AVL树的实现

平衡二叉树（Balanced Binary Tree）又被称为AVL树（有别于AVL算法），且具有以下性质：

它是一 棵空树或它的左右两个子树的高度差的绝对值不超过1，并且左右两个子树都是一棵平衡二叉树。


下面是我的实现，这个算法还是纠结了蛮久的

// AVL-Tree.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <crtdbg.h>
#include<vector>

#define MIN 1000000
struct TreeNode{
	int ele;
	TreeNode*lnode, *rnode, *parent;
};

TreeNode*minmax = NULL;
int minvalue = MIN;
void find_postion(TreeNode*node, int value)
{
	if (node == NULL)
		return;
	if (node->ele - value > 0 && node->ele - value < minvalue)
	{
		minmax = node;
		minvalue = node->ele - value;
	}
	find_postion(node->lnode, value);
	find_postion(node->rnode, value);
}
int depth_between(TreeNode*floor, TreeNode*ceiling)
{
	_ASSERTE(floor != NULL);
	int dep = 1;
	while (ceiling != floor)
	{
		floor = floor->parent;
		dep++;
	}
	return dep;
}


int maxdep = 0;
int mindep = MIN;
void depth(TreeNode*ceiling, TreeNode*node)
{
	if (node == NULL)
		return;
	int dep = depth_between(node, ceiling);
	if (node->lnode == NULL&&node->rnode == NULL&&dep < mindep)
	{
		mindep = dep;
	}
	if (dep > maxdep)
	{
		maxdep = dep;
	}
	depth(ceiling, node->lnode);
	depth(ceiling, node->rnode);
}




int tree_depth(TreeNode*node)
{
	maxdep = 0;
	mindep = MIN;
	depth(node, node);
	return maxdep;
}



int is_balence(TreeNode*node)
{
	return tree_depth(node->lnode) - tree_depth(node->rnode);
}

std::vector<TreeNode*>vec;

void inorder(TreeNode*node)
{
	if (node == NULL)
		return;
	inorder(node->lnode);
	vec.push_back(node);
	inorder(node->rnode);
}



void adjust(TreeNode*root, TreeNode*node)//插入删除后做调整
{
	while (node != NULL)
	{
		int aa = tree_depth(node->lnode);
		int bb = tree_depth(node->rnode);
		int tt = is_balence(node);
		if (tt > 1)
		{
			if (node->rnode == NULL)
			{
				if (node->lnode->rnode != NULL)
				{
					int temp = node->ele;
					node->ele = node->lnode->rnode->ele;
					node->lnode->rnode->ele = temp;
					node->rnode = node->lnode->rnode;
					node->lnode->rnode = NULL;
					node->rnode->parent = node;
					node = node->parent;
				}
				else
				{
					int temp = node->ele;
					node->ele = node->lnode->ele;
					node->lnode->ele = node->lnode->lnode->ele;
					node->rnode = node->lnode->lnode;
					node->rnode->parent = node;
					node->lnode->lnode = NULL;
					node->rnode->ele = temp;
					node = node->parent;
				}
			}
			else
			{
				
				TreeNode*t3 = node->lnode;
				_ASSERTE(t3 != NULL);
				
				while (t3->rnode != NULL)
				{
					t3 = t3->rnode;
				}
			
				TreeNode*t4;
				t4 = node->rnode;
				while (t4->rnode != NULL)
				{
					t4 = t4->rnode;
				}

				if (t4->parent->lnode == NULL)//旋转一次，便于后续插入
				{
					int temp = t4->parent->ele;
					t4->parent->ele = t4->ele;
					t4->ele = temp;
					t4->parent->lnode = t4;
					t4->parent->rnode = NULL;
				}
				TreeNode*t5 = t3->parent;
				if (t3->lnode != NULL)
				{
					t3->lnode->parent = t3->parent;
				}
				t3->parent->rnode = t3->lnode;
				t3->lnode = NULL;

				vec.clear();
				inorder(node->rnode);
				int temp = node->ele;
				node->ele = t3->ele;
				int t = vec[0]->ele;
				vec[0]->ele = temp;
				temp = vec.back()->ele;
				if (vec.size() == 1)
					temp = t;
				for (int i = 1; i < vec.size(); i++)
				{
					vec[i]->ele = vec[i - 1]->ele;
				}
				vec.back()->rnode = t3;
				//t3->lnode = t3->rnode = NULL;
				t3->ele = temp;
				t3->parent = vec.back();

				node = t5;
			}
		}//end of tt>1


		else if (tt < -1)
		{
			if (node->lnode==NULL)
			{
				if (node->rnode->rnode != NULL)
				{
					int temp = node->ele;
					node->ele = node->rnode->ele;
					node->rnode->ele = node->rnode->rnode->ele;
					node->lnode = node->rnode->rnode;
					node->rnode->rnode = NULL;
					node->lnode->ele = temp;
					node->lnode->parent = node;
					node = node->parent;
				}
				else
				{
					node->lnode = node->rnode->lnode;
					node->lnode->parent = node;
					node->rnode->lnode = NULL;
					int temp=node->lnode->ele;
					node->lnode->ele = node->ele;
					node->ele = temp;
					node = node->parent;
				}
			}
			else//node->lnode !=NULL
			{
				TreeNode*t1 = node->lnode;
				while (t1->rnode != NULL)
				{
					t1 = t1->rnode;
				}
				if (t1->parent->lnode == NULL)//旋转，便于后续插入
				{
					_ASSERTE(t1->lnode == NULL&&t1->rnode == NULL);
					int temp = t1->ele;
					t1->ele = t1->parent->ele;
					t1->parent->ele = temp;
					t1->parent->lnode = t1;
					t1->parent->rnode = NULL;
				}
				TreeNode*t2 = node->rnode->lnode;
				_ASSERTE(t2 != NULL);
				while (t2->lnode != NULL)
				{
					t2 = t2->lnode;
				}
				TreeNode*t3 = t2->parent;
				t2->parent->lnode = t2->rnode;
				if (t2->rnode!=NULL)
					t2->rnode->parent = t2->parent;
				t1->rnode = t2;
				t2->rnode = NULL;
				t2->parent = t1;
				int temp = node->ele;
				node->ele = t2->ele;
				t2->ele = temp;

				node = t3;
			}
		}//end of tt<-1
		
		else //-2<tt<2,无需调整
			node = node->parent;
	}

}



TreeNode* insert(TreeNode*root, int value)//插入
{
	if (root == NULL)//当前树为空
	{
		root = new TreeNode;
		root->ele = value;
		root->lnode = root->rnode = root->parent = NULL;
		return root;
	}

	minmax = NULL;
	minvalue = MIN;
	find_postion(root, value);
	if (minmax == NULL)//要插入的值比树中所有节点的都大
	{
		if (root->rnode == NULL)
		{
			TreeNode*node = new TreeNode;
			node->ele = value;
			node->parent = root;
			root->rnode = node;
			node->lnode = node->rnode = NULL;
			TreeNode*floor = NULL;
			maxdep = -1;
			depth(root, root);
			_ASSERTE(maxdep == 2);
			return root;
		}

		TreeNode*r_node = root;
		while (r_node->rnode != NULL)
		{
			r_node = r_node->rnode;
		}
		TreeNode*node = new TreeNode;
		node->ele = value;
		node->parent = r_node;
		r_node->rnode = node;
		node->lnode = node->rnode = NULL;
		adjust(root, r_node->parent);
		return root;
	}

	TreeNode*nn = minmax->lnode;
	if (nn == NULL)
	{
		TreeNode*node = new TreeNode;
		node->ele = value;
		node->lnode = node->rnode = NULL;
		minmax->lnode = node;
		node->parent = minmax;
		adjust(root, minmax->parent);//对树做调整
		return root;
	}
	while (nn->rnode != NULL)
	{
		nn = nn->rnode;
	}
	TreeNode*node = new TreeNode;
	node->ele = value;
	node->parent = nn;
	nn->rnode = node;
	node->lnode = node->rnode = NULL;
	adjust(root,nn->parent);//对树做调整
	return root;
}
TreeNode*bbb=NULL;
void find(TreeNode*node,const int value)//查找
{
	if (node != NULL)
	{
		if (node->ele == value)
			bbb=node;
		if (node->ele > value)
			find(node->lnode, value);
		else
			find(node->rnode, value);
	}
}


TreeNode*erase(TreeNode*root,const int value)//删除
{
	bbb = NULL;
	find(root, value);
	TreeNode*tobedel = bbb;
	if (tobedel != NULL)
	{
		if (tobedel == root)
		{
			if (root->lnode == NULL)
			{
				TreeNode*nn = root->rnode;
				nn->parent = NULL;
				delete root;
				return nn;
			}
			TreeNode*t1 = root->lnode;
			while (t1->rnode != NULL)
			{
				t1 = t1->rnode;
			}
			TreeNode*aa = t1->parent;
			t1->parent->rnode = t1->lnode;
			if (t1->lnode != NULL)
				t1->lnode->parent = t1->parent;

			t1->lnode = root->lnode;
			root->lnode->parent = t1;
			t1->parent = NULL;
			t1->rnode = root->rnode;
			if (root->rnode != NULL)
				root->rnode->parent = t1;
			if (aa == root)
				aa=t1;
			delete root;
			adjust(t1, aa);
			return t1;
		}

		if (tobedel->lnode == NULL)
		{
			tobedel->parent->lnode = tobedel->rnode;
			if (tobedel->rnode != NULL)
				tobedel->rnode->parent = tobedel->parent;
			TreeNode*aa = tobedel->parent;
			delete tobedel;
			adjust(root, aa);
			return root;
		}
		TreeNode*t1 = tobedel->lnode;
		while (t1->rnode != NULL)
		{
			t1 = t1->rnode;
		}
		
		t1->parent->rnode = t1->lnode;
		if (t1->lnode != NULL)
			t1->lnode->parent = t1->parent;
		t1->lnode = NULL;
		TreeNode*aa = t1->parent;
		if (tobedel->parent->lnode == tobedel)
		{
			tobedel->parent->lnode = t1;
			t1->parent = tobedel->parent;
			tobedel->parent->rnode = tobedel->rnode;
			if (tobedel->rnode != NULL)
				tobedel->rnode->parent = tobedel->parent;
			delete tobedel;
			adjust(root, aa);
			return root;
		}
		else
		{
			tobedel->parent->rnode = t1;
			t1->parent = tobedel->parent;
			tobedel->parent->rnode = tobedel->rnode;
			if (tobedel->rnode != NULL)
				tobedel->rnode->parent = tobedel->parent;
			delete tobedel;
			adjust(root, aa);
			return root;
		}
	}

	return root;
}


int _tmain(int argc, _TCHAR* argv[])
{
	TreeNode*root = NULL;
	root=insert(root, 100);
	root=insert(root, 200);
	root=insert(root, 300);
	root=insert(root, 50);
	root = insert(root, 20);
	root = insert(root, 500);
	root = insert(root, 700);
	root = insert(root, 1100);
	root = insert(root, 1500);
	root = insert(root, 900);
	root = insert(root, 1000);
	root = insert(root, 150);
	root = insert(root, 350);
	root = insert(root, 250);
	root = insert(root, 15);
	root = insert(root, 10);
	root = insert(root, 8);
	root = insert(root, 5);

	bbb = NULL;
	find(root, 150);
	TreeNode*aa = bbb;

	root = erase(root, 300);
	root = erase(root, 150);
	system("pause");
	return 0;
}


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原文地址：https://www.cnblogs.com/walccott/p/4956876.html