AVL-tree

//avl.h
#ifndef __AVL_H__
#define __AVL_H__

typedef int KEY_TYPE;

/* struct */
typedef struct AVL{
 KEY_TYPE key;
 int height;
 struct AVL* lchild;
 struct AVL* rchild;
}AVL;

AVL* New_Node(KEY_TYPE key, AVL* lchild, AVL* rchild, int height = 0);
inline int GetHeight(AVL* node);

AVL* RR_Rotate(AVL* k2);
AVL* LL_Rotate(AVL* k2);
AVL* LR_Rotate(AVL* k3);
AVL* RL_Rotate(AVL* k3);

AVL* Insert(AVL* root, KEY_TYPE key);
AVL* Delete(AVL* root, KEY_TYPE key);
void InOrder(AVL* root);

#endif

//avl.cpp
#include "AVL.h"
#include<iostream>

AVL* New_Node(KEY_TYPE key, AVL* lchild, AVL* rchild, int height)
{
    AVL* p_avl = new AVL;
    p_avl->key = key;
    p_avl->lchild = lchild;
    p_avl->rchild = rchild;
    p_avl->height = height;
    return p_avl;
}

inline int GetHeight(AVL* node)
{
    return (node==NULL)? -1:node->height;
}

inline int max(int a, int b)
{
    return a>b?a:b;
}

/* RR(Y rotates to the right):

        k2                   k1
       /  \                 /  \
      k1   Z     ==>       X   k2
     / \                      /  \
    X   Y                    Y    Z
*/
AVL* RR_Rotate(AVL* k2)
{
    AVL* k1 = k2->lchild;
    k2->lchild = k1->rchild;
    k1->rchild = k2;
    k2->height = max(GetHeight(k2->lchild), GetHeight(k2->rchild)) + 1;
    k1->height = max(GetHeight(k1->lchild), k2->height) + 1;
    return k1;
}

/* LL(Y rotates to the left):

        k2                       k1
       /  \                     /  \
      X    k1         ==>      k2   Z
          /  \                /  \
         Y    Z              X    Y
 */
AVL* LL_Rotate(AVL* k2)
{
    AVL* k1 = k2->rchild;
    k2->rchild = k1->lchild;
    k1->lchild = k2;
    k2->height = max(GetHeight(k2->lchild), GetHeight(k2->rchild)) + 1;
    k1->height = max(GetHeight(k1->rchild), k2->height) + 1;
    return k1;
}



/* LR(B rotates to the left, then C rotates to the right):

      k3                         k3                       k2
     /  \                       /  \                     /  \
    k1   D                     k2   D                   k1   k3
   /  \         ==>           /  \        ==>          / \   / \
  A    k2                    k1   C                   A  B  C   D
      /  \                  /  \
     B    C                A    B

*/
AVL* LR_Rotate(AVL* k3)
{
    k3->lchild = LL_Rotate(k3->lchild);
    return RR_Rotate(k3);
}


/*

       k3                         k3                          k2
      /  \                       /  \                        /  \
     A    k1                    A    k2                     k3   k1 
         /  \       ==>             /  \         ==>       /  \  / \
        k2   B                     C    k1                A   C D   B
       /  \                            /  \
      C    D                          D    B 

 */
AVL* RL_Rotate(AVL* k3)
{
    k3->rchild = RR_Rotate(k3->rchild);
    return LL_Rotate(k3);
}


AVL* Insert(AVL* root, KEY_TYPE key)
{
    if(root == NULL)
        return (root = New_Node(key, NULL, NULL));
    else if(key < root->key)
        root->lchild = Insert(root->lchild, key);
    else 
        root->rchild = Insert(root->rchild, key);
    
    root->height = max(GetHeight(root->lchild), GetHeight(root->rchild)) + 1;
    if(GetHeight(root->lchild) - GetHeight(root->rchild) == 2)
    {
        if(key < root->lchild->key)
            root = RR_Rotate(root);
        else
            root = LR_Rotate(root);
    }
    else if(GetHeight(root->rchild) - GetHeight(root->lchild) == 2)
    {
        if(key < root->rchild->key)
            root = RL_Rotate(root);
        else
            root = LL_Rotate(root);
    }
    return root;
}


AVL* Delete(AVL* root, KEY_TYPE key)
{
    if(!root)
        return NULL;
    if(key == root->key)
    {
        if(root->rchild == NULL)
        {
            AVL* temp = root;
            root = root->lchild;
            delete(temp);
            return root;
        }
        else
        {
            AVL* temp = root->rchild;
            while(temp->lchild)
                temp = temp->lchild;
            
            root->key = temp->key;
            
            root->rchild = Delete(root->rchild, temp->key);
        }
    }
    else if(key < root->key)
        root->lchild = Delete(root->lchild, key);
    else
        root->rchild = Delete(root->rchild, key);
    
    root->height = max(GetHeight(root->lchild), GetHeight(root->rchild)) + 1;
    if(GetHeight(root->rchild) - GetHeight(root->lchild) == 2)
    {
        if(GetHeight(root->rchild->rchild) >= GetHeight(root->rchild->lchild))
            root = LL_Rotate(root);
        else
            root = RL_Rotate(root);
    }
    else if(GetHeight(root->lchild) - GetHeight(root->rchild) == 2)
    {
        if(GetHeight(root->lchild->lchild) >= GetHeight(root->lchild->rchild))
            root = RR_Rotate(root);
        else
            root = LR_Rotate(root);
    }
    return root;
}


void InOrder(AVL* root)
{
    if(root)
    {
        InOrder(root->lchild);
        printf("key: %d height: %d ", root->key, root->height);
        if(root->lchild)
            printf("left child: %d ", root->lchild->key);
        if(root->rchild)
            printf("right child: %d ", root->rchild->key);
        printf("\n");
        InOrder(root->rchild);
    }
}

// main.cpp
#include<iostream>
#include "AVL.h"

int main(int argc, char* argv[])
{
    AVL* root = NULL;
    int vector[] = {15,6,7,17,20,2,4,13,9};

    const int length = sizeof(vector)/sizeof(int);
    for(int i = 0; i< length;i++)
        root = Insert(root, vector[i]);
    
    printf("\nInOrder: \n");
    InOrder(root);

    int input;
    printf("\nplease input the value you want to delete: ");
    scanf("%d",&input);
    
    while(1)
    {
        root = Delete(root, input);
        printf("\nAfter delete %u:\n",input);
        InOrder(root);
        printf("\nplease input another value you want to delete: ");
        scanf("%u",&input);
    }
    printf("\n");
    return 0;
}