二叉排序樹的插入與刪除可能會破壞二叉排序樹的性質，如今要求插入和刪除操作保持其性質

二叉排序樹或者是一棵空樹，或者是具有下列性質的二叉樹：
（1）若左子樹不空，則左子樹上全部結點的值均小於它的根結點的值；
（2）若右子樹不空。則右子樹上全部結點的值均大於或等於它的根結點的值；
（3）左、右子樹也分別為二叉排序樹；
（4）沒有鍵值相等的節點。

#include "stdafx.h"
#include<iostream>   
using namespace std;


struct BiNOde
{
	int ele;
	BiNOde* lnode;
	BiNOde* rnode;
};


BiNOde* nearnode = NULL;
int min = 100000;
BiNOde*tobedeleted = NULL;
BiNOde*parentoftobedeleted = NULL;


BiNOde*create_tree()
{
	BiNOde * root = new BiNOde;
	BiNOde*node1 = new BiNOde;
	BiNOde*node2 = new BiNOde;
	BiNOde*node3 = new BiNOde;
	BiNOde*node4 = new BiNOde;
	BiNOde*node5 = new BiNOde;
	BiNOde*node6 = new BiNOde;
	BiNOde*node7 = new BiNOde;
	BiNOde*node8 = new BiNOde;
	BiNOde*node9 = new BiNOde;
	BiNOde*node10 = new BiNOde;
	BiNOde*node11 = new BiNOde;
	BiNOde*node12 = new BiNOde;
	root->ele = 45;
	node1->ele = 38;
	node2->ele = 55;
	node3->ele = 33;
	node4->ele = 41;
	node5->ele = 19;
	node6->ele = 16;
	node7->ele = 52;
	node8->ele = 58;
	node9->ele = 50;
	node10->ele = 44;
	node11->ele = 35;
	node12->ele = 42;
	root->lnode = node1;
	root->rnode = node2;
	node1->lnode = node3;
	node1->rnode = node4;
	node2->lnode = node7;
	node2->rnode = node8;
	node3->lnode = node5;
	node3->rnode = NULL;//node11;
	node4->rnode = node10;
	node4->lnode = NULL;
	node5->lnode = node6;
	node5->rnode = NULL;
	node6->lnode = NULL;
	node6->rnode = NULL;
	node7->lnode = node9;
	node7->rnode = NULL;
	node8->lnode = NULL;
	node8->rnode = NULL;
	node9->lnode = NULL;
	node9->rnode = NULL;
	node10->lnode = node12;
	node10->rnode = NULL;
	node11->lnode = NULL;
	node11->rnode = NULL;
	//BiNOde*node12 = new BiNOde;    
	//node12->ele = 12;    
	node12->lnode = NULL;
	node12->rnode = NULL;
	//node6->lnode = node11;    
	return root;
}




void find(BiNOde*node, int value)
{
	if (node == NULL)
		return;
	int k = node->ele - value;
	if (k > 0)
		if (k < min)
		{
			min = k;
			nearnode = node;
		}
	find(node->lnode, value);
	find(node->rnode, value);


}




BiNOde*insert(BiNOde*root, int value)
{
	BiNOde* p = new BiNOde;
	p->ele = value;
	BiNOde*n;
	find(root, value);


	n = nearnode->lnode;
	nearnode->lnode = p;
	p->lnode = n;
	p->rnode = NULL;
	return root;
}




void searchnode(BiNOde*root, int value)
{
	tobedeleted = root;
	while (tobedeleted->ele != value)
	{
		parentoftobedeleted = tobedeleted;
		if (tobedeleted->ele > value)
			tobedeleted = tobedeleted->lnode;
		else
			tobedeleted = tobedeleted->rnode;
	}
}






BiNOde*delete_node(BiNOde*root, int value)
{
	BiNOde*minnode, *maxnode, *nn = NULL;
	searchnode(root, value);
	if (tobedeleted == root)
	{
		if (root->lnode == NULL)
		{
			root = root->rnode;
			delete tobedeleted;
			return root;
		}
		maxnode = root->lnode;
		if (maxnode->rnode == NULL)
		{
			maxnode->rnode = root->rnode;
			root = maxnode;
			delete tobedeleted;
			return root;
		}
		while (maxnode->rnode != NULL)
		{
			nn = maxnode;
			maxnode = maxnode->rnode;
		}
		nn->rnode = maxnode->lnode;
		maxnode->lnode = root->lnode;
		maxnode->rnode = root->rnode;
		root = maxnode;
		delete tobedeleted;
		return root;
	}


	if (tobedeleted->lnode == NULL&&tobedeleted->rnode == NULL)
	{
		if (parentoftobedeleted->lnode == tobedeleted)
		{


			parentoftobedeleted->lnode = NULL;
			delete tobedeleted;
			return root;
		}
		else
		{
			parentoftobedeleted->rnode = NULL;
			delete tobedeleted;
			return root;
		}
	}


	if (tobedeleted->lnode == NULL)
	{
		minnode = tobedeleted->rnode;
		if (minnode->lnode != NULL)
		{
			while (minnode->lnode != NULL)
			{
				nn = minnode;
				minnode = minnode->lnode;
			}
			nn->lnode = minnode->rnode;
		}
		if (parentoftobedeleted->lnode == tobedeleted)
		{
			parentoftobedeleted->lnode = minnode;
		}
		else
		{
			parentoftobedeleted->rnode = minnode;
		}
		if (minnode != tobedeleted->rnode)
			minnode->rnode = tobedeleted->rnode;
		delete tobedeleted;
		return root;
	}




	maxnode = tobedeleted->lnode;
	if (maxnode->rnode != NULL)
	{
		while (maxnode->rnode != NULL)
		{
			nn = maxnode;
			maxnode = maxnode->rnode;
		}
		nn->rnode = maxnode->lnode;
	}
	if (parentoftobedeleted->lnode == tobedeleted)
	{
		parentoftobedeleted->lnode = maxnode;
	}
	else
	{
		parentoftobedeleted->rnode = maxnode;
	}
	if (maxnode != tobedeleted->lnode)
	{
		maxnode->lnode = tobedeleted->lnode;
		maxnode->rnode = tobedeleted->rnode;
	}
	else
	{
		maxnode->rnode = tobedeleted->rnode;
	}
	delete tobedeleted;
	return root;


}

int _tmain(int argc, _TCHAR* argv[])
{
	BiNOde*root = create_tree();
	//insert(root, 37);
	root = delete_node(root, 38);
	cout << root->ele << endl;
	system("pause");
	return 0;
}

二叉排序樹的插入與刪除