概念
搜索二叉树是一种特殊的二叉树，其具有以下特点：
1.对于每个结点，它的左子树中的所有节点的值都小于该节点的值，而右子树中的所有节点的值都大于该节点的值。
2.左子树和右子树都是搜索二叉树。
这个 特性使得搜索二叉树可以用于高效地进行查找、插入和删除操作。通过利用节点之间的大小关系，我们可以快速定位到目标值所在的位置，避免不必要的比较操作。
在数据结构专栏已经讲解过了二叉树了：
下面直接讲解对搜索二叉树的实现。
实现搜索二叉树
二叉树结点模板
默认构造
查找
插入
bool Insert(const K& key)
{
if (_root == nullptr)
{
_root = new Node(key);
return true;
}
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (key > cur->_key)
{
parent = cur;
cur = cur->_right;
}
else if (key < cur->_key)
{
parent = cur;
cur = cur->_left;
}
else
{
return false;
}
}
cur = new Node(key);
if (key > parent->_key)
{
parent->_right = cur;
}
else
{
parent->_left = cur;
}
return true;
}
删除
bool Erase(const K& key)
{
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (key > cur->_key)
{
parent = cur;
cur = cur->_right;
}
else if (key < cur->_key)
{
parent = cur;
cur = cur->_left;
}
else
{
if (cur->_left == nullptr)
{
if (cur == _root)
{
_root = cur->_right;
}
else
{
if (cur == parent->_right)
{
parent->_right = cur->_right;
}
else
{
parent->_left = cur->_right;
}
}
delete cur;
return true;
}
else if (cur->_right == nullptr)
{
if (cur == _root)
{
_root = cur->_left;
}
else
{
if (cur == parent->_left)
{
parent->_left = cur->_left;
}
else
{
parent->_right = cur->_left;
}
}
delete cur;
return true;
}
else
{
Node* rightMinParent = cur;
Node* rightMin = cur->_right;
while (rightMin->_left)
{
rightMinParent = rightMin;
rightMin = rightMin->_left;
}
cur->_key = rightMin->_key;
if (rightMin == rightMinParent->_left)
{
rightMinParent->_left = rightMin->_right;
}
else
{
rightMinParent->_right = rightMin->_right;
}
delete rightMin;
return true;
}
}
}
return false;
}
拷贝、赋值、析构
递归版本的增删查
删除：
bool _EraseR(Node*& root,const K& key)
{
if (root == nullptr)
return false;
if (root->_key < key)
return _EraseR(root->_right, key);
else if (root->_key > key)
return _EraseR(root->_left, key);
else
{
Node* del = root;
if (root->_right == nullptr)
root = root->_left;
else if (root->_left == nullptr)
root = root->_right;
else
{
Node* rightMin = root->_right;
while (rightMin->_left)
rightMin = rightMin->_left;
swap(root->_key, rightMin->_key);
return _EraseR(root->_right, key);
}
delete del;
return true;
}
}
实现源码
#pragma once
namespace fnc
{
template<class K>
struct BSTreeNode
{
typedef BSTreeNode<K> Node;
Node* _left;
Node* _right;
K _key;
BSTreeNode(const K& key)
:_left(nullptr),
_right(nullptr),
_key(key)
{
}
};
template<class K>
class BSTree
{
typedef BSTreeNode<K> Node;
public:
//强制生成默认构造
BSTree() = default;
//拷贝构造
BSTree(const BSTree<K>& t)
{
_root = Copy(t._root);
}
//赋值
BSTree<K>& operator=(BSTree<K> t)
{
swap(_root, t._root);
return *this;
}
//析构
~BSTree()
{
Destory(_root);
cout << "Destory()" << endl;
}
//查找
bool Find(const K& key)
{
Node* cur = _root;
while (cur)
{
if (cur->_key < key)
{
cur = cur->_right;
}
else if (cur->_key > key)
{
cur = cur->_left;
}
else
{
return true;
}
}
return false;
}
//插入
bool Insert(const K& key)
{
if (_root == nullptr)
{
_root = new Node(key);
return true;
}
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (key > cur->_key)
{
parent = cur;
cur = cur->_right;
}
else if (key < cur->_key)
{
parent = cur;
cur = cur->_left;
}
else
{
return false;
}
}
cur = new Node(key);
if (key > parent->_key)
{
parent->_right = cur;
}
else
{
parent->_left = cur;
}
return true;
}
bool Erase(const K& key)
{
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (key > cur->_key)
{
parent = cur;
cur = cur->_right;
}
else if (key < cur->_key)
{
parent = cur;
cur = cur->_left;
}
else
{
if (cur->_left == nullptr)
{
if (cur == _root)
{
_root = cur->_right;
}
else
{
if (cur == parent->_right)
{
parent->_right = cur->_right;
}
else
{
parent->_left = cur->_right;
}
}
delete cur;
return true;
}
else if (cur->_right == nullptr)
{
if (cur == _root)
{
_root = cur->_left;
}
else
{
if (cur == parent->_left)
{
parent->_left = cur->_left;
}
else
{
parent->_right = cur->_left;
}
}
delete cur;
return true;
}
else
{
Node* rightMinParent = cur;
Node* rightMin = cur->_right;
while (rightMin->_left)
{
rightMinParent = rightMin;
rightMin = rightMin->_left;
}
cur->_key = rightMin->_key;
if (rightMin == rightMinParent->_left)
{
rightMinParent->_left = rightMin->_right;
}
else
{
rightMinParent->_right = rightMin->_right;
}
delete rightMin;
return true;
}
}
}
return false;
}
//打印
void InOrder()
{
_InOrder(_root);
cout << endl;
}
bool FindR(const K& key)
{
return _FindR(_root, key);
}
bool InsertR(const K& key)
{
return _InsertR(_root, key);
}
bool EraseR(const K& key)
{
return _EraseR(_root, key);
}
private:
bool _EraseR(Node*& root,const K& key)
{
if (root == nullptr)
return false;
if (root->_key < key)
return _EraseR(root->_right, key);
else if (root->_key > key)
return _EraseR(root->_left, key);
else
{
Node* del = root;
if (root->_right == nullptr)
root = root->_left;
else if (root->_left == nullptr)
root = root->_right;
else
{
Node* rightMin = root->_right;
while (rightMin->_left)
rightMin = rightMin->_left;
swap(root->_key, rightMin->_key);
return _EraseR(root->_right, key);
}
delete del;
return true;
}
}
bool _InsertR(Node*& root, const K& key)
{
if (root == nullptr)
{
root = new Node(key);
return true;
}
if (key > root->_key)
{
return _InsertR(root->_right, key);
}
else if (key < root->_key)
{
return _InsertR(root->_left, key);
}
else
{
return false;
}
}
bool _FindR(Node* root, const K& key)
{
if (root == nullptr)
{
return false;
}
if (root->_key < key)
{
return _FindR(root->_right, key);
}
else if (root->_key > key)
{
return _FindR(root->_left, key);
}
else
{
return true;
}
}
void Destory(Node* root)
{
if (root == nullptr)
return;
Destory(root->_left);
Destory(root->_right);
delete root;
}
Node* Copy(Node* root)
{
if (root == nullptr)
{
return nullptr;
}
Node* newRoot = new Node(root->_key);
newRoot->_left = Copy(root->_left);
newRoot->_right = Copy(root->_right);
return newRoot;
}
void _InOrder(Node* root)
{
if (root == nullptr)
{
return;
}
_InOrder(root->_left);
cout << root->_key << " ";
_InOrder(root->_right);
}
private:
Node* _root=nullptr;
};
}
![[<span style='color:red;'>C</span>++]17:<span style='color:red;'>二</span><span style='color:red;'>叉</span><span style='color:red;'>树</span><span style='color:red;'>进</span><span style='color:red;'>阶</span>](https://img-blog.csdnimg.cn/direct/41f872e53f5a49d5a6715729dcd6ef9b.png)
