【C++】二叉搜索树的概念与实现

目录

二叉搜索树

概念

key类型

概念

代码实现 

key_value类型

 概念

代码实现

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二叉搜索树

概念

⼆叉搜索树⼜称⼆叉排序树，它或者是⼀棵空树，或者是具有以下性质的⼆叉树: 左子树的值默认小于根节点，右子树的值默认大于根节点 。

⼆叉搜索树中可以⽀持插⼊相等的值，也可以不⽀持插⼊相等的值，具体看使⽤场景定义：map/set/multimap/multiset系列容器底层就是⼆叉搜索树，其中map/set不⽀持插⼊相等 值，multimap/multiset⽀持插⼊相等值 。

二叉搜索树的查找时间复杂度在O(logN)~O(N) 

key类型

概念

我们购买了一个停车场的位置，每次开车入库时安保会检测我们的车牌号释放存入后台，如果存在抬杆放行。

Key用于标识，不可以修改，否则会破坏树的性质！ 

代码实现 

单个节点的定义

template<class K>
class BTNode
{
public:K _key;// 左右节点BTNode<K>* _left;BTNode<K>* _right;BTNode(const K& data):_key(data),_left(nullptr),_right(nullptr){}
};

构造

• 默认构造：使用默认的即可
• 拷贝构造 ：注意需要深拷贝

Node* Copy(Node* root)
{if (root == nullptr)return nullptr;Node* newRoot = new Node(root->_key, root->_value);newRoot->_left = Copy(root->_left);newRoot->_right = Copy(root->_right);return newRoot;
}

 赋值重载

BSTree<K, V>& operator=(BSTree<K, V> tmp)
{swap(_root, tmp._root);return *this;
}

析构

走后序遍历进行析构delete

void Destory(Node* _root)
{if (_root == nullptr)return;Destory(_root->_left);Destory(_root->_right);delete _root;
}

Insert

bool Insert(const K& key)
{// 空树if (_root == nullptr){_root = new Node(key);return true;}Node* cur = _root;Node* parent = cur;while (cur){if (cur->_key < key){parent = cur;cur = cur->_right;}else if (cur->_key > key){parent = cur;cur = cur->_left;}else {return false;}}cur = new Node(key);if (parent->_key < key) parent->_right = cur;else parent->_left = cur;return true;
}

 Find

与Insert同理，大往右，小往左，相等返回true，找到结束没有返回false

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;
}

Erase

【1】先找到要删除的数据 

• 存在：执行第二步【2】
• 不存在返回false 

【2】删除数据的多种情况 

• 【1】情况一：0/1个孩子

        左节点为nullptr 

               

         右节点为nullptr

                    

• 【2】情况二：2个孩子

         

bool Erase(const K& key)
{Node* cur = _root;Node* parent = cur;while (cur){if (cur->_key < key){parent = cur;cur = cur->_right;}else if (cur->_key > key){parent = cur;cur = cur->_left;}else {// 删除// 情况1: 删除0/1个孩子的节点if (cur->_left == nullptr){// 特殊情况if (cur == _root){_root = cur->_right;}// 左孩子为空if (parent->_left == cur){parent->_left = cur->_right;}else {parent->_right = cur->_right;}delete cur;return true;}else if (cur->_right == nullptr){// 特殊情况if (cur == _root){_root = cur->_left;}// 右孩子为空if (parent->_left == cur){parent->_left = cur->_left;}else {parent->_right = cur->_left;}delete cur;return true;}else {// 左右都存在孩子Node* replace_parent = cur;Node* replace = cur->_right;// 右子树的最左节点while (replace->_left){replace_parent = replace;replace = replace->_left;}cur->_key = replace->_key;if (replace_parent->_left == replace)replace_parent->_left = replace->_right;elsereplace_parent->_right = replace->_right;delete replace;return true;}}}return false;
}

整体代码实现：

namespace Key
{// 二叉搜索树// 只存在增删查,没有改,改会破坏二叉搜索树的性质// 每个节点结构template<class K>class BTNode{public:K _key;// 左右节点BTNode<K>* _left;BTNode<K>* _right;BTNode(const K& data):_key(data),_left(nullptr),_right(nullptr){}};template<class K>class BSTree{using Node = BTNode<K>;public:BSTree() = default;BSTree(const BSTree<K>& t){_root = Copy(t._root);}BSTree<K>& operator=(BSTree<K> tmp){swap(_root, tmp._root);return *this;}~BSTree(){Destory(_root);_root = nullptr;}bool Insert(const K& key){// 空树if (_root == nullptr){_root = new Node(key);return true;}Node* cur = _root;Node* parent = cur;while (cur){if (cur->_key < key){parent = cur;cur = cur->_right;}else if (cur->_key > key){parent = cur;cur = cur->_left;}else {return false;}}cur = new Node(key);if (parent->_key < key) parent->_right = cur;else parent->_left = cur;return true;}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;}bool Erase(const K& key){Node* cur = _root;Node* parent = cur;while (cur){if (cur->_key < key){parent = cur;cur = cur->_right;}else if (cur->_key > key){parent = cur;cur = cur->_left;}else {// 删除// 情况1: 删除0/1个孩子的节点if (cur->_left == nullptr){// 特殊情况if (cur == _root){_root = cur->_right;}// 左孩子为空if (parent->_left == cur){parent->_left = cur->_right;}else {parent->_right = cur->_right;}delete cur;return true;}else if (cur->_right == nullptr){// 特殊情况if (cur == _root){_root = cur->_left;}// 右孩子为空if (parent->_left == cur){parent->_left = cur->_left;}else {parent->_right = cur->_left;}delete cur;return true;}else {// 左右都存在孩子Node* replace_parent = cur;Node* replace = cur->_right;// 右子树的最左节点while (replace->_left){replace_parent = replace;replace = replace->_left;}cur->_key = replace->_key;if (replace_parent->_left == replace)replace_parent->_left = replace->_right;elsereplace_parent->_right = replace->_right;delete replace;return true;}}}return false;}void InOrder(){_InOrder(_root);cout << endl;}private:void _InOrder(Node* _root){if (_root == nullptr)return;_InOrder(_root->_left);cout << _root->_key << " ";_InOrder(_root->_right);}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;}Node* _root = nullptr;};
}

key_value类型

 概念

我们统计一个书中相同单词的个数，Key就是这个单词，而value表示单词的个数。

Key用于标识不可以修改，但是我们可以修改value。 

代码实现

单个节点的定义

template<class K, class V>
class BTNode
{
public:K _key;V _value;// 左右节点BTNode<K, V>* _left;BTNode<K, V>* _right;BTNode(const K& key, const V& value):_key(key),_value(value), _left(nullptr), _right(nullptr){}
};

整体代码实现：

namespace Key_value
{// 二叉搜索树// 只存在增删查,没有改,改会破坏二叉搜索树的性质// 每个节点结构template<class K, class V>class BTNode{public:K _key;V _value;// 左右节点BTNode<K, V>* _left;BTNode<K, V>* _right;BTNode(const K& key, const V& value):_key(key),_value(value), _left(nullptr), _right(nullptr){}};template<class K, class V>class BSTree{using Node = BTNode<K, V>;public:BSTree() = default;BSTree(const BSTree<K, V>& t){_root = Copy(t._root);}BSTree<K, V>& operator=(BSTree<K, V> tmp){swap(_root, tmp._root);return *this;}~BSTree(){Destory(_root);_root = nullptr;}bool Insert(const K& key, const V& value){// 空树if (_root == nullptr){_root = new Node(key, value);return true;}Node* cur = _root;Node* parent = cur;while (cur){if (cur->_key < key){parent = cur;cur = cur->_right;}else if (cur->_key > key){parent = cur;cur = cur->_left;}else {return false;}}cur = new Node(key, value);if (parent->_key < key) parent->_right = cur;else parent->_left = cur;return true;}Node* 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 cur;}return nullptr;}bool Erase(const K& key){Node* cur = _root;Node* parent = cur;while (cur){if (cur->_key < key){parent = cur;cur = cur->_right;}else if (cur->_key > key){parent = cur;cur = cur->_left;}else {// 删除// 情况1: 删除0/1个孩子的节点if (cur->_left == nullptr){// 特殊情况if (cur == _root){_root = cur->_right;}// 左孩子为空if (parent->_left == cur){parent->_left = cur->_right;}else {parent->_right = cur->_right;}delete cur;return true;}else if (cur->_right == nullptr){// 特殊情况if (cur == _root){_root = cur->_left;}// 右孩子为空if (parent->_left == cur){parent->_left = cur->_left;}else {parent->_right = cur->_left;}delete cur;return true;}else {// 左右都存在孩子Node* replace_parent = cur;Node* replace = cur->_right;// 右子树的最左节点while (replace->_left){replace_parent = replace;replace = replace->_left;}cur->_key = replace->_key;if (replace_parent->_left == replace)replace_parent->_left = replace->_right;elsereplace_parent->_right = replace->_right;delete replace;return true;}}}return false;}void InOrder(){_InOrder(_root);cout << endl;}private:void _InOrder(Node* _root){if (_root == nullptr)return;_InOrder(_root->_left);cout << _root->_key << ":" << _root->_value << endl;_InOrder(_root->_right);}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, root->_value);newRoot->_left = Copy(root->_left);newRoot->_right = Copy(root->_right);return newRoot;}Node* _root = nullptr;};
}