今天下午闲着无聊，复习了一下“二叉查找树”，并用代码温习了一下。
对于二叉查找树，一般支持的操作有：查找关键字，最大值，最小值，前驱和后继等等的查询，对于高度为h的树，它们都可以在O(h)时间内完成。
BinaryTree.h
[cpp collapse=”true”]
#ifndef __BINARY_TREE_H__
#define __BINARY_TREE_H__
template < typename Key, typename Data > class BinaryTree;
/*! 树的节点 */
template < typename Key, typename Data >
class TreeNode
{
public:
//! 默认构造函数
TreeNode()
: m_pParent( NULL ),
m_pLChild( NULL ),
m_pRChild( NULL )
{
}
//! 构造函数
TreeNode( Key k, const Data & d )
: m_pParent( NULL ),
m_pLChild( NULL ),
m_pRChild( NULL ),
m_key( k ),
m_data( d )
{
}
//! 拷贝构造函数
TreeNode( const TreeNode< Key, Data > & node )
: m_pParent( NULL ),
m_pLChild( NULL ),
m_pRChild( NULL ),
m_key( node.m_key ),
m_data( node.m_data )
{
}
//! 赋值函数
TreeNode< Key, Data > & operator=( const TreeNode< Key, Data > & rhs )
{
m_key = rhs.m_key;
m_data = rhs.m_data;
return *this;
}
//! 获取键值
Key GetKey() const { return m_key; }
//! 获取数据
Data GetData() const { return m_data; }
//! 设置数据
void SetData( const Data & d ) { m_data = d; }
private:
Key m_key; //!< 关键字
Data m_data; //!< 数据
TreeNode *m_pParent; //!< 父节点
TreeNode *m_pLChild; //!< 左子节点
TreeNode *m_pRChild; //!< 右子节点
friend class BinaryTree< Key, Data >;
};
/*! 二叉查找树 */
template < typename Key, typename Data >
class BinaryTree
{
public:
BinaryTree()
:m_pRoot( NULL )
{
}
~BinaryTree()
{
while ( m_pRoot != NULL )
{
DeleteNode( m_pRoot );
}
}
typedef TreeNode< Key, Data > _TreeNode;
//! 查找
_TreeNode * Search( const Key & destK ) const;
//! 最小值
_TreeNode * Minimum( _TreeNode * pNode ) const;
//! 最大值
_TreeNode * Maximum( _TreeNode * pNode ) const;
//! 后继
_TreeNode * Successor( _TreeNode * pNode ) const;
//! 前任
_TreeNode * Predecessor( _TreeNode * pNode ) const;
//! 添加节点
void AddNode( const _TreeNode * pNode );
//! 删除节点
void DeleteNode( _TreeNode * pNode );
//! 获取根节点
_TreeNode * GetRootNode() const { return m_pRoot; }
private:
_TreeNode *m_pRoot; //! 根节点
};
template < typename Key, typename Data >
void BinaryTree< Key, Data >::AddNode( const _TreeNode * pNode )
{
assert( NULL != pNode &&
"pNode cannot be NULL" );
_TreeNode *newNode = new _TreeNode( *pNode );
_TreeNode *n1 = m_pRoot;
_TreeNode *n2 = NULL;
while ( NULL != n1 )
{
n2 = n1;
if ( newNode->m_key < n2->m_key )
{
n1 = n2->m_pLChild;
}
else
{
n1 = n2->m_pRChild;
}
}
if ( NULL == m_pRoot )
{
m_pRoot = newNode;
}
else
{
if ( newNode->m_key < n2->m_key )
{
n2->m_pLChild = newNode;
}
else
{
n2->m_pRChild = newNode;
}
newNode->m_pParent = n2;
}
}
template < typename Key, typename Data >
void BinaryTree< Key, Data >::DeleteNode( _TreeNode * pNode )
{
assert( NULL != pNode &&
"pNode cannot be NULL" );
_TreeNode * n1 = NULL;
_TreeNode * n2 = NULL;
//! n1是要删除的节点
if ( NULL == pNode->m_pLChild || NULL == pNode->m_pRChild )
{
//! 没有或者只有1个子节点，删除的节点时pNode
n1 = pNode;
}
else
{
//! 左右子节点都有，先删除pNode的后继结点
n1 = Successor( pNode ); // 该后继一定没有左节点
}
//! n2是n1唯一的一个子节点
if ( NULL != n1->m_pLChild )
{
n2 = n1->m_pLChild;
}
else
{
n2 = n1->m_pRChild;
}
//! 为删除n1所作的指针修改
if ( NULL != n2 )
{
n2->m_pParent = n1->m_pParent;
}
if ( NULL == n1->m_pParent )
{
// Root是唯一的一个父节点为空的节点
m_pRoot = n2;
}
else
{
if ( n1 == n1->m_pParent->m_pLChild )
{
n1->m_pParent->m_pLChild = n2;
}
else
{
n1->m_pParent->m_pRChild = n2;
}
}
if ( n1 != pNode )
{
//! pNode左右子节点都有的情况，
//! 用pNode的后继结点的关键字和附加数据替换掉pNode的关键字和附加数据
pNode->m_key = n1->m_key;
pNode->m_data = n1->m_data;
}
delete n1;
}
template < typename Key, typename Data >
TreeNode< Key, Data > * BinaryTree< Key, Data >::Search( const Key & destK ) const
{
_TreeNode *n = m_pRoot;
while ( NULL != n && destK != n->m_key )
{
if ( destK < n->m_key )
{
n = n->m_pLChild;
}
else
{
n = n->m_pRChild;
}
}
return n;
}
template < typename Key, typename Data >
TreeNode< Key, Data > * BinaryTree< Key, Data >::Minimum( _TreeNode * pNode ) const
{
assert( NULL != pNode &&
"pNode cannot be NULL" );
while ( NULL != pNode->m_pLChild )
{
pNode = pNode->m_pLChild;
}
return pNode;
}
template < typename Key, typename Data >
TreeNode< Key, Data > * BinaryTree< Key, Data >::Maximum( _TreeNode * pNode ) const
{
assert( NULL != pNode &&
"pNode cannot be NULL" );
while ( NULL != pNode->m_pRChild )
{
pNode = pNode->m_pRChild;
}
return pNode;
}
template < typename Key, typename Data >
TreeNode< Key, Data > * BinaryTree< Key, Data >::Successor( _TreeNode * pNode ) const
{
assert( NULL != pNode &&
"pNode cannot be NULL" );
//! 2 cases
if ( NULL == pNode->m_pRChild )
{
//! 1: 右子树为空
//! 向上查找直到遇到某个是其父节点的左儿子的节点时为止
while ( NULL != pNode->m_pParent && pNode->m_pParent->m_pLChild != pNode )
{
pNode = pNode->m_pParent;
}
return pNode->m_pParent;
}
else
{
//! 2: 右子树不为空，后继即为右子树中的最左节点
return Minimum( pNode->m_pRChild );
}
}
template < typename Key, typename Data >
TreeNode< Key, Data > * BinaryTree< Key, Data >::Predecessor( _TreeNode * pNode ) const
{
assert( NULL != pNode &&
"pNode cannot be NULL" );
//! 2 cases
if ( NULL == pNode->m_pRChild )
{
//! 1: 左子树为空
//! 向上查找直到遇到某个是其父节点的右儿子的节点时为止
while ( NULL != pNode->m_pParent && pNode->m_pParent->m_pRChild != pNode )
{
pNode = pNode->m_pParent;
}
return pNode->m_pParent;
}
else
{
//! 2: 左子树不为空，前任即为左子树中的最右节点
return Maximum( pNode->m_pLChild );
}
}
#endif
[/cpp]
测试BST
[cpp]
#include "BinaryTree.h"
int num[11] = { 15, 6, 18, 3, 2, 4, 7, 13, 9, 17, 20 };
int _tmain(int argc, _TCHAR* argv[])
{
BinaryTree< int, int > myTree;
typedef TreeNode< int, int > Node;
for ( int i = 0; i < 11; i ++ )
{
int x = num[i];
Node n( x, 0 );
myTree.AddNode( n );
}
Node *pRoot = myTree.GetRootNode();
Node *min = myTree.Minimum( pRoot );
Node *max = myTree.Maximum( pRoot );
Node *someNode = myTree.Search( 17 );
Node *pre = myTree.Predecessor( someNode );
Node *suc = myTree.Successor( someNode );
myTree.DeleteNode( suc );
return 0;
}
[/cpp]
参考资料：算法导论P151-P158
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