/*
 * testavl.cpp
 */
#include 
#include "avltree.h"

int main()
{
	AvlTree T;
	Position P;
	int i, j;

	T = MakeEmpty(NULL);
	for (i = 0, j = 0; i < 50; ++i, j = (j + 7) % 50)
	{
		T = Insert(j, T);
	}
	for (i = 0; i < 50; ++i)
	{
		if ((P = Find(i, T)) == NULL || Retrieve(P) != i)
		{
			printf("Error at %d\n", i);
		}
	}

	printf("Min is %d, Max is %d\n", Retrieve(FindMin(T)), 
		Retrieve(FindMax(T)));

	return 0;
}

/*
 * fatal.h
 */
#include 
#include 

#define Error(Str)		FatalError(Str)
#define FatalError(Str)	fprintf(stderr, "%s\n", Str), exit(-1)	

/*
 * avltree.h
 */
#ifndef _AVL_TREE_H
#define _AVL_TREE_H

#ifndef NULL
#define NULL (0)
#endif

typedef int ElementType;

struct AvlNode;
typedef struct AvlNode *Position;
typedef struct AvlNode *AvlTree;

#ifdef __cplusplus
extern "C" {
#endif

AvlTree MakeEmpty(AvlTree T);
Position Find(ElementType X, AvlTree T);
Position FindMin(AvlTree T);
Position FindMax(AvlTree T);
AvlTree Insert(ElementType X, AvlTree T);
AvlTree Delete(ElementType X, AvlTree T);
ElementType Retrieve(Position P);

#ifdef __cplusplus
}
#endif

#endif

/*
 * avltree.cpp
 */
#include 
#include "fatal.h"
#include "avltree.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)
	{
		return NULL;
	}
	else if (T->Right == NULL)
	{
		return T;
	}
	else
	{
		return FindMax(T->Right);
	}
}

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;
}

/* Case 1(left-left):
 * 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 */
}

/* Case 4(right-right)
 * This function can be called only if K1 has a right child.
 * Perfrom 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 */
}

/* Case 2:
 * 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);
}

/* Case 3:
 * 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 = (AvlTree)malloc(sizeof(struct AvlNode));
		if (T == NULL)
		{
			FatalError("Out of space!");
		}
		else
		{
			T->Element = X;
			T->Height = 0;
			T->Left = NULL;
			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;
}