AVL树的介绍见http://blog.csdn.net/pngynghay/article/details/22443525，本文给出的是AVL树的一种实现。

采用非递归方式，效率较好，经过常规测试，不过，在删除节点的方法中，与《数据结构》中删除步骤有点出入，可能会有bug，待进一步测试。

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <errno.h>
#include <assert.h>

typedef enum
{
	EH = 0,
	LH = 1,
	RH = -1
}bh_t;


typedef enum
{
	FALSE = 0,
	TRUE = 1
}bool_t;

typedef int ElemType;

typedef struct BSTNode
{
	ElemType key;
	int bf;
	struct BSTNode *lchild,*rchild,*parent;
}BSTNode,*BSTree;

bool_t  searchAVL(BSTree root,ElemType key, BSTNode **parent)
{
	BSTNode *tmp = NULL;
	assert(root != NULL);
	*parent = root->parent;
	tmp = root;
	while(NULL != tmp)
	{
		if(tmp->key == key)
		{
			return TRUE;
		}

		*parent = tmp;
		if(tmp->key > key)
		{
			tmp = tmp->lchild;
		}
		else
		{
			tmp = tmp->rchild;
		}
	}
	return FALSE;
}

/* get the minimum node*/
BSTNode* minNode(BSTNode* root)
{
	if (root == NULL)
	{
		return NULL;
	}
	while (root->lchild != NULL)
	{
		root = root->lchild;
	}
	return root;
}

/* get the maximum node*/
BSTNode* maxNode(BSTNode* root)
{
	if (root == NULL)
	{
		return NULL;
	}
	while (root->rchild != NULL)
	{
		root = root->rchild;
	}
	return root;
}

/* get the previous node*/
BSTNode* preNode(BSTNode* target)
{
	if (target == NULL)
	{
		return NULL;
	}
	if (target->lchild != NULL)
	{
		return maxNode(target->lchild);
	}
	while ((target->parent!=NULL) && (target!=target->parent->rchild))
	{
		target = target->parent;
	}
	return target->parent;
}

/* get the next node*/
BSTNode* nextNode(BSTNode* target)
{
	if (target == NULL)
	{
		return NULL;
	}
	if (target->rchild != NULL)
	{
		return minNode(target->rchild);
	}
	while ((target->parent!=NULL) && (target!=target->parent->lchild))
	{
		target = target->parent;
	}
	return target->parent;
}

BSTNode* leftbalance(BSTNode* root, BSTNode* parent, BSTNode* child)
{
	BSTNode *cur;
	assert((parent != NULL)&&(child != NULL));
	/* LR */
	if (child->bf == RH)
	{
		cur = child->rchild;
		cur->parent = parent->parent;
		child->rchild = cur->lchild;
		if (cur->lchild != NULL)
		{
			cur->lchild->parent = child;
		}
		parent->lchild = cur->rchild;
		if (cur->rchild != NULL)
		{
			cur->rchild->parent = parent;
		}
		cur->lchild = child;
		cur->rchild = parent;
		child->parent = cur;

		if (parent->parent != NULL)
		{
			if (parent->parent->lchild == parent)
			{
				parent->parent->lchild = cur;
			}
			else 
			{
				parent->parent->rchild = cur;
			}
		}
		else
		{
			root = cur;
		}
		parent->parent = cur;
		if (cur->bf == EH)
		{
			parent->bf = EH;
			child->bf = EH;
		}
		else if (cur->bf == RH)
		{
			parent->bf = EH;
			child->bf = LH;
		}
		else
		{
			parent->bf = RH;
			child->bf = EH;
		}
		cur->bf = EH;
	}
	/* LL */
	else 
	{
		child->parent = parent->parent;
		parent->lchild = child->rchild;
		if (child->rchild != NULL)
		{
			child->rchild->parent = parent;
		}
		child->rchild = parent;
		if (parent->parent != NULL)
		{
			if (parent->parent->lchild == parent)
			{
				parent->parent->lchild = child;
			}
			else 
			{
				parent->parent->rchild = child;
			}
		}
		else
		{
			root = child;
		}
		parent->parent = child;
		/* when insert */
		if (child->bf == LH) 
		{
			child->bf = EH;
			parent->bf = EH;
		}
		/* when delete*/
		else 
		{
			child->bf = RH;
			parent->bf = LH;
		}
	}
	return root;
}

BSTNode* rightbalance(BSTNode* root, BSTNode* parent, BSTNode* child)
{
	BSTNode *cur;
	assert((parent != NULL)&&(child != NULL));
	/* RL */
	if (child->bf == LH) 
	{
		cur = child->lchild;
		cur->parent = parent->parent;
		child->lchild = cur->rchild;
		if (cur->rchild != NULL)
		{
			cur->rchild->parent = child;
		}
		parent->rchild = cur->lchild;
		if (cur->lchild != NULL)
		{
			cur->lchild->parent = parent;
		}
		cur->lchild = parent;
		cur->rchild = child;
		child->parent = cur;
		if (parent->parent != NULL)
		{
			if (parent->parent->lchild == parent)
			{
				parent->parent->lchild = cur;
			}
			else
			{
				parent->parent->rchild = cur;
			}
		}
		else
		{
			root = cur;
		}
		parent->parent = cur;
		if (cur->bf == EH)
		{
			parent->bf = EH;
			child->bf = EH;
		}
		else if (cur->bf == LH)
		{
			parent->bf = EH;
			child->bf = RH;
		}
		else
		{
			parent->bf = LH;
			child->bf = EH;
		}
		cur->bf = EH;
	}
	/* RR */
	else 
	{
		child->parent = parent->parent;
		parent->rchild = child->lchild;
		if (child->lchild != NULL)
			child->lchild->parent = parent;
		child->lchild = parent;
		if (parent->parent != NULL)
		{
			if (parent->parent->lchild == parent)
			{
				parent->parent->lchild = child;
			}
			else
			{
				parent->parent->rchild = child;
			}
		}
		else
		{
			root = child;
		}
		parent->parent = child;
		/* when insert */
		if (child->bf == RH) 
		{
			child->bf = EH;
			parent->bf = EH;
		}
		/* when delete*/
		else
		{
			child->bf = LH;
			parent->bf = RH;
		}
	}
	return root;
}


BSTNode* insertNode(ElemType key, BSTNode* root)
{
	BSTNode *parent = NULL, *cur = NULL, *child = NULL;
	assert (root != NULL);
	/* node exists*/
	if (searchAVL(root,key,&parent))
	{
		return root;
	}
	cur = (BSTNode*)malloc(sizeof(BSTNode));
	cur->parent = parent;
	cur->key = key;
	cur->lchild = NULL;
	cur->rchild = NULL;
	cur->bf = EH;
	if (key<parent->key)
	{
		parent->lchild = cur;
		child = parent->lchild;
	}
	else
	{
		parent->rchild = cur;
		child = parent->rchild;
	}
	/*get the minimax tree needed to be adjusted*/
	while ((parent != NULL)) 
	{
		if (child == parent->lchild)
		{
			if (parent->bf == RH)
			{
				parent->bf = EH;
				return root;
			}
			else if (parent->bf == EH)
			{
				root = leftbalance(root, parent, child);
				break;
			}
			else
			{
				parent->bf = LH;
				child = parent;
				parent = parent->parent;
			}
		}
		else
		{
			if (parent->bf == LH) //是右孩子，不会引起不平衡
			{
				parent->bf = EH;
				return root;
			}
			else if (parent->bf == RH) //是右孩子，并且引起parent的不平衡

			{
				root = rightbalance(root, parent, child);
				break;
			}
			else //是右孩子，并且可能引起parent的parent的不平衡
			{
				parent->bf = RH;
				child = parent;
				parent = parent->parent;
			}
		}
	}

	return root;
}


BSTNode* deleteNode(ElemType key, BSTNode* root)
{
	BSTNode *dNode=NULL, *parent=NULL, *child = NULL;
	ElemType temp;
	assert(root!=NULL);
	if (!searchAVL(root,key,&parent))
	{
		return root;
	}

	if (parent == NULL)
	{
		dNode = root;
	}
	else if ((parent->lchild!=NULL)&&(parent->lchild->key==key))
	{
		dNode = parent->lchild;
	}
	else 
	{
		dNode = parent->rchild;
	}

	child = dNode;
	while ((child->lchild!=NULL)||(child->rchild!=NULL)) //确定需要删除的结点
	{
		if (child->bf == LH)
		{
			child = preNode(dNode);
		}
		else 
		{
			child = nextNode(dNode);
		}
		temp = child->key;
		child->key = dNode->key;
		dNode->key = temp;
		dNode = child;
	}

	child = dNode;
	parent = dNode->parent;

	while ((parent != NULL)) //查找需要调整的最小子树
	{
		if (child == parent->lchild)
		{
			if (parent->bf == LH)
			{
				parent->bf = EH;
				child = parent;
				parent = parent->parent;
			}
			else if (parent->bf == RH)
			{
				child = parent->rchild;
				root = rightbalance(root, parent, child);
				break;
			}
			else
			{
				parent->bf = RH;
				break;
			}
		}
		else
		{
			if (parent->bf == RH)
			{
				parent->bf = EH;
				child = parent;
				parent = parent->parent;
			}
			else if (parent->bf == LH)
			{

				child = parent->lchild;
				root = leftbalance(root, parent, child);
				break;
			}
			else 
			{
				parent->bf = LH;
				break;
			}
		}
	}
	if (dNode->parent != NULL)
	{
		if (dNode == dNode->parent->lchild)
		{
			dNode->parent->lchild = NULL;
		}
		else 
		{
			dNode->parent->rchild = NULL;
		}
	}
	free(dNode);
	dNode = NULL;
	if (root == dNode)
	{
		root = NULL; //root被删除, 避免野指针
	}
	return root;
}

BSTNode* createAVL(int *data, int size)
{
	int i, j;
	BSTNode *root;
	if (size<1)
	{
		return NULL;
	}
	root = (BSTNode*)malloc(sizeof(BSTNode));
	root->parent = NULL;
	root->lchild = NULL;
	root->rchild = NULL;
	root->key = data[0];
	root->bf = 0;

	for(i=1;i<size;i++)
		root = insertNode(data[i], root);
	return root;
}

void destroyAVL(BSTNode* root)
{
	if (root != NULL)
	{
		destroyAVL(root->lchild);
		destroyAVL(root->rchild);
		free(root);
		root=NULL;
	}

}


void InOrderTraverse(BSTree root)
{
	if(NULL != root)
	{
		InOrderTraverse(root->lchild);
		printf("%d\t",root->key);
		InOrderTraverse(root->rchild);
	}
}


void PreOrderTraverse(BSTree root)
{
	if(NULL != root)
	{
		printf("%d\t",root->key);
		PreOrderTraverse(root->lchild);
		PreOrderTraverse(root->rchild);
	}
}

int main(int argc, char *argv[])
{
	int data[] = {1, 5, 7, 4, 3, 2, 11, 9, 10,100};
	BSTNode* root;
	root = createAVL(data, sizeof(data)/sizeof(data[0]));

	printf("\n++++++++++++++++++++++++++++\n");
	InOrderTraverse(root);
	printf("\n");
	PreOrderTraverse(root);

	root = deleteNode(5, root);
	printf("\n++++++++delete 5++++++++++\n");
	InOrderTraverse(root);
	printf("\n");
	PreOrderTraverse(root);

	root = deleteNode(3, root);
	printf("\n++++++++delete 3++++++++++\n");
	InOrderTraverse(root);
	printf("\n");
	PreOrderTraverse(root);

	root = deleteNode(1, root);
	printf("\n++++++++delete 1++++++++++\n");
	InOrderTraverse(root);
	printf("\n");
	PreOrderTraverse(root);

	root = deleteNode(7, root);
	printf("\n++++++++delete 7++++++++++\n");
	InOrderTraverse(root);
	printf("\n");
	PreOrderTraverse(root);

	root = deleteNode(4, root);
	printf("\n++++++++delete 4++++++++++\n");
	InOrderTraverse(root);
	printf("\n");
	PreOrderTraverse(root);

	root = deleteNode(2, root);
	printf("\n++++++++delete 2++++++++++\n");
	InOrderTraverse(root);
	printf("\n");
	PreOrderTraverse(root);
	printf("\n");

	destroyAVL(root);
}

AVL树C语言实现,布布扣,bubuko.com

AVL树C语言实现