二叉树

Posted 2021-02-12 guoshuai-ouc

二叉树的基本操作（C++）

1. 首先创建二叉树结构，以及二叉树的类，定义在BinaryTree.h中

 1 #ifndef _BINARYTREE_H
 2 #define _BINARYTREE_H
 3 #include "pch.h"
 4 #include <iostream>
 5 
 6 using namespace std;
 7 
 8 typedef struct TreeNode
 9 {
10     char val;            //节点的数据类型
11     TreeNode * left;     //左子树
12     TreeNode * right;    //右子树
13     TreeNode(char x):val(x), left(nullptr), right(nullptr) {}
14 
15 }TreeNode, *BiTree;
16 
17 class BinaryTree
18 {
19 public:
20     BinaryTree() {}
21     ~BinaryTree() {}
22     void TreeCreate();            //递归的创建二叉树的节点
23     int getSize();                //递归得到树的节点数目
24     int getHeight();              //递归得到树的高度
25     void preOrder();              //前序遍历
26     void inOrder();               //中序遍历
27     void postOrder();             //后序遍历
28     void distroy();               //删除二叉树
29 
30 private:
31     BiTree create();                        //递归的创建二叉树的节点
32     void preOrder(BiTree root);             //前序遍历
33     void inOrder(BiTree root);              //中序遍历
34     void postOrder(BiTree root);            //后序遍历
35     void distroy(BiTree root);              //摧毁树
36     int getHeight(BiTree root);             //递归得到树的高度
37     void AddNode(const char key, int direction, BiTree root);         //添加节点
38     BiTree m_root;                          //根节点
39     int size;                               //节点总数
40 };
41 
42 #endif

2. 具体实现    BinaryTree.cpp

# include "BinaryTree.h"

#pragma region 私有成员函数
//添加节点
//key为要插入的值，direction是从左子树插入还是右子树插入，root为从哪个节点插入
void BinaryTree::AddNode(const char key, int direction, BiTree root)
{
    if (direction == 0)
    {
        //从左子树插入
        if (root->left == NULL)
            root->left = new TreeNode(key);
        else
            AddNode(key, direction, root->left);
    }
    else if (direction == 1)
    {
        //从右子树插入
        if (root->right == NULL)
            root->right = new TreeNode(key);
        else
            AddNode(key, direction, root->right);
    }
}

//二叉树的建立，按前序遍历(root->left->right)的方式建立二叉树
BiTree BinaryTree::create()
{
    BiTree current = NULL;
    char val;
    cin >> val;//输入键值

    if (val == ‘#‘)//标识当前子树为空，转向下一节点
    {
        return NULL;
    }
    else
    {   //递归的创建左右子树  
        size++;//记录节点数
        current = new TreeNode(val);
        current->left = create();
        current->right = create();
        return current;
    }
}

//删除二叉树
void BinaryTree::distroy(BiTree root)
{
    if (root)
    {
        distroy(root->left);
        distroy(root->right);
        delete root;
        root = NULL;
        size = 0;
    }
}

//递归得到树的高度
int BinaryTree::getHeight(BiTree root)
{
    if (root == NULL)
        return 0;
    int left_height = getHeight(root->left);
    int right_height = getHeight(root->right);
    return (left_height > right_height) ? (left_height + 1) : (right_height + 1);
}

//前序遍历  root->left->right
void BinaryTree::preOrder(BiTree root)
{
    if (root == NULL)
        return;
    else
    {
        cout << root->val << "  -->  ";     //首先打印根节点
        preOrder(root->left);               //接着遍历左子树
        preOrder(root->right);              //接着遍历右子树
    }
}

//中序遍历  left->root->right
void BinaryTree::inOrder(BiTree root)
{
    if (root == NULL)
        return;
    else
    {
        inOrder(root->left);                //首先遍历左子树
        cout << root->val << "  -->  ";     //接着打印根节点
        inOrder(root->right);               //接着遍历右子树
    }
}

//后序遍历   left->right->root
void BinaryTree::postOrder(BiTree root)
{
    if (root == NULL)
        return;
    else
    {
        postOrder(root->left);              //首先遍历左子树
        postOrder(root->right);             //接着遍历右子树
        cout << root->val << "  -->  ";     //接着打印根节点
    }
}
#pragma endregion


#pragma region 公有成员函数
//二叉树的建立
void BinaryTree::TreeCreate()
{
    size = 0;
    m_root =create();
}

//删除二叉树
void BinaryTree::distroy()
{
    distroy(m_root);
}

//递归得到树的高度
int BinaryTree::getHeight()
{
    return getHeight(m_root);
}

//前序遍历
void BinaryTree::preOrder()
{
    cout << "前序遍历的结果如下：" << endl;
    preOrder(m_root);
    cout << endl;
}

//中序遍历
void BinaryTree::inOrder()
{
    cout << "中序遍历的结果如下：" << endl;
    inOrder(m_root);
    cout << endl;
}

//后序遍历
void BinaryTree::postOrder()
{
    cout << "后序遍历的结果如下：" << endl;
    postOrder(m_root);
    cout << endl;
}

//获取大小
int BinaryTree::getSize()
{
    //这里是创建时候直接进行了计数
    //也可以利用遍历的方式获取，当节点有值，就加1
    return size;
}
#pragma endregion

3.主函数调用

int main()
{
    BinaryTree tree;
    cout << "按前序遍历方式创建树" << endl;
    //"ABDG##H###CE#I##F##";
    tree.TreeCreate();
    cout << "树的高度为：" << tree.getHeight() << endl;
    cout << "树的节点为：" << tree.getSize() << endl;
    tree.preOrder();            //前序遍历
    tree.inOrder();             //中序遍历
    tree.postOrder();           //后序遍历
    tree.distroy();             //摧毁树
    system("pause");
}