二叉树搜索树的应用

编程入门行业动态更新时间:2024-10-28 13:13:48

二叉树搜索树的应用

1. 二叉树搜索树的应用
2. 二叉搜索树的性能分析
3. 二叉树进阶面试题

1. 二叉树搜索树的应用

K模型：K模型即只有key作为关键码，结构中只需要存储Key即可，关键码即为需要搜索到的值。（确定一个值在不在）
比如：给一个单词word，判断该单词是否拼写正确，具体方式如下：以词库中所有单词集合中的每个单词作为key，构建一棵二叉搜索树在二叉搜索树中检索该单词是否存在，存在则拼写正确，不存在则拼写错误。
KV模型：每一个关键码key，都有与之对应的值Value，即<Key, Value>的键值对。（）
该种方式在现实生活中非常常见：
比如英汉词典就是英文与中文的对应关系，通过英文可以快速找到与其对应的中文，英文单词与其对应的中文<word, chinese>就构成一种键值对；
再比如统计单词次数，统计成功后，给定单词就可快速找到其出现的次数，单词与其出现次数就是<word, count>就构成一种键值对。

改造二叉搜索树为KV结构

#pragma once
#include <iostream>
using namespace std;namespace KV
{template <class K,class V>struct BSTreeNode{BSTreeNode<K,V>* _left;BSTreeNode<K,V>* _right;K _key;V _value;	BSTreeNode(const K& key, const V& value):_left(nullptr), _right(nullptr), _key(key),_value(value){}};template <class K,class V>class BSTree{typedef BSTreeNode<K,V> Node;public://插入bool Insert(const K& key, const V& value){if (_root == nullptr){_root = new Node(key,value); return true;}Node* cur = _root;Node* parent = nullptr;while (cur){parent = cur;if (key > cur->_key){cur = cur->_right;}else if (key < cur->_key){cur = cur->_left;}else{return false;}}cur = new Node(key,value);if (key > parent->_key){parent->_right = cur;}if (key < parent->_key){parent->_left = cur;}return true;}//中序打印void InOrder(){_InOrder(_root);cout << endl;}//查找Node * Find(const K& key){Node* cur = _root;while (cur){if (key > cur->_key){cur = cur->_right;}else if (key < cur->_key){cur = cur->_left;}else{return cur;}}return nullptr;}//删除bool Erase(const K& key){Node* cur = _root;Node* parent = nullptr;while (cur){if (key > cur->_key){parent = cur;cur = cur->_right;}else if (key < cur->_key){parent = cur;cur = cur->_left;}else{//开删if (cur->_left == nullptr){//左为空if (cur == _root){_root = cur->_right;}else if (cur == parent->_left){parent->_left = cur->_right;}else{parent->_right = cur->_right;}}else if (cur->_right == nullptr){//右为空if (cur == _root){_root = cur->_left;}else if (cur == parent->_left){parent->_left = cur->_left;}else{parent->_right = cur->_left;}}else{//左右都不为空Node* SubLeft = cur->_right;Node* _parent = cur;while (SubLeft->_left){_parent = SubLeft;SubLeft = SubLeft->_left;}swap(cur->_key, SubLeft->_key);if (SubLeft == _parent->_left){_parent->_left = SubLeft->_right;}else{_parent->_right = SubLeft->_right;}}return true;}}return false;}private:void _InOrder(Node* root){if (root == nullptr){return;}_InOrder(root->_left);cout << root->_key << ":" << root->_value << endl;_InOrder(root->_right);}private:Node* _root = nullptr;};}

统计水果出现次数

int main()
{string arr[] = { "苹果", "西瓜", "苹果", "西瓜", "苹果", "苹果", "西瓜","苹果", "香蕉", "苹果", "香蕉" };KV::BSTree<string, int> CountTree;for (auto &e : arr){KV::BSTreeNode<string, int>* ret = CountTree.Find(e);if (ret == nullptr){CountTree.Insert(e,1);}else{ret->_value++;}}CountTree.InOrder();return 0;
}

输入单词，查找单词对应的中文翻译

int main()
{KV::BSTree<string, string> dict;dict.Insert("sort", "快排");dict.Insert("left", "左边");dict.Insert("right", "右边");dict.Insert("insert", "插入");dict.Insert("key", "键值");string str;while (cin>>str){KV::BSTreeNode<string, string>* ret = dict.Find(str);if (ret){cout << ret->_value << endl;}else{cout << " 无此单词" << endl;}}return 0;
}