#include <math.h>
#include <vector>
using namespace std;
#define max(a,b)  ((a)>(b)?(a):(b))
template<typename E>
class AVL_TMP
{ 
 template <typename E>
 class AVL_NODE
 {
 public:
  AVL_NODE():ln(0),rn(0),depth(0){}
  AVL_NODE( const E& e):data(e),ln(0),rn(0),depth(0){}
  ~AVL_NODE(){ if (ln) delete ln; if (rn) delete rn; }

  bool operator < (E& e){  return data < e; }
  bool operator > (E& e){  return data > e; }
  bool operator == (E& e){ return data == e; }
  bool operator != (E& e){ return data != e; }

  E getdata(){return data;}
  
  E data;
  int depth;
  AVL_NODE<E> *ln,*rn;
 };
 
public: 
 typedef E dataType;
 typedef AVL_TMP<E> Myt;
 typedef AVL_NODE<E> n;
 typedef n* npos;
 typedef npos iterator;
 enum unbalanceType {LL,RR,LR,RL};
 AVL_TMP():root(0),size(0),depth(-1){}
 ~AVL_TMP(){ if(root) delete root; }

 iterator begin(){return root;}
 bool insert(const E& e);
 npos find(const E& e);
 npos findpre(const E& e);
 bool del(dataType);
 bool balance(AVL_TMP<E>::iterator pos){
  if(pos == NULL) throw 0;
  int lh,rh;
  if(pos->ln == NULL ) lh = -1;
  else lh = pos->ln->depth;
  if(pos->rn == NULL ) rh = -1;
  else rh = pos->rn->depth;
  return abs( lh - rh ) < 2 ;
 }
 virtual void frontOrder(){};
 virtual void midOrder(){ };

protected:
 void LLr(AVL_TMP<E>::iterator pos,AVL_TMP<E>::iterator prePos);
 void LRr(AVL_TMP<E>::iterator pos,AVL_TMP<E>::iterator prePos);
 void RRr(AVL_TMP<E>::iterator pos,AVL_TMP<E>::iterator prePos);
 void RLr(AVL_TMP<E>::iterator pos,AVL_TMP<E>::iterator prePos);
 void updateDepth(AVL_TMP<E>::iterator pos);
 bool delAux(E const& e,AVL_TMP<E>::iterator pos = NULL);
 iterator findMax(iterator );
 iterator findMin(iterator );
 bool upTree(int iDepth,iterator itRoot,unsigned long iSize){depth = iDepth;root = itRoot;size = iSize; return true;}
 bool upRoutineDepth(vector<iterator>&);
 bool adjust(iterator a,iterator b,iterator c,iterator prePos = NULL);
 npos root;
 int depth;
 unsigned long size;
};
template<typename E>
bool AVL_TMP<E>::adjust(iterator a,iterator b,iterator c,iterator prePos){
 bool b1,b2;
 b1 = b == a->ln;
 b2 = c == b->ln;
 unbalanceType ub;
 if(b1&&!b2)   ub = LR;
 if(!b1&&b2)   ub = RL;
 if(b1&&b2)    ub = LL;
 if(!b1&&!b2)  ub = RR;
 switch(ub) {
  case  LL :LLr(a,prePos);
   break;
  case  LR :LRr(a, prePos);
   break;
  case  RR :RRr(a,prePos);
   break;
  case  RL :RLr(a,prePos);
   break;
 }  //end switch
 return true;
}
template<typename E>
bool AVL_TMP<E>::upRoutineDepth(vector<iterator>&routine){
 //該函數主要是將路徑節點的深度更新并且使得那些不平衡的節點平衡
 int size = routine.size();
 while (size--) {
  updateDepth(routine[size]);
  if (!balance(routine[size])) {//不平衡得調整
   iterator cur = routine[size],prePos = NULL;
   if(size-1>=0)
    prePos = routine[size-1];
   //檢查當前不平衡節點的哪顆子樹的高度更高
   bool bl = cur->ln != NULL;
   bool br = cur->rn != NULL;
   if (!bl) {//肯定有右孩子
    if(cur->rn->ln) RLr(cur,prePos);
    else RRr(cur,prePos);
   }
   else{//有左孩子
    if (!br) {//沒右孩子
     if (cur->ln->ln) LLr(cur,prePos);
     else LRr(cur,prePos);
    }
    else{ //有右孩子,此時需要檢查左右孩子的高度，則右子樹高度至少為1
     //因此左子樹高度至少為3，則左子樹的節點個數肯定大于4
     if (cur->ln->depth > cur->rn->depth) LLr(cur,prePos);
     else RRr(cur,prePos);
    }
   }
  }
 }
 return true;
}
template<typename E>
AVL_TMP<E>::iterator AVL_TMP<E>::findMax(AVL_TMP<E>::iterator pos){//以pos為根的樹的最大值的節點
 if (!pos) return NULL;
 iterator p = pos;
 while(p->rn) p = p->rn;
 return p;
}
template<typename E>
AVL_TMP<E>::iterator AVL_TMP<E>::findMin(AVL_TMP<E>::iterator pos){
 iterator p = pos;
 while (p->ln) p = p->ln;
 return p;
}
template<typename E>
void AVL_TMP<E>::updateDepth(AVL_TMP<E>::iterator pos){
 bool b1 = pos->ln == NULL,b2 = pos->rn ==NULL;
 switch(b1) {
 case true:
  if(b2) pos->depth = 0;
  else pos->depth = pos->rn->depth+1;
  break;
 default: //false
  if(b2)  pos->depth = pos->ln->depth+1;
  else pos->depth = max(pos->ln->depth , pos->rn->depth )+1;
 }
 if(pos == root) depth = pos->depth;
}
template<typename E>
void AVL_TMP<E>::LLr(AVL_TMP<E>::iterator pos,AVL_TMP<E>::iterator prePos){
 typename AVL_TMP<E>::iterator t, a = pos, b = t = pos->ln ;
 pos->ln = t->rn;
 t->rn = pos;
 if(root == a) root = b;
 if(prePos != NULL)
  if(prePos->ln == a) prePos->ln = b;
  else prePos->rn =  b;
 updateDepth(a);updateDepth(b);
}
template<typename E>
void AVL_TMP<E>::LRr(AVL_TMP<E>::iterator pos,AVL_TMP<E>::iterator prePos){
 AVL_TMP<E>::iterator a = pos,b = pos ->ln, c = b->rn;
 b->rn = c->ln ; a->ln = c->rn;
 c->ln = b;  c->rn =a;
 if(a == root ) root = c ;
 if(prePos != NULL)
  if(prePos->ln == a) prePos->ln = c;
  else prePos->rn =  c;
 updateDepth(a);updateDepth(b);updateDepth(c);
}
template<typename E>
void AVL_TMP<E>::RRr(AVL_TMP<E>::iterator pos,AVL_TMP<E>::iterator prePos ){
 AVL_TMP<E>::iterator a = pos ,t, b = t = pos->rn ;
 pos->rn = t->ln;
 t->ln = pos;
 if(prePos != NULL)
  if(prePos->ln == a) prePos->ln = b;
  else prePos->rn =  b;
 if(root == a) root = b;
 updateDepth(a);updateDepth(b);
}
template<typename E>
void AVL_TMP<E>::RLr(AVL_TMP<E>::iterator pos,AVL_TMP<E>::iterator prePos){
 AVL_TMP<E>::iterator a = pos, b = pos->rn , c = b->ln;
 a->rn = c->ln ;  b->ln = c->rn;
 c->ln = a; c->rn = b;
 if(prePos != NULL)
  if(prePos->ln == a) prePos->ln = c;
  else prePos->rn =  c;
 if( a == root) root = c;
 updateDepth(a);updateDepth(b);updateDepth(c);
}
template<typename E>
bool AVL_TMP<E>::insert(const E& e){
 if(root == NULL) {root = new AVL_NODE<E>(e); size++; depth = root->depth;return true;}
 bool bUpdateDepth = false;
 vector<AVL_TMP<E>::iterator> routin;
 typename AVL_TMP<E>::iterator p = root,pos,prePos;
 for (int i = 0 ; i < size ;i++ ) {
  routin.push_back(p);
  if(p->data > e){
   if ( p->ln == NULL ) {
    p->ln = pos = new AVL_NODE<E>(e);
    bUpdateDepth = p->rn == NULL;
    break;
   }
   else { p = p->ln ; continue;}
  }
  if(p->data  < e){
   if (p->rn == NULL) {
    p->rn = pos = new AVL_NODE<E>(e) ;
    bUpdateDepth = p->ln == NULL;
    break;
   }
   else {  p = p->rn ; continue;}
  }
  return false;   //already exists
 }  //insertion finished
 size++;
 if(size <= 2 ) {
  updateDepth(root);
  return true;
 }
 if(!bUpdateDepth) return true;   //balance
 
 bool unAdjusted = true;
 // check for balance and adjust depth
 for (i = routin.size()-1; i  >=0 ; i-- ) {
  if(!balance(routin.at(i)))
   if(unAdjusted) {  //  unbalance! get unbalance type
    if(i-1 >= 0) prePos = routin.at(i-1);
    else prePos = NULL;
    AVL_TMP<E>::iterator a = routin.at(i) , b = routin.at(i+1) , c;
    if(i+2 >= routin.size() ) c = pos;
    else c = routin.at(i+2);
    bool b1,b2;
    b1 = b == a->ln;
    b2 = c == b->ln;
    unbalanceType ub;
    if(b1&&!b2)   ub = LR;
    if(!b1&&b2)   ub = RL;
    if(b1&&b2)    ub = LL;
    if(!b1&&!b2)  ub = RR;

    switch(ub) {
     case  LL :LLr(routin.at(i),prePos);
      break;
     case  LR :LRr(routin.at(i),prePos);
      break;
     case  RR :RRr(routin.at(i),prePos);
      break;
     case  RL :RLr(routin.at(i),prePos);
      break;
    }  //end switch
    unAdjusted = false;
   }  //end if
 updateDepth(routin.at(i));  //update the depth of the node in the routin
 depth = root->depth;
 }//end for
 return true;
};
template<typename E>
AVL_TMP<E>::npos AVL_TMP<E>::find(const E& e){//search for position
   npos p=root;
   while (p&&p->data!=e)
    if(e>p->data) p=p->rn;
    else p= p->ln;
   return p;
}
template<typename E>
AVL_TMP<E>::npos AVL_TMP<E>::findpre(const E& e){//search for parent node position
   npos p,pre;
   p=pre=root;
   while (p&&p->data!=e) {
    pre = p;
    if (e>p->data) p=p->rn;
    else p = p->ln;
   }
   if(p) if(p->data==e) return NULL;//already existed
   return pre;
}
template<typename E>
bool AVL_TMP<E>::delAux(E const& e,AVL_TMP<E>::iterator pos){
 // 1.遞歸刪除節點，直到刪除的是葉子節點 
 // 2. 刪除葉子節點,更新樹的數據成員
 // 3. 更新路徑上的節點深度并且檢查平衡因子 
 static vector<iterator> routine;
 iterator p = pos;
 bool bUpdate = false;
 if(!pos){//第一次調用
  p = root;
  while (p&&e!=p->data) {//找到節點，并且將尋找路徑存入表中
   routine.push_back(p);
   if(p->data > e) p = p->ln;
   else p = p->rn;
  }
  if(p == NULL){ //沒找到
   routine.clear(); 
   return false;
  }
  else pos = p;
 }
 if (pos->ln||pos->rn) {//不是葉子節點，則該節點有孩子節點，可能是一個或者兩個
  routine.push_back(pos);//還得往下刪除
  if (pos->ln&&!pos->rn){ //情況一: 只有有左孩子
   //找到左子樹中的最大值的位置
   iterator max = pos->ln;
   while (max->rn) { routine.push_back(max); max = max->rn;}
   bUpdate = false;
   //偽刪除
   pos->data = max->data;
   delAux(max->data,max);
  }
  else if (!pos->ln&&pos->rn) { //情況二：只有右孩子
   //找到右子樹中的最小值
   iterator min = pos->rn;
   while (min->ln) { routine.push_back(min); min = min->ln;}
   bUpdate = false;
   //偽刪除
   pos->data = min->data;
   delAux(min->data,min);
  }
  else //情況三：有倆個孩子
  {
   //找到左子樹中的最大值
   iterator max = pos->ln;
   while (max->rn) { routine.push_back(max); max = max->rn;}
   bUpdate = false;
   //偽刪除
   pos->data = max->data;
   delAux(max->data,max);
  }
 }
 else
 {//是葉子節點
  //有三種情況，是其父節點的左子樹且沒有兄弟，是其父節點的右子樹且沒有兄弟，有兄弟
  //取得其父節點
  iterator parent = NULL;
  if (routine.size()) //有父節點
   parent = routine[routine.size()-1];
  else{//即該節點是根節點,無根節點
   delete root;
   routine.clear();
   upTree(-1,NULL,0);
   return true;
  }  //完成根節點的刪除
  //有父節點
  if (pos == parent->ln&&!parent->rn) {//情況一：是父節點的左孩子且沒兄弟
   //刪除節點
   parent->ln = NULL;
   delete pos;
   //需要更新路徑上的節點的深度
   bUpdate = true;
   upRoutineDepth(routine);
   upTree(root->depth,root,size-1);
   routine.clear();
   //改寫父節點的孩子指針
  }//完成情況一葉子節點的刪除
  else{
   if (pos == parent->rn && !parent->ln ) { //情況二：是父節點的右孩子且沒兄弟
    parent->rn = NULL;
    delete pos; 
    bUpdate = true;
    upRoutineDepth(routine);
    upTree(root->depth,root,size-1);
    routine.clear();
   }//完成情況二葉子節點的刪除
   else{//情況三：有兄弟
    //只需要將節點刪除，并清理路徑表就可以了
    if (pos == parent->ln) parent->ln = NULL;
    else parent->rn = NULL;
    delete pos;
    routine.clear();
   }//完成情況三的葉子節點刪除
  }
 }
 return true;
}

template<typename E>
bool AVL_TMP<E>::del(dataType e){
 return delAux(e);
}