#include<iostream>
#include<stdlib.h>
using namespace std;
#define TRUE 1
#define FALSE 0
#define NULL 0
class AVL;
class AVLNODE
{
    friend class AVL;
private:
    int data;
    AVLNODE *left,*right;
    int bf;
};
class AVL
{
private:
    AVLNODE *root;
public:
    AVLNODE *loc,*par;
    AVL()
    {
        root=NULL;
    }
    int insert(int);
    void displayitem();
    void display(AVLNODE *);
    void removeitem(int);
    void remove1(AVLNODE *,AVLNODE *,int);
    void remove2(AVLNODE *,AVLNODE *,int);
    void search(int x);
    void search1(AVLNODE *,int);
};
int AVL::insert(int x)
{
    AVLNODE *a,*b,*c,*f,*p,*q,*y,*clchild,*crchild;
    int found,unbalanced;
    int d;
    if(!root) //special case empty tree
    {
        y=new AVLNODE;
        y->data=x;
        root=y;
        root->bf=0;
        root->left=root->right=NULL;
        return TRUE;
    }
//phase 1:locate insertion point for x.a keeps track of the most
// recent node with balance factor +/-1,and f is the parent of a
// q follows p through the tree.
    f=NULL;
    a=p=root;
    q=NULL;
    found=FALSE;
    while(p&&!found)
    {
        //search for insertion point for x
        if(p->bf)
        {
            a=p;
            f=q;
        }
        if(x<p->data) //take left branch
        {
            q=p;
            p=p->left;
        }
        else if(x>p->data)
        {
            q=p;
            p=p->right;
        }
        else
        {
            y=p;
            found=TRUE;
        }
    } //end while
//phase 2:insert and rebalance.x is not in the tree and
// may be inserted as the appropriate child of q.
    if(!found)
    {
        y = new AVLNODE;
        y->data=x;
        y->left=y->right=NULL;
        y->bf=0;
        if(x<q->data) //insert as left child
            q->left=y;
        else
            q->right=y; //insert as right child
//adjust balance factors of nodes on path from a to q
//note that by the definition of a,all nodes on this
//path must have balance factors of 0 and so will change
//to +/- d=+1 implies that x is inserted in the left
// subtree of a d=-1 implies
//to that x inserted in the right subtree of a.
        if(x>a->data)
        {
            p=a->right;
            b=p;
            d=-1;
        }
        else
        {
            p=a->left;
            b=p;
            d=1;
        }
        while(p!=y)
            if(x>p->data) //height of right increases by 1
            {
                p->bf=-1;
                p=p->right;
            }
            else //height of left increases by 1
            {
                p->bf=1;
                p=p->left;
            }
//is tree unbalanced
        unbalanced=TRUE;
        if(!(a->bf)||!(a->bf+d))
        {
            //tree still balanced
            a->bf+=d;
            unbalanced=FALSE;
        }
        if(unbalanced) //tree unbalanced,determine rotation type
        {
            if(d==1)
            {
                //left imbalance
                if(b->bf==1) //rotation type LL
                {
                    a->left=b->right;
                    b->right=a;
                    a->bf=0;
                    b->bf=0;
                }
                else //rotation type LR
                {
                    c=b->right;
                    b->right=c->left;
                    a->left=c->right;
                    c->left=b;
                    c->right=a;
                    switch(c->bf)
                    {
                    case 1:
                        a->bf=-1; //LR(b)
                        b->bf=0;
                        break;
                    case -1:
                        b->bf=1; //LR(c)
                        a->bf=0;
                        break;
                    case 0:
                        b->bf=0; //LR(a)
                        a->bf=0;
                        break;
                    }
                    c->bf=0;
                    b=c; //b is the new root
                } //end of LR
            } //end of left imbalance
            else //right imbalance
            {
                if(b->bf==-1) //rotation type RR
                {
                    a->right=b->left;
                    b->left=a;
                    a->bf=0;
                    b->bf=0;
                }
                else //rotation type LR
                {
                    c=b->right;
                    b->right=c->left;
                    a->right=c->left;
                    c->right=b;
                    c->left=a;
                    switch(c->bf)
                    {
                    case 1:
                        a->bf=-1; //LR(b)
                        b->bf=0;
                        break;
                    case -1:
                        b->bf=1; //LR(c)
                        a->bf=0;
                        break;
                    case 0:
                        b->bf=0; //LR(a)
                        a->bf=0;
                        break;
                    }
                    c->bf=0;
                    b=c; //b is the new root
                } //end of LR
            }
//subtree with root b has been rebalanced and is the new subtree
            if(!f)
                root=b;
            else if(a==f->left)
                f->left=b;
            else if(a==f->right)
                f->right=b;
        } //end of if unbalanced
        return TRUE;
    } //end of if(!found)
    return FALSE;
} //end of AVL INSERTION
void AVL::displayitem()
{
    display(root);
}
void AVL::display(AVLNODE *temp)
{
    if(temp==NULL)
        return;
    cout<<temp->data<<" ";
    display(temp->left);
    display(temp->right);
}
void AVL::removeitem(int x)
{
    search(x);
    if(loc==NULL)
    {
        cout<<"\nitem is not in tree :(";
        return;
    }
    if(loc->right!=NULL&&loc->left!=NULL)
        remove1(loc,par,x);
    else
        remove2(loc,par,x);
}
void AVL::remove1(AVLNODE *l,AVLNODE *p,int x)
{
    AVLNODE *ptr,*save,*suc,*psuc;
    ptr=l->right;
    save=l;
    while(ptr->left!=NULL)
    {
        save=ptr;
        ptr=ptr->left;
    }
    suc=ptr;
    psuc=save;
    remove2(suc,psuc,x);
    if(p!=NULL)
        if(l==p->left)
            p->left=suc;
        else
            p->right=suc;
    else
        root=l;
    suc->left=l->left;
    suc->right=l->right;
    return;
}
void AVL::remove2(AVLNODE *s,AVLNODE *p,int x)
{
    AVLNODE *child;
    if(s->left==NULL && s->right==NULL)
        child=NULL;
    else if(s->left!=NULL)
        child=s->left;
    else
        child=s->right;
    if(p!=NULL)
        if(s==p->left)
            p->left=child;
        else
            p->right=child;
    else
        root=child;
}
void AVL::search(int x)
{
    search1(root,x);
}
void AVL::search1(AVLNODE *temp,int x)
{
    AVLNODE *ptr,*save;
    int flag;
    if(temp==NULL)
    {
        cout<<"\nthe tree is empty";
        return;
    }
    if(temp->data==x)
    {
        cout<<"\nThe item is root and is found :)";
        par=NULL;
        loc=temp;
        par->left=NULL;
        par->right=NULL;
        return;
    }
    if( x < temp->data)
    {
        ptr=temp->left;
        save=temp;
    }
    else
    {
        ptr=temp->right;
        save=temp;
    }
    while(ptr!=NULL)
    {
        if(x==ptr->data)
        {
            flag=1;
            cout<<"\nItemfound :)";
            loc=ptr;
            par=save;
        }
        if(x<ptr->data)
            ptr=ptr->left;
        else
            ptr=ptr->right;
    }
    if(flag!=1)
    {
        cout<<"Item is not there in tree :(";
        loc=NULL;
        par=NULL;
        cout<<loc;
        cout<<par;
    }
}
main()
{
    AVL a;
    int x,y,c;
    char ch;
    do
    {
        cout<<"\n1.Insert";
        cout<<"\n2.Display";
        cout<<"\n3.Delete";
        cout<<"\n4.Search";
        cout<<"\n5.Exit";
        cout<<"\nEnter your choice of operation on AVL Tree :";
        cin>>c;
        switch(c)
        {
        case 1:
            cout<<"\nEnter an Element to be inserted into Tree :";
            cin>>x;
            a.insert(x);
            break;
        case 2:
            a.displayitem();
            break;
        case 3:
            cout<<"\nEnter an item for Deletion :";
            cin>>y;
            a.removeitem(y);
            break;
        case 4:
            cout<<"\nEnter an element to perform Search :";
            cin>>c;
            a.search(c);
            break;
        case 5:
            exit(0);
            break;
        default :
            cout<<"\nInvalid option try again";
        }
        cout<<"\nDo u want to continue (y/n) :";
        cin>>ch;
    }
    while(ch=='y'||ch=='Y');
}

 OUTPUT:

1.Insert
2.Display
3.Delete
4.Search
5.Exit
Enter your choice of operation on AVL Tree :1
 
Enter an Element to be inserted into Tree :10
 
Do u want to continue (y/n) :y
 
1.Insert
2.Display
3.Delete
4.Search
5.Exit
Enter your choice of operation on AVL Tree :1
 
Enter an Element to be inserted into Tree :14
 
Do u want to continue (y/n) :y
 
1.Insert
2.Display
3.Delete
4.Search
5.Exit
Enter your choice of operation on AVL Tree :1
 
Enter an Element to be inserted into Tree :9
 
Do u want to continue (y/n) :y
 
1.Insert
2.Display
3.Delete
4.Search
5.Exit
Enter your choice of operation on AVL Tree :2
10 9 14
Do u want to continue (y/n) :y
 
1.Insert
2.Display
3.Delete
4.Search
5.Exit
Enter your choice of operation on AVL Tree :4
 
Enter an element to perform Search :14
 
Itemfound :)
Do u want to continue (y/n) :n