Data Structure and Algorithm Fundamentals (Wang Zhuo) (29): Binary Sorting Tree

Table of contents

Binary Sort Tree

Preconditions:

Binary sort search (recursive algorithm)

Run the framework/build idea:

Program implementation:

standard answer:

Insertion into a binary permutation tree

Deletion of binary permutation tree

Generation of binary permutation tree

---

Binary Sort Tree

Preconditions:

#include<iostream>
using namespace std;

typedef int KeyType;
typedef int InfoType;

struct ElemType
{
    KeyType key;  //关键字
    InfoType otherinfo;  //其他数据域
};

struct BSTNode
{
    ElemType data;  //数据域
    struct BSTNode* lchild, * rchild;  //左右孩子指针
};
typedef BSTNode * BSTree;
BSTree T;  //定义二叉排序树T

Binary sort search (recursive algorithm)

Run the framework/build idea:

    //If the tree is empty, return empty
    //After thinking about it later, the empty tree is also the type of binary tree, so being empty is the same as success, directly output
    //Compare key and root node
    //Success: output

    //Failure: greater than looking at the right subtree, less than looking at the left subtree

    // loop to repeat the operation

Program implementation:

BSTree SearchBST(BSTree T, KeyType key)
{
    //若树为空，返回空
    // 后面转念一想，空树也是这个二叉树类型，所以为空就像和成功一样，直接输出
    //比较key和根节点
    // 成功：输出
    if ((key == T->data.key) || (!T))
        return T;
    //失败：大于看右子树，小于看左子树
    else if (key > T->data.key)
    {
        T = T->rchild;
        return  SearchBST(T, key);
    }
    else if (key < T->data.key)
    {
        T = T->rchild;
        return  SearchBST(T, key);
    }
    //循环重复该操作
}

standard answer:

Just put:

        T = T->rchild;
        return  SearchBST(T, key);

combined into one step:

         return SearchBST(T->rchild, key); //Continue to search in the right subtree

BSTree SearchBST(BSTree T, KeyType key)
{
    if ((key == T->data.key) || (!T))
        return T;
    else if (key > T->data.key)
        return SearchBST(T->lchild, key);
    else
        return SearchBST(T->rchild, key);
}

---

Insertion into a binary permutation tree

//二叉排列树的插入
void InsertBSTree(BSTree& T, ElemType& e)
{
    if (!T)
    {
        T =new BSTNode;
        T->data = e;
    }

    if (T->data.key == e.key);
    //已有该元素，退出
    else if (e.key > T->data.key)
        InsertBSTree(T->rchild, e);
    else if (e.key < T->data.key)
        InsertBSTree(T->lchild, e);
}

Deletion of binary permutation tree

more complex

---

Generation of binary permutation tree

// 二叉排列树的生成
void CreatBSTree(BSTree & T)
{
    //输入序列（也可以从形参传入）
    cout << "input info about the tree" << endl;
    vector<ElemType> vec;
    ElemType input;
    while (cin >> input.key)
    {
        vec.push_back(input);
    }
    //调用插入算法
    for (vector<ElemType>::iterator it = vec.begin(); it != vec.end(); ++it)
    {
        InsertBSTree(T, *it);
    }
}