C++二叉搜索树的模拟实现以及实现中常见的问题
目录
- 1.需要访问私有节点的另外一种方法
- 2.搜索二叉树的删除
-
- 递归删除
- 3.代码：
1.需要访问私有节点的另外一种方法
我们在写完中序遍历后，
我们要调用这个函数的时候我们需要调用这个函数
并且需要传递根节点
但是C++的成员（根节点）一般是私有的，拿不到这个节点
两种方法：
1.实现一个getroot函数，这样就可以直接访问到根节点
2.直接套用一层，写一个子函数
void InOrder()
{
_InOrder(_root);
}
void _InOrder(Node* root)
{
.....//实现请看后面
}
2.搜索二叉树的删除
递归删除
缺点：
当递归深度很高的时候，就会很麻烦
什么情况下，生成的二叉树深度很高？
给定的数组，按照有序或者接近有序的方式进行插入的时候就会很高
3.代码：
#pragma once
// key
namespace k {
template<class K>
struct BSTreeNode//struct BinarySearchTreeNode
{
BSTreeNode<K>* _left;
BSTreeNode<K>* _right;
K _key;
//构造函数
BSTreeNode(const K& key)
:_left(nullptr)
, _right(nullptr)
, _key(key)
{}
};
template<class K>
struct BSTree
{
typedef BSTreeNode<K> Node;
public:
BSTree()
:_root(nullptr)
{}
bool Insert(const K& key)
{
if (_root == nullptr)
{
_root = new Node(key);
return true;
}
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);
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* 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
{
// 找到，开始删除
if (cur->_left == nullptr)
{
if (parent == nullptr)//根节点的情况
{
_root = cur->_right;
}
else
{
if (parent->_left == cur)
parent->_left = cur->_right;
else
parent->_right = cur->_right;
}
delete cur;
}
else if (cur->_right == nullptr)
{
if (parent == nullptr)
{
_root = cur->_left;
}
else
{
if (parent->_left == cur)
parent->_left = cur->_left;
else
parent->_right = cur->_left;
}
delete cur;
}
else//左右都不为空
{
Node* minParent = cur;
Node* min = cur->_right;
while (min->_left)
{
minParent = min;
min = min->_left;
}
cur->_key = min->_key;
if (minParent->_left == min)
minParent->_left = min->_right;
else
minParent->_right = min->_right;
delete min;
}
return true;
}
}
//没有找到这个值，说明删除失败
return false;
}
//递归式插入
bool InsertR(const K& key)
{
return _InsertR(_root, key);
}
Node* FindR(const K& key)
{
return _FindR(_root, key);
}
bool EraseR(const K& key)
{
return _EraseR(_root, key);
}
//我们在写完中序遍历后，
//我们要调用这个函数的时候我们需要调用这个函数
//并且需要传递根节点
//但是C++的成员（根节点）一般是私有的，拿不到这个节点
//两种方法：
//1.实现一个getroot函数，这样就可以直接访问到根节点
//2.直接套用一层，写一个子函数
void InOrder()
{
_InOrder(_root);
}
private://子函数设置称为私有的
bool _InsertR(Node*& root, const K& key)
{
if (root == nullptr)
{
root = new Node(key);
return true;
}
if (root->_key < key)
return _InsertR(root->_right, key);
else if (root->_key > key)
return _InsertR(root->_left, key);
else//相等就不需要插入了
return false;
}
//递归查找
Node* _FindR(Node* root, const K& key)
{
if (root == nullptr) return nullptr;
if (root->_key < key) return _FindR(root->_right, key);
else if (root->_key > key) return _FindR(root->_left, key);
else return root;
}
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->_left == nullptr)
{
root = root->_right;
}
else if (root->_right == nullptr)
{
root = root->_left;
}
else
{
Node* min = root->_right;
while (min->_left)
{
min = min->_left;
}
swap(min->_key, root->_key);
// 递归到右子树去删除
return _EraseR(root->_right, key);
}
delete del;
return true;
}
}
void _InOrder(Node* root)
{
if (root == nullptr)
{
return;
}
_InOrder(root->_left);
cout << root->_key << " ";
_InOrder(root->_right);
}
private:
Node* _root;
};
void TestBSTree()
{
BSTree<int> t;
int a[] = { 5, 3, 4, 1, 7, 8, 2, 6, 0, 9,5,5 };
for (auto e : a)
{
t.Insert(e);
}
// 排序加去重
t.InOrder();
t.EraseR(7);
t.InOrder();
cout << endl;
t.EraseR(5);
t.InOrder();
cout << endl;
t.EraseR(0);
t.InOrder();
cout << endl;
for (auto e : a)
{
t.EraseR(e);
t.InOrder();
cout << endl;
}
}
}
namespace KV
{
template<class K, class V>
struct BSTreeNode
{
BSTreeNode<K, V>* _left;
BSTreeNode<K, V>* _right;
K _key;
V _value;
//pair _kv;
BSTreeNode(const K& key, const V& value)
:_left(nullptr)
, _right(nullptr)
, _key(key)
, _value(value)
{}
};
template<class K, class V>
struct BSTree
{
typedef BSTreeNode<K, V> Node;
public:
BSTree()
:_root(nullptr)
{}
bool Insert(const K& key, const V& value)
{
if (_root == nullptr)
{
_root = new Node(key, value);
return true;
}
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)
{
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* 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
{
// 找到，准备开始删除
if (cur->_left == nullptr)
{
if (parent == nullptr)
{
_root = cur->_right;
}
else
{
if (parent->_left == cur)
parent->_left = cur->_right;
else
parent->_right = cur->_right;
}
delete cur;
}
else if (cur->_right == nullptr)
{
if (parent == nullptr)
{
_root = cur->_left;
}
else
{
if (parent->_left == cur)
parent->_left = cur->_left;
else
parent->_right = cur->_left;
}
delete cur;
}
else
{
Node* minParent = cur;
Node* min = cur->_right;
while (min->_left)
{
minParent = min;
min = min->_left;
}
cur->_key = min->_key;
cur->_value = min->_value;
if (minParent->_left == min)
minParent->_left = min->_right;
else
minParent->_right = min->_right;
delete min;
}
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);
}
private:
Node* _root;
};
void TestBSTree1()
{
// 字典KV模型
BSTree<string, string> dict;
dict.Insert("sort", "排序");
dict.Insert("left", "左边");
dict.Insert("right", "右边");
dict.Insert("map", "地图、映射");
//...
string str;
while (cin >> str)
{
BSTreeNode<string, string>* ret = dict.Find(str);
if (ret)
{
cout << "对应中文解释：" << ret->_value << endl;
}
else
{
cout << "无此单词" << endl;
}
}
}
void TestBSTree2()
{
// 统计水果出现次数
string arr[] = { "苹果", "西瓜","草莓", "苹果", "西瓜", "苹果", "苹果", "西瓜", "苹果", "香蕉", "苹果", "香蕉" };
BSTree<string, int> countTree;
for (auto& str : arr)
{
//BSTreeNode* ret = countTree.Find(str);
auto ret = countTree.Find(str);
if (ret != nullptr)
{
ret->_value++;
}
else
{
countTree.Insert(str, 1);
}
}
countTree.InOrder();
}
}