AVL树实现

AVL树的节点声明

#ifndef _AvlTree_H

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

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);

#endif

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

计算AVL节点高度

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

向AVL树插入节点

AvlTree Insert(ElementType X,AvlTree T)
{
	if(T == NULL)
	{
		T = malloc(sizeof(struct AvlNode));
		if(T == NULL)
			FataError("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 = SingleRotateWinthLeft(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 = SingleRotateWinthRight(T);
			else
				T = DoubleRotateWithRight(T);
	}
	T->Height = Max(Height(T->Left),Height(T->Right)) + 1;
	return T;
}

执行单旋转操作

static Position SingleRotateWinthLeft(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;
}

执行双旋转操作

static Position DoubleRotateWithLeft(Position K3)
{
	K3->Left = SingleRotateWithRight(K3->Left);
	return SingleRotateWithLeft(K3);
}