);
splay(p);
}
else {
root = p.right;
if(root!=null)((SplayTreeNode<E>)root).parent=null;
}
}
else if(pointer.right==null)
{
if(p!=null)
{
keep_left(pointer);
splay(p);
}
else {
root = p.left;
if(root!=null)((SplayTreeNode<E>)root).parent=null;
}
}
else
{
SplayTreeNode<E> todo=(SplayTreeNode<E>)pointer.left;
SplayTreeNode<E> todoP=null;
while(todo.right!=null)
{
todoP=todo;
todo=(SplayTreeNode<E>)todo.right;
}
pointer.key=todo.key;
if (todoP != null) {
todoP.right = todo.left;
if (todo.left != null)
((SplayTreeNode<E>) todo.left).parent = todoP;
}
else
{
pointer.left=null;
}
splay(pointer.parent);
}
return true;
}
private void keep_left(SplayTreeNode<E> pointer) {
SplayTreeNode<E> p=pointer.parent;
if(p.left==pointer)
{
p.left=pointer.left;
if(p.left!=null)((SplayTreeNode<E>)p.left).parent=p;
}
else if(p.right==pointer)
{
p.right=pointer.left;
if(p.right!=null)((SplayTreeNode<E>)p.right).parent=p;
}
}
private void keep_right(SplayTreeNode<E> pointer) {
SplayTreeNode<E> p=pointer.parent;
if(p.left==pointer)
{
p.left=pointer.right;
if(p.left!=null)((SplayTreeNode<E>)p.left).parent=p;
}
else if(p.right==pointer)
{
p.right=pointer.right;
if(p.right!=null)((SplayTreeNode<E>)p.right).parent=p;
}
}
protected void splay(SplayTreeNode<E> cur) {
if(cur==null)return;
while(cur!=root)
{
if(cur.parent==root)
{
//single Rotation
SingleRotation(cur,cur.parent);
cur.parent=null;
root=cur;
}
else if(cur.parent.left==cur&&cur.parent.parent.left==cur.parent)
{
cur=Left_ZigZig(cur,cur.parent,cur.parent.parent);
}
else if(cur.parent.right==cur&&cur.parent.parent.right==cur.parent)
{
cur=Right_ZigZig(cur,cur.parent,cur.parent.parent);
}
else if(cur.parent.left==cur&&cur.parent.parent.right==cur.parent)
{
cur=RL_ZigZag(cur,cur.parent,cur.parent.parent);
}
else if(cur.parent.right==cur&&cur.parent.parent.left==cur.parent)
{
cur=LR_ZigZag(cur,cur.parent,cur.parent.parent);
}
else
{
System.out.println("Oooops!!!");
}
}
}
private SplayTreeNode<E> LR_ZigZag(SplayTreeNode<E> cur,
SplayTreeNode<E> p, SplayTreeNode<E> g) {
SplayTreeNode<E> gp=g.parent;
g.left=cur.right;
setParent(cur.right,g);
g.parent=cur;
cur.right=g;
p.right=cur.left;
setParent(cur.left,p);
p.parent=cur;
cur.left=p;
if(gp!=null)
{
if(gp.left==g)
{
gp.left=cur;
}
else
{
gp.right=cur;
}
}
else root=cur;
cur.parent=gp;
return cur;
}
private SplayTreeNode<E> RL_ZigZag(SplayTreeNode<E> cur,
SplayTreeNode<E> p, SplayTreeNode<E> g) {
SplayTreeNode<E> gp=g.parent;
g.right=cur.left;
setParent(cur.left,g);
g.parent=cur;
cur.left=g;
p.left=cur.right;
setParent(cur.right,p);
p.parent=cur;
cur.right=p;
if(gp!=null)
{
if(gp.left==g)
{
gp.left=cur;
}
else
{
gp.right=cur;
}
}
else root=cur;
cur.parent=gp;
return cur;
}
protected SplayTreeNode<E> Right_ZigZig(SplayTreeNode<E> cur, SplayTreeNode<E> p,
SplayTreeNode<E> g) {
SplayTreeNode<E> gp=g.parent;
g.right=p.left;
setParent(p.left,g);
p.right=cur.left;
setParent(cur.left,p);
g.parent=p;
p.left=g;
p.parent=cur;
cur.left=p;
if(gp!=null)
{
if(gp.left==g)
{
gp.left=cur;
}
else
{
gp.right=cur;
}
}
else root=cur;
cur.parent=gp;
return cur;
}
protected SplayTreeNode<E> Left_ZigZig(SplayTreeNode<E> cur, SplayTreeNode<E> p,
SplayTreeNode<E> g) {
SplayTreeNode<E> gp=g.parent;
g.left=p.right;
setParent(p.right,g);
g.parent=p;
p.right=g;
p.left=cur.right;
setParent(cur.right,p);
p.parent=cur;
cur.right=p;
if(gp!=null)
{
if(gp.left==g)
{
gp.left=cur;
}
else
{
gp.right=cur;
}
}
else root=cur;
cur.parent=gp;
return cur;
}
final void setParent(BSTNode<E> c, BSTNode<E> p) {
if(c!=null)((SplayTreeNode<E>)c).parent=(SplayTreeNode<E>)p;
}
private void SingleRotation(SplayTreeNode<E> cur, SplayTreeNode<E> p) {
if(p.left==cur)
{
p.left=cur.right;
if(cur.right!=null)((SplayTreeNode<E>)cur.right).parent=p;
cur.right=p;
p.parent=cur;
}
else if(p.right==cur)
{
p.right=cur.left;
if(cur.left!=null)((SplayTreeNode<E>)cur.left).parent=p;
cur.left=p;
p.parent=cur;
}
}
@Override
public void insert(E ele) {
if (root == null) {
root = new SplayTreeNode<E>(null,ele);
return;
}
_insert((SplayTreeNode<E>)root,ele);
}
private final void _insert(SplayTreeNode<E> pointer,E ele)
{
int cmp=pointer.key.compareTo(ele);
if(cmp==0)
{
throw new IllegalArgumentException();
}
if(cmp>0)
{
if(pointer.left==null)
{
pointer.left =new SplayTreeNode<E>(pointer,ele);
splay((SplayTreeNode<E>)pointer.left);
return;
}
_insert((SplayTreeNode<E>)pointer.left,ele);
}
else
{
if(pointer.right==null)
{
pointer.right=new SplayTreeNode<E>(pointer,ele);
splay((SplayTreeNode<E>)pointer.right);
return ;
}
_insert((SplayTreeNode<E>)pointer.right,ele);
}
}
@Override
public boolean search(E ele) {
return _search((SplayTreeNode<E>)root,ele);
}
private boolean _search(SplayTreeNode<E> pointer, E ele) {
if(pointer==null)return false;
int cmp=pointer.key.compareTo(ele);
if(cmp==0)
{
splay(pointer);
return true;
}
if(cmp>0)
{
return _search((SplayTreeNode<E>)pointer.left,ele);
}
else
{
return _search((SplayTreeNode<E>)pointer.right,ele);
}
}
/**
*
*/
public SplayTree() {
}
}
半伸展树仅仅改变一下一字旋转时的操作：
package algorithms.tree;
/**
* @author yovn
*
*/
public class SemiPlayTree<E extends Comparable<E>>extends SplayTree<E> {
@Override
protected algorithms.tree.SplayTree.SplayTreeNode<E> Left_ZigZig(
algorithms.tree.SplayTree.SplayTreeNode<E> cur,
algorithms.tree.SplayTree.SplayTreeNode<E> p,
algorithms.tree.SplayTree.SplayTreeNode<E> g) {
SplayTreeNode<E> gp=g.parent;
g.left=p.right;
setParent(p.right,g);
p.right=g;
g.parent=p;
if(gp!=null)
{
if(gp.left==g)
{
gp.left=p;
}
else
{
gp.right=p;
}
}
else root=p;
p.parent=gp;
return p;
}
@Override
protected algorithms.tree.SplayTree.SplayTreeNode<E> Right_ZigZig(
algorithms.tree.SplayTree.SplayTreeNode<E> cur,
algorithms.tree.SplayTree.SplayTreeNode<E> p,
algorithms.tree.SplayTree.SplayTreeNode<E> g) {
SplayTreeNode<E> gp=g.parent;
g.right=p.left;
setParent(p.left,g);
p.left=g;
g.parent=p;
if(gp!=null)
{
if(gp.left==g)
{
gp.left=p;
}
else
{
gp.right=p;
}
}
else root=p;
p.parent=gp;
return p;
}
}