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1.二叉搜索树概念
2.二叉搜索树非递归实现
2.1初始结构定义
template<class K>
struct BSTreeNode
{
BSTreeNode<K>* _left;
BSTreeNode<K>* _right;
K _key;
//构造函数
BSTreeNode(const K& key)
:_left(nullptr)
, _right(nullptr)
, _key(key)
{}
};
2.2二叉搜索树插入
bool Insert(const K& key)
{
//空树,创建根结点
if (_root == nullptr)
{
_root = new Node(key);
return true;
}
Node* parent = nullptr;
Node* cur = _root;
//寻找待插入结点的位置
while (cur)
{
//如果待插入结点比cur指向的结点大,则去该结点的右边去找
if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
//如果待插入结点比cur指向的结点小,则去该结点的左边去找
else if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
//二叉搜索树不允许有重复的值。
else
{
return false;
}
}
//走到这里说明找到插入的位置了,可以创建结点进行插入
cur = new Node(key);
//如果比父结点大,则在其右边插入
if (parent->_key < key)
{
parent->_right = cur;
}
//如果比父结点小,则在其左边插入
else
{
parent->_left = cur;
}
return true;
}
2.3二叉搜索树查找
bool Find(const K& key)
{
Node* cur = _root;
while (cur)
{
//如果cur的key值比key小,则在其右边查找
if (cur->_key < key)
{
cur = cur->_right;
}
//如果cur的key值比key大,则在其左边查找
else if (cur->_key > key)
{
cur = cur->_left;
}
//找到key值,返回true
else
{
return true;
}
}
//走到这说明没找到,返回false
return false;
}
2.4二叉搜索树删除
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,所有情况的图解均在代码段下
if (cur->_left == nullptr)
{ //此种情况对应图1
if (parent == nullptr)
{
_root = cur->_right;
}
else
{ //此种情况对应图2
if (parent->_left == cur)
parent->_left = cur->_right;
else
parent->_right = cur->_right;
}
delete cur;
}
//此种情况和上面的类似
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;
}
//走到这说明左右都不为空
else
{
Node* minParent = cur;
Node* min = cur->_right;
while (min->_left)
{
minParent = min;
min = min->_left;
}
cur->_key = min->_key;
//此种情况对应图3
if (minParent->_left == min)
minParent->_left = min->_right;
else
minParent->_right = min->_right;
delete min;
}
return true;
}
}
return false;
}
图1
图2
图3
2.5二叉搜索树中序遍历
public:
void InOrder()
{
_InOrder(_root);
cout << endl;
}
private:
void _InOrder(Node* root)
{
if (root == nullptr)
{
return;
}
//左子树
_InOrder(root->_left);
//根
cout << root->_key << " ";
//右子树
_InOrder(root->_right);
}
这里解释一下这边为什么要用这种写法,因为_root是私有类型,所以就没办法作为参数传递,所以我们就用一个子函数来作为输出型参数。
就比如这样
void InOrder(Node* root)
{
if (root == nullptr)
{
return;
}
InOrder(root->_left);
cout << root->_key << " ";
InOrder(root->_right);
}
要调用此函数就一定得传根结点,根结点又是私有的,所以用上面的方法可以解决。
3.二叉搜索树递归实现
3.1二叉搜索树插入
public:
bool InsertR(const K& key)
{
return _InsertR(_root, key);
}
private:
bool _InsertR(Node*& root, const K& key)
{
if (root == nullptr)
{
root = new Node(key);
return true;
}
//key值比当前结点大,则从此结点右树寻找
if (root->_key < key)
return _InsertR(root->_right, key);
//key值比当前结点小,则从此结点左树寻找
else if (root->_key > key)
return _InsertR(root->_left, key);
//相等,则插入失败
else
return false;
}
3.2二叉搜索树查找
public:
Node* FindR(const K& key)
{
return _FindR(_root, key);
}
private:
Node* _FindR(Node* root, const K& key)
{
if (root == nullptr)
{
return nullptr;
}
//key值比当前结点大,则从此结点右树寻找
if (root->_key < key)
{
return _FindR(root->_right, key);
}
//key值比当前结点小,则从此结点左树寻找
else if (root->_key > key)
{
return _FindR(root->_left, key);
}
//相等,则查找成功
else
{
return root;
}
}
3.3二叉搜索树删除
public:
bool EraseR(const K& key)
{
return _EraseR(_root, key);
}
private:
bool _EraseR(Node*& root, const K& key)
{
if (root == nullptr)
return false;
//key值比当前结点大,则从此结点右树寻找
if (root->_key < key)
{
return _EraseR(root->_right, key);
}
//key值比当前结点小,则从此结点左树寻找
else if (root->_key > key)
{
return _EraseR(root->_left, key);
}
//此时开始删结点
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);
return _EraseR(root->_right, key);
}
delete del;
return true;
}
}
4.key-value版本二叉搜索树
实际上这个版本的二叉搜索树只要在原来代码的基础上加一个value值然后对初始化和插入做修改即可。
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>
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;
};
}
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