【C++】实现一个二叉搜索树

二叉搜索树的概念

1.结点定义

2.构造、析构、拷贝构造、赋值重载

3.插入、删除、查找、排序

3.1插入

3.2插入递归版

3.3查找指定值

3.3查找指定值递归版

3.4中序遍历

3.5删除

最后

二叉搜索树的概念

二叉搜索树又称为二叉排序树或二叉查找树，它或者是一棵空树，或者是具有以下性质的二叉树：

非空左子树上所有结点的值都小于根结点的值。
非空右子树上所有结点的值都大于根结点的值。
左右子树都是二叉搜索树。

1.结点定义

template<class K>
struct BSTreeNode
{BSTreeNode<K>* _left;BSTreeNode<K>* _right;K _key;BSTreeNode(const K& key):_key(key),_left(nullptr),_right(nullptr){}
};

2.构造、析构、拷贝构造、赋值重载

    //构造函数BSTree(): _root(nullptr){}//析构函数~BSTree(){//递归删除Destroy(_root);_root = nullptr;}//拷贝构造BSTree(const BSTree<K>& t){//递归去拷贝_root = Copy(t._root);}//赋值重载BSTree<K>& operator=(BSTree<K> t)//注意这里传参，传值传参，默认已经拷贝构造新的一份了{swap(_root, t._root);//这里直接交换return 就好return *this;}Node* Copy(Node* root){//前序遍历if (root == nullptr){return nullptr;}Node* newRoot = new Node(root->_key);//建立联系，不是简单的调用newRoot->_left = Copy(root->_left);newRoot->_right = Copy(root->_right);return newRoot;}void Destroy(Node* root){if (root == nullptr){return;}Destroy(_root->_left);Destroy(_root->_right);delete(root);}

3.插入、删除、查找、排序

3.1插入

bool Insert(const K& key){//不允许相等数据插入版本，减少冗余//空树if (_root == nullptr){_root = new Node(key);return true;}//正常插入Node* cur = _root;Node* parent = _root;while (cur != nullptr){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;}

3.2插入递归版

bool InsertR(const K& key)//注意参数{return _InsertR(_root, key);}
bool _InsertR(Node* &root,const K& key){if (root == nullptr){root = new Node(key);return true;}if (root->_key > key){return _InsertR(root->_left, key);}else if (root->_key < key){return _InsertR(root->_right, key);}else{//相等return false;}}

3.3查找指定值

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

3.3查找指定值递归版

    bool FindR(const K& key){return _FindR(_root, key);}bool _FindR(Node*& root, const K& key){if (root == nullptr){return false;}if (root->_key == key){return true;}if (root->_key > key){return _FindR(root->_left, key);}else {return _FindR(root->_right, key);}}

3.4中序遍历

    void InOrder(){_InOrder(_root);}void _InOrder(Node* root){if (root == nullptr){return;}_InOrder(root->_left);cout << root->_key << " ";_InOrder(root->_right);}

3.5删除

bool Erase(const K& key){Node* cur = _root;Node* parent = _root;while (cur){//找到节点if (cur->_key > key){parent = cur;cur = cur->_left;}else if (cur->_key < key){parent = cur;cur = cur->_right;}else{//找到了//删除没有孩子或者只有一种孩子的节点//这个是普通节点if (cur->_right == nullptr){if (parent->_left == cur){parent->_left = cur->_left;}if (parent->_right == cur){parent->_right = cur->_left;}if(parent==cur)//是根结点{parent = parent->_left;}delete(cur);return true;}else if(cur->_left==nullptr){if (parent->_left == cur){parent->_left = cur->_right;}if (parent->_right == cur){parent->_right = cur->_right;}if (parent == cur)//是根结点{parent = parent->_right;}delete(cur);return true;}else{//左右都不为空//替换法删除,找右子树的最小值Node* miniright = cur->_right;Node* minirightp = cur;while (miniright->_left != nullptr){minirightp = miniright;miniright = miniright->_left;}cur->_key = miniright->_key;if (minirightp->_left == miniright){minirightp->_left = miniright->_right;}if (minirightp->_right == miniright){minirightp->_right = miniright->_right;}delete(miniright);return true;}}}return false;}