【数据结构】：二叉搜索树

来源：互联网发布：兔子软件安装器编辑：程序博客网时间：2024/06/16 11:25

二叉搜索树，也称有序二叉树,排序二叉树，是指一棵空树或者具有下列性质的二叉树：

若任意节点的左子树不空，则左子树上所有结点的值均小于它的根结点的值；
若任意节点的右子树不空，则右子树上所有结点的值均大于它的根结点的值；
任意节点的左、右子树也分别为二叉查找树。
没有键值相等的节点。

因此，搜索二叉树中没有键值冗余的节点，通常可用来去重排序。

如图所示就是一棵二叉搜索树：
这里写图片描述
中序遍历结果为：0 1 2 3 4 5 6 7 8 9

需要注意的是：二叉搜索树在进行删除和插入操作后都需要再次进行调整，新得到的树也应该是二叉搜索树。

具体代码实现如下：

#include<iostream>using namespace std;template<class K>class BinaraySearchNode{public:    BinaraySearchNode<K>* _left;    BinaraySearchNode<K>* _right;    BinaraySearchNode<K>* _parent;    K  _key;    BinaraySearchNode(const K& key)        :_left(NULL)        , _right(NULL)        , _parent(NULL)        , _key(key)    {}};template<class K>class BinarySearch{public:    typedef BinaraySearchNode<K> Node;    BinarySearch()        :_root(NULL)    {}    //插入    bool InSert(const K& key)    {        if (_root == NULL)        {            _root = new Node(key);            return true;        }        Node* parent = NULL;        Node* cur = _root;        while (cur)        {            if (cur->_key > key)            {                parent = cur;                cur = cur->_left;            }            else if (cur->_key < key)            {                parent = cur;                cur = cur->_right;            }            else                return false;        }        Node* tmp = new Node(key);        if (parent->_key > key)            parent->_left = tmp;        else if (parent->_key < key)            parent->_right = tmp;        return true;    }    //查找    Node* Find(const K& key)const    {        Node* cur = _root;        while (cur)        {            if (cur->_key > key)                cur = cur->_left;            else if (cur->_key < key)                cur = cur->_right;            return cur;        }        return NULL;    }    //删除节点    bool Remove(const K& key)    {        if (_root == NULL)            return false;        Node* parent = NULL;        Node* cur = _root;        while (cur)        {            if (key > cur->_key)            {                parent = cur;                cur = cur->_right;            }            else if (key < cur->_key)            {                parent = cur;                cur = cur->_left;            }            else//等于            {                if (cur->_left == NULL)                {                    parent = cur->_parent;                    if (parent == NULL)                    {                        _root = cur->_right;                        delete cur;                        cur = NULL;                        return true;                    }                    if (cur == parent->_left)                    {                        parent->_left = cur->_right;                    }                    else                    {                        parent->_right = cur->_right;                    }                    delete cur;                    cur = NULL;                }                if (cur->_right == NULL)                {                    parent = cur->_parent;                    if (parent == NULL)                    {                        _root = cur->_left;                        delete cur;                        cur = NULL;                        return true;                    }                    if (cur == parent->_left)                    {                        parent->_left = cur->_left;                    }                    else                    {                        parent->_right = cur->_left;                    }                    delete cur;                    cur = NULL;                }                if (cur->_left != NULL && cur->_right != NULL)                {                    //替换法(注意根节点为空的情况）                    Node* subRight = cur->_right;                    Node* subParent = cur;                    while (subRight->_left)                    {                        subParent = subRight;                        subRight = subRight->_left;                    }                    cur->_key = subRight->_key;                    if (subParent->_right == subRight)                        subParent->_right = subRight->_right;                    else                        subParent->_left = subRight->_left;                    delete subRight;                    subRight = NULL;                }                return  true;            }        }        return false;    }    //递归插入    bool _InSertR(Node*& root, const K& key)//递归插入    {        if (root == NULL)            return root = new Node(key);        if (root->_key < key)            return _InSertR(root->right, key);        if (root->_key > key)            return _InSertR(root->_left, key);    }    //递归删除    bool _RemoveR(Node*& root, const K& key)//注意：这里要加引用    {        if (root == NULL)            return false;        if (root->_left == NULL && root->_right == NULL)        {            if (root->_key == key)            {                delete root;                return true;            }            else                return false;        }        if (root->_key > key)            RemoveR(root->_left, key);        if (root->_key < key)            RemoveR(root->_right, key);        else        {            Node* cur = root;            if (cur->_left == NULL)            {                parent = cur->_parent;                if (parent == NULL)                {                    root = root->_right;                    delete cur;                    cur = NULL;                }                if (cur == parent->_left)                {                    parent->_left = cur->_right;                }                else                {                    parent->_right = cur->_right;                }                delete cur;                cur = NULL;            }            if (cur->_right == NULL)            {                parent = cur->_parent;                if (parent == NULL)                {                    _root = cur->_left;                    delete cur;                    cur = NULL;                    return true;                }                if (cur == parent->_left)                {                    parent->_left = cur->_left;                }                else                {                    parent->_right = cur->_left;                }                delete cur;                cur = NULL;            }            if (cur->_left != NULL && cur->_right != NULL)            {                //替换法                Node* subRight = cur->_right;                Node* subParent = cur;                while (subRight->_left)                {                    subParent = subRight;                    subRight = subRight->_left;                }                cur->_key = subRight->_key;                if (subParent->_right == subRight)                    subParent->_right = subRight->_right;                else                    subParent->_left = subRight->_left;                delete subRight;                subRight = NULL;            }            return  true;        }    }    //中序遍历    void InOrder()    {        _InOrder(_root);    }protected:    void _InOrder(Node* root)    {        if (root == NULL)            return;        else        {            _InOrder(root->_left);            cout << root->_key << " ";            _InOrder(root->_right);        }    }private:    Node* _root;};void Test(){    BinarySearch<int> bs;    int a[] = { 5, 3,1,0,4,7,6,8,9,2};    for (size_t i = 0; i < (sizeof(a) / sizeof(a[0])); ++i)    {        bs.InSert(a[i]);    }    bs.InOrder();    cout << endl;    bs.Remove(5);    bs.InOrder();};

#define _CRT_SECURE_NO_WARNINGS 1#include"binarysearch.h"int main(){    Test();    system("pause");    return 0;}

这里写图片描述

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