Inserting AVL tree in C

Question

I was implementing an AVL tree and its operations like rotation.
And in the end when I tried to insert an array, the result seemed
different. And anyone tell me what went wrong! Thank you !

#include <stdio.h>
#include <stdlib.h>
#define LH +1   
#define RH -1   
#define EQ 0
typedef int BOOL;
typedef struct node
{
    int bf;   
    struct node *left;
    struct node *right;
    int val;
}treeNode;  
void L_Rotate(treeNode **T)
{
    treeNode *p = (*T)->right;  
    (*T)->right = p->left;  
    p->left=*T;
    *T=p;
}
void R_Rotate(treeNode **T) 
{
    treeNode *p=(*T)->left;  
    (*T)->left=p->right;   
    p->right=*T;  
    *T=p; 
}
void Left_Balance(treeNode **T)
{
    treeNode *p=(*T)->left;
    treeNode *q;
    switch(p->bf)
    {
        case LH:  
            p->bf=(*T)->bf=EQ;
            R_Rotate(T); 
            break;
        case RH:  
            q = p->right; 
            switch(q->bf)
           {
               case LH: 
                   (*T)->bf=RH;
                   p->bf=EQ;
                   break;
               case EQ: 
                   (*T)->bf=q->bf=EQ;
                   break;
               case RH: 
                   p->bf=LH;
                   (*T)=EQ;
                   break;
           }
            q->bf=EQ;
            L_Rotate(&p);
            R_Rotate(T);
    }
}
void Right_Balance(treeNode **T)
{
    treeNode *p=(*T)->right;
    treeNode *q;
    switch(p->bf)
    {
        case RH:
            (*T)->bf=p->bf=EQ;
            L_Rotate(T);
            break;
        case LH:
            q=p->left;
            switch(q->bf)
           {
               case LH:
                   (*T)->bf=EQ;
                   p->bf=RH;
                   break;
               case RH:
                   (*T)->bf=LH;
                   p->bf=EQ;
                   break;
           }
            q->bf=EQ;
            R_Rotate(&p);
            L_Rotate(T);
    }
}
int insertAVL (treeNode **T,int key, BOOL *taller)
{
    if(!*T)
    {
        *T=malloc(sizeof(treeNode));
        if(!*T) return 0;
        (*T)->left=(*T)->right=NULL;
        (*T)->bf=EQ;
        *taller = 1;
        (*T)->val=key;
    }
    else
    {
        if(key==(*T)->val)
        {
            *taller= 0;
            return 0;
        }
        else if(key<(*T)->val)
        {
            if(!insertAVL(&(*T)->left,key,taller))  return 0;
            if(*taller)
            {
                switch((*T)->bf)
                {
                    case LH:
                        Left_Balance(T);
                        *taller=0;
                        break;
                    case RH:
                        (*T)->bf=EQ;
                        *taller =0;
                        break;
                    case EQ:
                        (*T)->bf=LH;
                        *taller =1;
                        break;
                }
            }
        }
        else
        {
            if(!insertAVL(&(*T)->right,key,taller))  return 0;
            if(*taller)
            {
                switch((*T)->bf)
                {
                    case LH:
                        (*T)->bf=EQ;
                        *taller=0;
                        break;
                    case EQ:
                        (*T)->bf=RH;
                        *taller=1;
                        break;
                    case RH:
                        Right_Balance(T);
                        *taller =0;
                        break;
                }
            }
        }
    }
    return 1;
}
void preOrder(treeNode *T)
{
    if(!T)
    {
        return;
    }
    printf("%d\n",T->val);
    preOrder(T->left);
    preOrder(T->right);
}
int main() {
    int i;
    int a[10]={3,2,1,4,5,6,7,10,9,8};
    treeNode *T=NULL;

    BOOL taller;
    for(i=0;i<10;i++)
    {
        insertAVL(&T,a[i],&taller);
        preOrder(T);
        printf("-------\n");
    }

    return 0;
}

I traversed the tree after each insertion into the tree, the results are
right until I inserted 9 into the tree.

Answer 1

When you modify the tree (or a subtree), you pass in a pointer to the head pointer, so that changes are reflected in the original link, either the global head or one of the left/right links of a node. That's a good practice, in my opinion.

When you balance the tree, you do the same, but there's a pitfall:

treeNode *p = (*T)->left;

// ... some stuff ...

L_Rotate(&p);
R_Rotate(T);

Here, p is a local copy of (*T)->left . You end up modifying a local variable (which will go out of scope right away), but not the actual link in the parent node; the node is "eaten".

You could either make p a treeNode ** as well or, given that you don't change the pointer itself, change your rotation code to:

L_Rotate(&(*T)->left);
R_Rotate(T);

Likewise for the other rotation.

Answer 2

I also noticed your balance left/right functions aren't symmetrical and the right-balancing code misses the EQ case. I did some tries to add it and to rewrite Right_Balance to be symmetrical of Left_Balance but that solves nothing. The problem is not (only) here.

If I am not wrong to manage an AVL you have to take into account the height of each cell to decide how to balance after the insertion of a new value.

In your case there is no height but bf able to get the 3 values LH/RH/EQ, in a way bf is equivalent to a height into the range 1 up to 3. But after the insertion of 10 the cell having the value 4 has in fact the height 4 and you cannot manage that and for me this is why you cannot after insert 9 correctly after 10.