文章目录
- 1.搜索二叉树的概念
- 2.搜索二叉树的模拟实现
-
- [2.1 搜索二叉树的结构](#2.1 搜索二叉树的结构)
- [2.2 插入](#2.2 插入)
- [2.3 查找](#2.3 查找)
- [2.4 删除](#2.4 删除)
- [2.5 中序遍历](#2.5 中序遍历)
- [2.6 完整代码](#2.6 完整代码)
- 3.二叉搜索树的两种模型
-
- [3.1 两种模型](#3.1 两种模型)
- [3.2 key_value模型搜索二叉树](#3.2 key_value模型搜索二叉树)
- 4.两种二叉树的测试
1.搜索二叉树的概念
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:
①若它的左子树不为空，则左子树上所有节点的值都小于根节点的值
②若它的右子树不为空，则右子树上所有节点的值都大于根节点的值
③它的左右子树也分别为二叉搜索树
下面便是一个例子：
2.搜索二叉树的模拟实现
2.1 搜索二叉树的结构
cpp
template<class K>
struct BSTreeNode
{
BSTreeNode<K>* _left;
BSTreeNode<K>* _right;
K _key;
BSTreeNode(const K& key)
:_left(nullptr)
, _right(nullptr)
, _key(key)
{}2.2 插入
cpp
bool Insert(const K& key)
{
if (_root == nullptr)
{
_root = new Node(key);
return true;
}
//找插入位置
Node* parents = nullptr;
Node* cur = _root;
while (cur != nullptr)
{
if (cur->_key < key)
{
parents = cur;
cur = cur->_right;
}
else if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else
{
return false;
}
}
//插入
cur = new Node(key);
if (parent->_key < key)
{
parent->_right = cur;
}
else
{
parent->_left = cur;
}
return true;
}
2.3 查找
cpp
bool Find(const K& key)
{
Node* cur = _root;
while (cur != nullptr)
{
if (cur->_key < key)
{
cur = cur->_right;
}
else if (cur->_key > key)
{
cur = cur->_left;
}
else
{
return true;
}
}
return false;
}
2.4 删除
cpp
bool Erase(const K& key)
{
Node* parent = nullptr;
Node* cur = _root;
while (cur != nullptr)
{
if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else
{
//找到节点后准备删除，有三种情况
//1.第一种情况
if (cur->_left == nullptr)// 左为空，父亲指向我的右
{
if (cur == _root)
{
_root = cur->_right;
}
else
{
if (cur == parent->_left)
{
parent->_left = cur->_right;
}
else
{
parent->_right = cur->_right;
}
}
delete cur;
}
//2.第二种情况
else if (cur->_right == nullptr)// 右为空，父亲指向我的左
{
if (cur == _root)
{
_root = cur->_left;
}
else
{
if (cur == parent->_left)
{
parent->_left = cur->_left;
}
else
{
parent->_right = cur->_left;
}
}
delete cur;
}
//3.第三种情况
else
{
// 左右都不为空，替换法删除
// 查找右子树的最左(小)节点替代删除
Node* rightMinParent = cur;
Node* rightMin = cur->_right;
while (rightMin->_left)//找右子树的最小节点
{
rightMinParent = rightMin;
rightMin = rightMin->_left;
}
swap(cur->_key, rightMin->_key);
if (rightMinParent->_left == rightMin)
rightMinParent->_left = rightMin->_right;
else
rightMinParent->_right = rightMin->_right;
delete rightMin;
}
return true;
}
}
}
第三种情况替换遵守一个个规则： 替换要找左子树的最大节点 或者右子树的最小节点
2.5 中序遍历
cpp
void InOrder()
{
_InOrder(_root);
cout << endl;
}
void _InOrder(Node* root)
{
if (root == nullptr)
{
return;
}
_InOrder(root->_left);
cout << root->_key << " ";
_InOrder(root->_right);
}2.6 完整代码
cpp
#pragma once
#include<string>
namespace key
{
template<class K>
struct BSTreeNode
{
BSTreeNode<K>* _left;
BSTreeNode<K>* _right;
K _key;
BSTreeNode(const K& key)
:_left(nullptr)
, _right(nullptr)
, _key(key)
{}
};
template<class K>
class BSTree
{
typedef BSTreeNode<K> Node;
public:
bool Insert(const K& key)
{
if (_root == nullptr)
{
_root = new Node(key);
return true;
}
//找插入位置
Node* parents = nullptr;
Node* cur = _root;
while (cur != nullptr)
{
if (cur->_key < key)
{
parents = cur;
cur = cur->_right;
}
else if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else
{
return false;
}
}
//插入
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 != nullptr)
{
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* parent = nullptr;
Node* cur = _root;
while (cur != nullptr)
{
if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else
{
//找到节点后准备删除，有三种情况
//1.第一种情况
if (cur->_left == nullptr)// 左为空，父亲指向我的右
{
if (cur == _root)
{
_root = cur->_right;
}
else
{
if (cur == parent->_left)
{
parent->_left = cur->_right;
}
else
{
parent->_right = cur->_right;
}
}
delete cur;
}
//2.第二种情况
else if (cur->_right == nullptr)// 右为空，父亲指向我的左
{
if (cur == _root)
{
_root = cur->_left;
}
else
{
if (cur == parent->_left)
{
parent->_left = cur->_left;
}
else
{
parent->_right = cur->_left;
}
}
delete cur;
}
//3.第三种情况
else
{
// 左右都不为空，替换法删除
// 查找右子树的最左(小)节点替代删除
Node* rightMinParent = cur;
Node* rightMin = cur->_right;
while (rightMin->_left)//找右子树的最小节点
{
rightMinParent = rightMin;
rightMin = rightMin->_left;
}
swap(cur->_key, rightMin->_key);
if (rightMinParent->_left == rightMin)
rightMinParent->_left = rightMin->_right;
else
rightMinParent->_right = rightMin->_right;
delete rightMin;
}
return true;
}
}
}
void InOrder()
{
_InOrder(_root);
cout << endl;
}
void _InOrder(Node* root)
{
if (root == nullptr)
{
return;
}
_InOrder(root->_left);
cout << root->_key << " ";
_InOrder(root->_right);
}
private:
Node* _root = nullptr;
};
}3.二叉搜索树的两种模型
3.1 两种模型
①K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。
也就是上面的那种情况。
②KV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。
2.1 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；
2.2 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
3.2 key_value模型搜索二叉树
cpp
#pragma once
#include<string>
#include<iostream>
using namespace std;
namespace key_value
{
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:
bool Insert(const K& key, const V& value)
{
if (_root == nullptr)
{
_root = new Node(key, value);
return true;
}
//找插入位置
Node* parent = nullptr;
Node* cur = _root;
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)//为了返回对应值value值的节点，要修改原来的bool类型
{
Node* cur = _root;
while (cur)
{
if (cur->_key < key)
{
cur = cur->_right;
}
else if (cur->_key > key)
{
cur = cur->_left;
}
else
{
return cur;
}
}
return cur;
}
bool Erase(const K& key)
{
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else
{
// 删除
// 左为空，父亲指向我的右
if (cur->_left == nullptr)
{
//if(parent == nullptr)
if (cur == _root)
{
_root = cur->_right;
}
else
{
if (cur == parent->_left)
{
parent->_left = cur->_right;
}
else
{
parent->_right = cur->_right;
}
}
delete cur;
}
else if (cur->_right == nullptr)
{
//if(parent == nullptr)
if (cur == _root)
{
_root = cur->_left;
}
else
{
// 右为空，父亲指向我的左
if (cur == parent->_left)
{
parent->_left = cur->_left;
}
else
{
parent->_right = cur->_left;
}
}
delete cur;
}
else
{
// 左右都不为空，替换法删除
//
// 查找右子树的最左节点替代删除
Node* rightMinParent = cur;
Node* rightMin = cur->_right;
while (rightMin->_left)
{
rightMinParent = rightMin;
rightMin = rightMin->_left;
}
swap(cur->_key, rightMin->_key);
if (rightMinParent->_left == rightMin)
rightMinParent->_left = rightMin->_right;
else
rightMinParent->_right = rightMin->_right;
delete rightMin;
}
return true;
}
}
return false;
}
void _InOrder(Node* root)
{
if (root == nullptr)
{
return;
}
_InOrder(root->_left);
cout << root->_key << ":" << root->_value << endl;
_InOrder(root->_right);
}
void InOrder()
{
_InOrder(_root);
cout << endl;
}
private:
Node* _root = nullptr;
};
}4.两种二叉树的测试
test.cpp:
cpp
#define _CRT_SECURE_NO_WARNINGS 1
#include "BStree(k).h"
#include"BStree(kv).h"
int main()
{
key::TestBSTree1();
cout << "-----------------------------------------------------------------" << endl;
key_value::TestBSTree();
return 0;
}key搜索二叉树：
cpp
void TestBSTree1()
{
int a[] = { 8, 3, 1, 10, 6, 4, 7, 14, 13 };
BSTree<int> t1;
for (auto e : a)
{
t1.Insert(e);
}
t1.InOrder();
//t1.Erase(3);
t1.Erase(8);
t1.InOrder();
for (auto e : a)
{
t1.Erase(e);
t1.InOrder();
}
}key_value搜索二叉树：
cpp
void TestBSTree()
{
string strs[] = { "苹果", "西瓜", "苹果", "樱桃", "苹果", "樱桃", "苹果", "樱桃", "苹果" };
// 统计水果出现的次
BSTree<string, int> countTree;
for (auto str : strs)
{
auto ret = countTree.Find(str);
if (ret == NULL)
{
countTree.Insert(str, 1);
}
else
{
ret->_value++;
}
}
countTree.InOrder();
cout << "请输入英文单词，如果词典中有该单词，则输出该单词的中文；如果词库没有，则输出'单词拼写错误'\n";
BSTree<string, string> dict;
dict.Insert("insert", "插入");
dict.Insert("erase", "删除");
dict.Insert("left", "左边");
dict.Insert("string", "字符串");
string str;
while (cin >> str)
{
auto ret = dict.Find(str);
if (ret)
{
cout << str << ":" << ret->_value << endl;
}
else
{
cout << "单词拼写错误" << endl;
}
}
}