二叉查找树(Binary Sort Tree)

       在数据顺序存储时 如果无序我们用顺序查找， 有序时我们用折半查找法，插值查找法，斐波那契查找法。 但是当需要插入跟删除

时就需要用到链式

存储了  这时我们引入二叉排序树(二叉搜索树)。

          线索二叉树node->left .data <  node.data < node->right.data;

        中序遍历时为递增数列 InOrderTraverse;

删除节点时 重点注意下；有4种  

1.从node->left 找最大值替换node;

2.从node->right找最小值替换node;

3.将node->right整体移动到node->left最大值的右边；

4.将node->left整体移动到node->right最小值的左边；

不过考虑到树的深度最好采用前两种 这就设计到树的左右节点平衡的问题了AVL树

#include <iostream>    
#include <vector>    
using namespace std;    
typedef struct treenode    
{    
    int data;    
    struct treenode *left;    
    struct treenode *right;    
}TREE_NODE;//节点    
typedef struct Bstree    
{    
    TREE_NODE* root;    
    int size;    
}BSTREE;//二叉树    
BSTREE* create_tree() //创建    
{    
    BSTREE* tree = new(BSTREE);    
    tree->root = NULL;    
    tree->size = 0;    
    return tree;    
}    
TREE_NODE* create_node(int data) //创建节点    
{    
    TREE_NODE* node =new(TREE_NODE);    
    node->data = data;    
    node->left = NULL;    
    node->right = NULL;    
}    
void insert(TREE_NODE* node, TREE_NODE** root)  //插入一个节点到那个位置    
{    
    if(NULL == *root)    
    {    
        *root = node;    
    }    
    else    
    {    
        if(node->data > (*root)->data)    
        {    
            insert(node, & (*root)->right);    
        }    
        else    
        {    
            insert(node, &(*root)->left);    
        }    
    }    
}    
void PreOrderTraverse(TREE_NODE* root) //先序遍历    
{    
    if(root)    
    {    
        cout << root->data <<endl;    
        PreOrderTraverse(root->left);    
        PreOrderTraverse(root->right);    
    }    
}    
void InOrderTraverse(TREE_NODE* root) //中序遍历    
{    
    if(root)    
    {    
        InOrderTraverse(root->left);    
        cout << root->data <<endl;    
        InOrderTraverse(root->right);    
    }    
}    
void PostOrderTraverse(TREE_NODE * root) //后序遍历    
{    
    if(root)    
    {    
        PostOrderTraverse(root->left);    
        PostOrderTraverse(root->right);    
        cout << root->data <<endl;    
    }    
}    
void bstree_insert(int data, BSTREE* tree) //插入一个节点    
{    
    insert(create_node(data), &tree->root);    
    (tree->size)++;    
}    
TREE_NODE** bstree_find(int data, TREE_NODE** root)  //查找DATA 对应的位置    
{    
    if(NULL==*root)    
    {    
        return root;    
    }    
    if(data >(*root)->data)    
    {    
        return bstree_find(data,& (*root)->right);    
    }    
    else if(data < (*root)->data)    
    {    
        return bstree_find(data, & (*root)->left);    
    }    
    else    
    {    
        return root;    
    }
	
	//下面是非递归查找*root
	if(NULL==*root)
	{
		return root;
	}
	TREE_NODE* temp = *root;
	while(temp && ( temp->data !=data ))
	{
		if(data > temp->data)
		{
			temp = temp->right;
		}
		else if(data < temp->data)
		{
			temp = temp->left;
		}
		if(temp)
		{
			return &temp;
		}
		else
		{
			return &temp;
		}
	}
}    
void del_node(TREE_NODE* node) //删除 该节点    
{    
    delete(node);    
}
  
bool bstree_erase(int data, BSTREE* tree)  //树中 插入  传入的是地址 如果想修改 这一地址变量就要 根据地址的地址 修改    
{    
    TREE_NODE** node = bstree_find(data, & tree->root);    
    if(*node)    
    {    
        TREE_NODE* temp = *node;
		if( ((*node)->right==NULL) &&((*node)->left==NULL))//如果为叶子节点
		{
			*node = NULL;
			del_node(temp);    
			--tree->size;
		}
		if(((*node)->right==NULL) &&((*node)->left!=NULL))//node的right为空
		{
			*node = (*node)->left;
			del_node(temp);    
			--tree->size;
		}
		else if(((*node)->right!=NULL) &&((*node)->left==NULL))//node的left为空
		{
			*node = (*node)->right;
			del_node(temp);    
			--tree->size;
		}
		//下面是左右子树都不为空 删除时任一种情况 最好用1 2 种
		
		//node的左右都不为空将left中最大的数顶替已经删除的node
        if(((*node)->left != NULL) && ((*node)->right != NULL))    
        {
			TREE_NODE* s = (*node)->left;
			while(s->right)
			{
				temp=s;
				s=s->right;
			}
			(*node)->data = s->data;
			if(temp != *node)
			{
				temp->righ = s->left;
			}
			else
			{
				temp->left =s->left;//类似左子树
			}
			del_node(s);    
			--tree->size;
        }
		
		//node的左右都不为空将right中最小的数顶替已经删除的node
		if(((*node)->left != NULL) && ((*node)->right != NULL))    
        {
			TREE_NODE* s = (*node)->right;
			while(s->left)
			{
				temp=s;
				s=s->left;
			}
			(*node)->data = s->data;
			if(temp != *node)
			{
				temp->left = s->right;
			}
			else
			{
				temp->right =s->right;//类似右子树
			}
			del_node(s);    
			--tree->size;
        }
		//node的左右都不为空,直接将右边整体移动到左边最大值下面
		if(((*node)->left != NULL) && ((*node)->right != NULL))    
        {
			TREE_NODE* s = (*node)->left;
			while(s->right)
			{
				s=s->right;
			}
			s->right = (*node)->right;
			*node = (*node)->left;
			del_node(s);    
			--tree->size;
        }
		//node的左右都不为空,直接将左边边整体移动到右边最小值下面
		if(((*node)->left != NULL) && ((*node)->right != NULL))    
        {
			TREE_NODE* s = (*node)->right;
			while(s->left)
			{
				s=s->left;
			}
			s->left = (*node)->left;
			*node = (*node)->right;
			del_node(s);    
			--tree->size;
        }
        return true;    
    }    
    return false;    
}
 
void bstree_updata(BSTREE* tree,int old,int now) //新旧替换更新    
{    
    while(bstree_erase(old,tree))    
    {    
        bstree_insert(now,tree);    
    }    
}    
void clear_node(TREE_NODE** root)  //清楚节点    
{    
    if(*root)    
    {    
        clear_node(&(*root)->left);    
        clear_node(&(*root)->right);    
        del_node(*root);    
        *root = NULL;    
    }    
}    
void clear_tree(BSTREE* tree)  //clear_tree    
{    
    clear_node(&tree->root);    
    tree->size = 0;    
}    
void bstree_destroy(BSTREE* tree) //bstree_destroy    
{    
    clear_tree(tree);    
    delete(tree);    
}    
int bstree_size(BSTREE* tree) //大小    
{    
    return tree->size;    
}    
int bstree_deep(TREE_NODE* root)  //深度DEPTH    
{    
    if(root)    
    {    
        int Hleft = bstree_deep(root->left);    
        int Hright = bstree_deep(root->right);    
        return Hleft>Hright ? Hleft+1 : Hright+1;    
    }    
    return 0;    
}    
void printNodeByLevel(TREE_NODE* root) //层序遍历    
{    
    if(root ==NULL)    
    {    
        return;    
    }    
    vector<TREE_NODE*>vec;    
    vec.push_back(root);    
    int cur=0;    
    int last =1;    
    while(cur<vec.size() )    
    {    
        last = vec.size();    
        while(cur<last)    
        {    
            cout<<vec[cur]->data<<" ";    
            if(vec[cur]->left != NULL)    
            {    
                vec.push_back(vec[cur]->left);    
            }    
            if(vec[cur]->right != NULL)    
            {    
                vec.push_back(vec[cur]->right);    
            }    
            ++cur;    
        }    
        cout<<endl;    
    }    
}   
void print(TREE_NODE* root)  
{  
    if(root==NULL)  
    {  
        return;  
    }  
    vector<TREE_NODE*>vec;  
    vec.push_back(root);  
    int cur=0;  
    while(cur<vec.size())  
    {  
        cout<<vec[cur]->data<<" ";  
        if(vec[cur]->left != NULL)  
        {  
            vec.push_back(vec[cur]->left);  
        }  
        if(vec[cur]->right != NULL)  
        {  
            vec.push_back(vec[cur]->right);  
        }  
        ++cur;  
    }  
    cout<<endl;  
}   
int main()    
{    
    BSTREE* tree = create_tree();    
    bstree_insert(5, tree);    
    bstree_insert(6, tree);    
    bstree_insert(2, tree);    
    bstree_insert(1, tree);    
    bstree_insert(4, tree);    
    bstree_insert(3, tree);    
    cout << "the level print:
";    
    printNodeByLevel(tree->root);    
    cout << "the first print:
";    
    PreOrderTraverse(tree->root);    
    cout << "the middle print:
";    
    InOrderTraverse(tree->root);    
    cout << "the endl print:
";    
    PostOrderTraverse(tree->root);    
    cout<<"the tree deep:
";    
    cout<<bstree_deep(tree->root)<<endl;    
    bstree_erase(2,tree);    
    cout << "delete  num of 2:
";    
    cout << "after delete 2  print:
";    
    PreOrderTraverse(tree->root);    
    cout << "destroy the tree:
";    
    bstree_destroy(tree);    
    return 0;    
}