一.二叉搜索树的性质
1.每一个节点都有一个key作为搜索依据，每一个节点的key都不同。
2.左子树的key值比根节点小。
3.右子树的key值比根节点的大。
4.左右子树都是二叉搜索树。
二.结构
1.节点(BinarySerachTreeNode)
template<class K,class V>
struct SearchBinTreeNode
{
SearchBinTreeNode<K, V>* _left;
SearchBinTreeNode<K, V>* _right;
K _key;
V _value;
SearchBinTreeNode(const K& key, const V& value)
:_left(NULL)
, _right(NULL)
, _key(key)
, _value(value)
{}
};
三.Insert接口
bool Insert(const K& key, const V& value)
{
if (_root == NULL)
{
_root = new Node(key, value);
return true;
}
Node* cur = _root; //标志待插入的位置
Node* parent = NULL; //标志待插入为的父亲节点
while (cur) //寻找插入位置
{
if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else
{
return false; //待插入的key已经存在
}
}
if (parent->_key > key) //寻找待插入点是在父亲的左边/右边
{
parent->_left = new Node(key, value);
}
else
{
parent->_right = new Node(key, value);
}
return true;
}
四.Find接口
Node* Find(const K& key)
{
if (_root == NULL)
{
return NULL;
}
Node* cur = _root;
while (cur)
{
if (cur->_key > key)
{
cur = cur->_left;
}
else if (cur->_key < key)
{
cur = cur->_right;
}
else
{
cout << cur->_key << endl;
return cur;
}
}
return NULL;
}
五.Remove接口
bool Remove(const K& key)
{
if (_root == NULL) //处理没有节点
{
return false;
}
if (_root->_left == NULL && _root->_right == NULL) //处理只有一个节点的情况
{
if (_root->_key == key) //判断key值
{
delete _root;
_root = NULL;
return true;
}
else
{
return false;
}
}
Node* cur = _root;
Node* parent = NULL;
while (cur) //寻找待删除的节点
{
if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else //cur->_key == key（找到）
{
Node* del = cur;
if (cur->_left == NULL) //待删除节点左边为NULL
{
if (parent == NULL)
{
_root = cur->_right;
}
else
{
if (parent->_left == cur)
parent->_left = cur->_right;
else
parent->_right = cur->_right;
}
}
else if (cur->_right == NULL) //待删除节点右边为NULL
{
if (parent == NULL)
{
_root = cur->_left;
}
else
{
if (parent->_left == cur)
parent->_left = cur->_left;
else
parent->_right = cur->_left;
}
}
else //左右都不为空
{
//找到相对于当前结点右边的最左节点，这个节点一定是相对于当前结点右子树种最小的一个。
parent = cur;
Node* leftFirst = cur->_right;
while (leftFirst->_left)
{
parent = leftFirst;
leftFirst = leftFirst->_left;
}
swap(cur->_key, leftFirst->_key);
swap(cur->_value, leftFirst->_value);
del = leftFirst;
if (parent->_left == leftFirst)
parent->_left = leftFirst->_right;
else
parent->_right = leftFirst->_right;
}
delete del;
return true;
}
}
return false;
}
a.分别处理没有节点，一个节点，多个节点的情况
b.分为左为NULL，右为NULL，左右都不为NULL的情况
c.处理左右都不为NULL的情况，需要找到相当于当前结点右子树中key值最小的一个（leftfirst），将当前结点和leftfirst交换，那么需要删除的节点就变成leftfirst。
六.递归实现
void Insert_R(const K& key, const V& value)
{
_Insert_R(_root, key, value);
}
Node* Find_R(const K& key)
{
return _Find_R(_root,key);
}
void Remove_R(const K& key)
{
_Remove_R(_root, key);
}
protected:
void _LevelOrder(Node* root)
{
if (root == NULL)
return;
_LevelOrder(root->_left);
cout << root->_key << " ";
_LevelOrder(root->_right);
}
bool _Insert_R(Node*& root, const K& key, const V& value) //递归写法
{
if (root == NULL)
{
root = new Node(key, value);
return true;
}
if (root->_key == key)
{
return false;
}
else if (root->_key > key)
{
_Insert_R(root->_left, key, value);
}
else
{
_Insert_R(root->_right, key, value);
}
}
Node* _Find_R(Node*& root,const K& key)
{
if (root == NULL)
{
return NULL;
}
if (root->_key > key)
{
_Find_R(root->_left, key);
}
else if (root->_key < key)
{
_Find_R(root->_right, key);
}
else
{
cout << root->_key << endl;
return root;
}
}
bool _Remove_R(Node*& root, const K& key)
{
if (root == NULL)
return false;
if (root->_key > key)
{
_Remove_R(root->_left, key);
}
else if (root->_key < key)
{
_Remove_R(root->_right, key);
}
else
{
//Node* del = root;
if (root->_left == NULL)
{
root = root->_right;
}
else if (root->_right == NULL)
{
root = root->_left;
}
else
{
Node* leftfirst = root->_right;
while (leftfirst->_left)
{
leftfirst = leftfirst->_left;
}
swap(root->_key, leftfirst->_key);
swap(root->_value, leftfirst->_value);
//del = leftfirst;
_Remove_R(root->_right, key);
}
/*if (del != NULL)
{
delete del;
}*/
return true;
}
}
七.代码
#pragma once
#include<iostream>
using namespace std;
template<class K,class V>
struct SearchBinTreeNode
{
SearchBinTreeNode<K, V>* _left;
SearchBinTreeNode<K, V>* _right;
K _key;
V _value;
SearchBinTreeNode(const K& key, const V& value)
:_left(NULL)
, _right(NULL)
, _key(key)
, _value(value)
{}
};
template<class K,class V>
class SearchBinTree
{
typedef SearchBinTreeNode<K, V> Node;
public:
SearchBinTree()
:_root(NULL)
{}
~SearchBinTree()
{
if (_root != NULL)
{
delete _root;
}
}
bool Insert(const K& key, const V& value)
{
if (_root == NULL)
{
_root = new Node(key, value);
return true;
}
Node* cur = _root;
Node* parent = NULL;
while (cur)
{
if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else
{
return false;
}
}
if (parent->_key > key)
{
parent->_left = new Node(key, value);
}
else
{
parent->_right = new Node(key, value);
}
return true;
}
Node* Find(const K& key)
{
if (_root == NULL)
{
return NULL;
}
Node* cur = _root;
while (cur)
{
if (cur->_key > key)
{
cur = cur->_left;
}
else if (cur->_key < key)
{
cur = cur->_right;
}
else
{
cout << cur->_key << endl;
return cur;
}
}
return NULL;
}
bool Remove(const K& key)
{
if (_root == NULL)
{
return false;
}
if (_root->_left == NULL && _root->_right == NULL)
{
if (_root->_key == key)
{
delete _root;
_root = NULL;
return true;
}
else
{
return false;
}
}
Node* cur = _root;
Node* parent = NULL;
while (cur)
{
if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else //cur->_key == key
{
Node* del = cur;
if (cur->_left == NULL)
{
if (parent == NULL)
{
_root = cur->_right;
}
else
{
if (parent->_left == cur)
parent->_left = cur->_right;
else
parent->_right = cur->_right;
}
}
else if (cur->_right == NULL)
{
if (parent == NULL)
{
_root = cur->_left;
}
else
{
if (parent->_left == cur)
parent->_left = cur->_left;
else
parent->_right = cur->_left;
}
}
else
{
//找到最左
parent = cur;
Node* leftFirst = cur->_right;
while (leftFirst->_left)
{
parent = leftFirst;
leftFirst = leftFirst->_left;
}
swap(cur->_key, leftFirst->_key);
swap(cur->_value, leftFirst->_value);
del = leftFirst;
if (parent->_left == leftFirst)
parent->_left = leftFirst->_right;
else
parent->_right = leftFirst->_right;
}
delete del;
return true;
}
}
return false;
}
void LevelOrder()
{
_LevelOrder(_root);
cout << endl;
}
void Insert_R(const K& key, const V& value)
{
_Insert_R(_root, key, value);
}
Node* Find_R(const K& key)
{
return _Find_R(_root,key);
}
void Remove_R(const K& key)
{
_Remove_R(_root, key);
}
protected:
void _LevelOrder(Node* root)
{
if (root == NULL)
return;
_LevelOrder(root->_left);
cout << root->_key << " ";
_LevelOrder(root->_right);
}
bool _Insert_R(Node*& root, const K& key, const V& value) //递归写法
{
if (root == NULL)
{
root = new Node(key, value);
return true;
}
if (root->_key == key)
{
return false;
}
else if (root->_key > key)
{
_Insert_R(root->_left, key, value);
}
else
{
_Insert_R(root->_right, key, value);
}
}
Node* _Find_R(Node*& root,const K& key)
{
if (root == NULL)
{
return NULL;
}
if (root->_key > key)
{
_Find_R(root->_left, key);
}
else if (root->_key < key)
{
_Find_R(root->_right, key);
}
else
{
cout << root->_key << endl;
return root;
}
}
bool _Remove_R(Node*& root, const K& key)
{
if (root == NULL)
return false;
if (root->_key > key)
{
_Remove_R(root->_left, key);
}
else if (root->_key < key)
{
_Remove_R(root->_right, key);
}
else
{
//Node* del = root;
if (root->_left == NULL)
{
root = root->_right;
}
else if (root->_right == NULL)
{
root = root->_left;
}
else
{
Node* leftfirst = root->_right;
while (leftfirst->_left)
{
leftfirst = leftfirst->_left;
}
swap(root->_key, leftfirst->_key);
swap(root->_value, leftfirst->_value);
//del = leftfirst;
_Remove_R(root->_right, key);
}
/*if (del != NULL)
{
delete del;
}*/
return true;
}
}
protected:
Node* _root;
};
void TestSearchBinTree()
{
SearchBinTree<int, int> S;
S.Insert(5,1);
S.Insert(3,1);
S.Insert(4,1);
S.Insert(1,1);
S.Insert(7,1);
S.Insert(8,1);
S.Insert(2,1);
S.Insert(6,1);
S.Insert(0,1);
S.Insert(9,1);
S.Find(6);
S.LevelOrder();
S.Remove(0);
S.Remove(3);
S.Remove(5);
S.Remove(7);
S.Remove(9);
//S.Remove(1);
//S.Remove(2);
//S.Remove(4);
//S.Remove(6);
//S.Remove(8);
S.LevelOrder();
}
void TestSearchBinTree1()
{
SearchBinTree<int, int> S;
S.Insert_R(5, 1);
S.Insert_R(3, 1);
S.Insert_R(4, 1);
S.Insert_R(1, 1);
S.Insert_R(7, 1);
S.Insert_R(8, 1);
S.Insert_R(2, 1);
S.Insert_R(6, 1);
S.Insert_R(0, 1);
S.Insert_R(9, 1);
S.Find(6);
S.LevelOrder();
S.Find_R(6);
/*SearchBinTreeNode<int, int>* ret = S.Find_R(6);
cout << ret->_key << endl;*/
S.Remove_R(0);
S.Remove_R(3);
S.Remove_R(5);
S.Remove_R(7);
S.Remove_R(9);
S.Remove_R(1);
S.Remove_R(2);
S.Remove_R(4);
S.Remove_R(6);
S.Remove_R(8);
S.LevelOrder();
}
以上就是本人在学习过程中的一些经验总结。当然，本人能力有限，难免会有纰漏，希望大家可以指正。
时间： 2024-11-06 22:39:55