二叉查找树-插入、查找某个值节点、查找前驱或后继、删除

 

/*
二叉查找树 插入 查找前驱、后继 删除
https://www.cnblogs.com/skywang12345/p/3576373.html*/
#include <iostream>
#include <stack>
using namespace std;

struct BSTNode
{
    int val;
    BSTNode *left;
    BSTNode *right;
    BSTNode *parent;
    BSTNode(int v, BSTNode *l, BSTNode *r, BSTNode *p) :val(v), left(l), right(r), parent(p) {}
};
/*插入节点node到root指向的二叉查找树中*/
void insert(BSTNode *root, BSTNode *node)
{
    if (node == nullptr)
        return;
    if (root == nullptr)
    {
        node->parent = nullptr;
        root = node;
        return;
    }
    BSTNode *temp = root;
    BSTNode *parent = nullptr;//保存待插入节点的父节点
    while (temp)
    {
        parent = temp;
        if (node->val > temp->val)
            temp = temp->right;
        else
            temp = temp->left;
    }
    node->parent = parent;
    if (node->val > parent->val)
        parent->right = node;
    else
        parent->left = node;
}
/*二叉查找树中序遍历 升序*/
void inorderprint(BSTNode *root)
{
    if (root == nullptr) return;
    stack<BSTNode *> s;
    BSTNode *curr = root;
    while (curr || !s.empty())
    {
        if (curr)
        {
            s.push(curr);
            curr = curr->left;
        }
        else
        {
            cout << s.top()->val << " ";
            curr = s.top()->right;
            s.pop();
            
        }
    }
}
/*查找某个值的节点*/
BSTNode *search(BSTNode *root, int sval)
{
    if (root == nullptr) return nullptr;
    BSTNode *temp = root;
    while (temp)
    {
        if (temp->val > sval)
            temp = temp->left;
        else if(temp->val < sval)
            temp = temp->right;
        else
            return temp;
    }
    return nullptr;
}
/*二叉查找树值最小的节点*/
BSTNode *minkeynode(BSTNode* root)
{
    if (!root) return nullptr;
    BSTNode *temp = root;
    while (temp->left)
    {
        temp = temp->left;
    }
    return temp;
}
BSTNode *maxkeynode(BSTNode* root)
{
    if (!root) return nullptr;
    BSTNode *temp = root;
    while (temp->right)
    {
        temp = temp->right;
    }
    return temp;
}
/*前驱节点(有无左子)-查找"二叉树中数据值小于该结点"的"最大结点"*/
BSTNode *prenode(BSTNode* root, int val)
{
    if (!root) return nullptr;
    BSTNode *node = search(root, val);//找到该值的节点
    if (!node) return nullptr;
    
    //有左子,则以左子为根的最大节点为当前节点的前驱
    if (node->left)
        return maxkeynode(node->left);
    
    //无左子:(1)为右子,则其前驱为其父节点;
    //          (2)为左子,则查找"x的最低的父结点,并且该父结点要具有右孩子",找到的这个"最低的父结点"就是"x的前驱结点"。
    BSTNode *parent = node->parent;
    while (parent && parent->left == node)//如果当前节点是最左子,则parent最后是空,返回空是正确的
    {
        node = parent;
        parent = parent->parent;
    }
    return parent;
}

/*后继节点(有无右子)-查找"二叉树中数据值大于该结点"的"最小结点"。*/
BSTNode *postnode(BSTNode *root, int val)
{
    if (!root) return nullptr;
    BSTNode *node = search(root, val);
    if (!node) return nullptr;

    //有右子,后继:右子为根的最小节点(最左节点
    if (node->right)
        return minkeynode(node->right);

    //无右子, 1、为左子,后继是其父;
    //           2、为右子,寻找最低父节点,该父节点有左子
    BSTNode *parent = node->parent;
    while (parent && parent->right == node)
    {
        node = parent;
        parent = parent->parent;
    }
    return parent;
}

/*删除*/
void transplant(BSTNode *root, BSTNode *oldnode, BSTNode *newnode)
{//new覆盖old,维护new的父节点与new指向关系。newnode可以为空
    //parent指向new
    if (!oldnode->parent) root = newnode;
    else if (oldnode == oldnode->parent->left) oldnode->parent->left = newnode;
    else oldnode->parent->right = newnode;
    //new指向parent
    if (newnode) newnode->parent = oldnode->parent;
}
void removenode(BSTNode *root, int val)
{
    if (!root) return;
    BSTNode *node = search(root, val);
    if (!node) return;

    if (!node->left) transplant(root, node, node->right);//1、无左子,不管是否有右子,直接用右子覆盖
    else if (!node->right) transplant(root, node, node->left);//2、有左子:2.1、无右子,直接用左子覆盖
    else
    {//2、有左子:2.2、有右子
        BSTNode *nodeSucc = minkeynode(node->right);//node的后继
        //2.2.1、待删除node的后继不是其右子,用后继的右子覆盖后继,并让后继接管node的右子树(修node右子和该后继的父子关系)
        //之后用该后继覆盖node并接管node的左子
        if (nodeSucc->parent != node)
        {
            transplant(root, nodeSucc, nodeSucc->right);
            nodeSucc->right = node->right;//后继接管node的右子树
            nodeSucc->right->parent = nodeSucc;
        }
        //2.2.2、node的后继是其右子(即右子无左子),用后继覆盖node并接管node的左子
        transplant(root, node, nodeSucc);
        nodeSucc->left = node->left;//接管node的左子
        nodeSucc->left->parent = nodeSucc;
    }
    delete node;
}

int main()
{
    BSTNode *root = new BSTNode{ 88,NULL,NULL,NULL };
    if (!root)
        return -1;
    BSTNode *node1 = new BSTNode{ 47,NULL,NULL,NULL };
    insert(root, node1);
    BSTNode *node2 = new BSTNode{ 98,NULL,NULL,NULL };
    insert(root, node2);
    BSTNode *node3 = new BSTNode{ 46,NULL,NULL,NULL };
    insert(root, node3);
    BSTNode *node4 = new BSTNode{ 19,NULL,NULL,NULL };
    insert(root, node4);
    BSTNode *node5 = new BSTNode{ 55,NULL,NULL,NULL };
    insert(root, node5);
    BSTNode *node6 = new BSTNode{ 50,NULL,NULL,NULL };
    insert(root, node6);

    cout << "二叉查找树通过插入构建后的中序遍历结果:";
    inorderprint(root);
    cout << endl;
    
    cout << "查找19结果:" << search(root, 19) << endl;//没找到返回空
    cout << "查找10结果:" << search(root, 10) << endl;
    
    cout << "二叉查找树最小节点值:" << minkeynode(root)->val << endl;
    cout << "二叉查找树最大节点值:" << maxkeynode(root)->val << endl;

    cout << "查找某个值的前驱节点:" << prenode(root, 50)->val << endl;//无前驱返回nullptr
    cout << "查找某个值的后继节点:" << postnode(root, 50)->val << endl;
        
    cout << "删除某个节点后中序遍历结果:";
    removenode(root, 19);
    inorderprint(root);
    cout << endl;
    

}

 

posted @ 2019-05-23 20:16  前进的code  阅读(853)  评论(0编辑  收藏  举报