二叉搜索樹
二叉搜索樹是基於二叉樹的一種結構,對於一個二叉樹它的左節點小於它的根節點,它的右節點大於它的根節點,它的每個子樹的結構相同
其結構以及接口實現過程如下
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)
:_key(key)
, _value(value)
, _left(NULL)
, _right(NULL)
{}
};
template<class K,class V>
class BSTree
{
typedef BSTreeNode<K, V> Node;
public:
BSTree()
:_root(NULL)
{}
~BSTree()
{
_Destroy(_root);
}
public:
bool Insert(const K&key, const V&value)//插入節點
{
if (_root == NULL)
{
_root = new Node(key, value);
return true;
}
Node*parent = NULL;
Node*cur = _root;
while (cur)
{
if (cur->_value<value)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_value>value)
{
parent = cur;
cur = cur->_left;
}
else
return false;
}
if (value > parent->_value)
parent->_right = new Node(key, value);
else
parent->_left = new Node(key, value);
return true;
}
bool Insert_R(const K&key, const V&value)//遞歸控制
{
return _Insert_R(_root,key,value);
}
Node*Find_R(const V&value)//遞歸
{
return _Find_R(_root, value);
}
Node*Find(const V&value)//尋找結點
{
Node*cur = _root;
while (cur)
{
if (cur->_value > value)
cur = cur->_right;
else if (cur->_value < value)
cur = cur->_right;
else//cur->_value = value
return cur;
}
return NULL;//未找到
}
bool Remove(const V&value)//刪除結點,刪除成功返回true,若不存在value則返回false
{
//1.刪除結點左或右爲空(或左右均爲空),左爲空則父節點直接指向右,刪除這個結點,若右爲空則父節點直接指向左
//2.刪除的左右結點均不爲空,則找到這個結點左樹的最右節點或右樹的最左節點替換
Node*cur = _root;
Node*parent = NULL;
while (cur)
{
if (cur->_value > value)
{
parent = cur;
cur = cur->_left;
}
else if (cur->_value < value)
{
parent = cur;
cur = cur->_right;
}
else
break;
}
if (cur == NULL)
return false;
Node*del;
//情況1
if (cur->_left == NULL)
{
del = cur;
if (parent == NULL)//根結點
{
_root = cur->_right;
}
else
{
if (parent->_left == cur)
parent->_left = cur->_right;
else
parent->_right = cur->_right;
}
}
else if (cur->_right == NULL)
{
del = cur;
if (parent == NULL)
{
_root = cur->_left;
}
else
{
if (parent->_left = cur)
parent->_left = cur->_left;
else
parent->_right = cur->_left;
}
}
else//情況2
{
parent = cur;
Node*firstLeft = cur->_right;//找這個結點右節點的最左結點
while (firstLeft->_left)
{
parent = firstLeft;
firstLeft = firstLeft->_left;
}
del = firstLeft;
cur->_key = firstLeft->_key;
cur->_value = firstLeft->_value;
if (parent->_left == firstLeft)
{
parent->_left = firstLeft->_right;
}
else
parent->_right = firstLeft->_right;
}
delete del;
return true;
}
bool Remove_R(const V&value)
{
return _Remove_R(_root, value);
}
void InOrder()//中序遍歷,即二叉樹敗絮
{
_InOrder(_root);
cout << endl;
}
private:
void _Destroy(Node*root)
{
if (root == NULL)
return;
_Destroy(root->_left);
_Destroy(root->_right);
delete root;
}
void _InOrder(Node*root)
{
if (root == NULL)
return;
_InOrder(root->_left);
cout << root->_value<<" ";
_InOrder(root->_right);
}
bool _Insert_R(Node*&root,const K&key,const V&value)
{
if (root == NULL)
{
root = new Node(key, value);
return true;
}
if (value > root->_value)
return _Insert_R(root->_right, key, value);//遞歸右樹
else if (value<root->_value)
return _Insert_R(root->_left,key,value);//遞歸左樹
return false;
}
Node*_Find_R(Node*root, const V&value)
{
if (root->_value == value)
return root;
if (value>root->_value)
return _Find_R(root->_right, value);
else if (value < root->_value)
return _Find_R(root->_left, value);
else
return NULL;//根爲空或者未找到
}
bool _Remove_R(Node*&root, const V&value)
{
if (root == NULL)
return false;
if (root->_value>value)
return _Remove_R(root->_left, value);
else if (root->_value < value)
return _Remove_R(root->_right, value);
else//root->_value == value
{
Node*del = root;
if (root->_left == NULL)
root = root->_right;
else if (root->_right == NULL)
root = root->_left;
else//左右均不爲空
{
Node*parent = root;
Node*cur = root->_left;
while (cur->_left)
{
parent = cur;
cur = cur->_left;
}
swap(cur->_value, root->_value);
swap(cur->_key, root->_key);
del = cur;
parent->_left = cur->_right;
}
delete del;
}
return true;
}
private:
Node*_root;
};