C++进阶--搜索二叉树-编程知识

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：

二叉树1
二叉树2

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

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默认构造

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查找

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插入

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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;}

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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;}

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拷贝、赋值、析构

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递归版本的增删查

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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;}}

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实现源码

#pragma oncenamespace 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;};
}