AVL Tree

#include "avltree.h"
#include <stdlib.h>
#include "fatal.h"

struct AvlNode
{
ElementType Element;
AvlTree  Left;
AvlTree  Right;
int      Height;
};

AvlTree MakeEmpty( AvlTree T )
{
if( T != NULL )
{
MakeEmpty( T->Left );
MakeEmpty( T->Right );
free( T );
}
return NULL;
}

Position Find( ElementType X, AvlTree T )
{
if( T == NULL )
return NULL;
if( X < T->Element )
return Find( X, T->Left );
else
if( X > T->Element )
return Find( X, T->Right );
else
return T;
}

Position FindMin( AvlTree T )
{
if( T == NULL )
return NULL;
else
if( T->Left == NULL )
return T;
else
return FindMin( T->Left );
}

Position FindMax( AvlTree T )
{
if( T != NULL )
while( T->Right != NULL )
T = T->Right;

return T;
}


static int Height( Position P )
{
if( P == NULL )
return -1;
else
return P->Height;
}


static int Max( int Lhs, int Rhs )
{
return Lhs > Rhs ? Lhs : Rhs;
}


/* This function can be called only if K2 has a left child */
/* Perform a rotate between a node (K2) and its left child */
/* Update heights, then return new root */

static Position SingleRotateWithLeft( Position K2 )
{
Position K1;

K1 = K2->Left;
K2->Left = K1->Right;
K1->Right = K2;

K2->Height = Max( Height( K2->Left ), Height( K2->Right ) ) + 1;
K1->Height = Max( Height( K1->Left ), K2->Height ) + 1;

return K1;  /* New root */
}


/* This function can be called only if K1 has a right child */
/* Perform a rotate between a node (K1) and its right child */
/* Update heights, then return new root */

static Position SingleRotateWithRight( Position K1 )
{
Position K2;

K2 = K1->Right;
K1->Right = K2->Left;
K2->Left = K1;

K1->Height = Max( Height( K1->Left ), Height( K1->Right ) ) + 1;
K2->Height = Max( Height( K2->Right ), K1->Height ) + 1;

return K2;  /* New root */
}


/* This function can be called only if K3 has a left */
/* child and K3's left child has a right child */
/* Do the left-right double rotation */
/* Update heights, then return new root */

static Position DoubleRotateWithLeft( Position K3 )
{
/* Rotate between K1 and K2 */
K3->Left = SingleRotateWithRight( K3->Left );

/* Rotate between K3 and K2 */
return SingleRotateWithLeft( K3 );
}


/* This function can be called only if K1 has a right */
/* child and K1's right child has a left child */
/* Do the right-left double rotation */
/* Update heights, then return new root */

static Position DoubleRotateWithRight( Position K1 )
{
/* Rotate between K3 and K2 */
K1->Right = SingleRotateWithLeft( K1->Right );

/* Rotate between K1 and K2 */
return SingleRotateWithRight( K1 );
}



AvlTree Insert( ElementType X, AvlTree T )
{
if( T == NULL )
{
/* Create and return a one-node tree */
T = malloc( sizeof( struct AvlNode ) );
if( T == NULL )
FatalError( "Out of space!!!" );
else
{
T->Element = X; T->Height = 0;
T->Left = T->Right = NULL;
}
}
else
if( X < T->Element )
{
T->Left = Insert( X, T->Left );
if( Height( T->Left ) - Height( T->Right ) == 2 )
if( X < T->Left->Element )
T = SingleRotateWithLeft( T );
else
T = DoubleRotateWithLeft( T );
}
else
if( X > T->Element )
{
T->Right = Insert( X, T->Right );
if( Height( T->Right ) - Height( T->Left ) == 2 )
if( X > T->Right->Element )
T = SingleRotateWithRight( T );
else
T = DoubleRotateWithRight( T );
}
/* Else X is in the tree already; we'll do nothing */

T->Height = Max( Height( T->Left ), Height( T->Right ) ) + 1;
return T;
}


AvlTree Delete( ElementType X, AvlTree T )
{
printf( "Sorry; Delete is unimplemented; %d remains\n", X );
return T;
}

ElementType Retrieve( Position P )
{
return P->Element;
}