【数据结构】65_二叉树中属性操作的实现

二叉树的属性操作

二叉树中结点的数目

• 定义功能： count(node)

  • 在 node 为根结点的二叉树中统计结点数目

编程实验：二叉树中结点的数目

int count(BTreeNode<T> *node) const
{
    return (node != nullptr) ? (count(node->left) + count(node->right) + 1) : 0;
}

int count() const override
{
    return count(root());
}

二叉树的高度

• 定义功能：height(node)

  • 获取 node 为根结点的二叉树的高度

编程实验：二叉树的高度

int height(BTreeNode<T> *node) const
{
    int ret = 0;

    if (node != nullptr)
    {
        int lh = height(node->left);
        int rh = height(node->right);

        ret = ((lh > rh) ? lh : rh) + 1;
    }

    return ret;
}

int height() const override
{
    return height(root());
}

二叉树的度数

• 定义功能：degree(node)

  • 获取 node 为根结点的二叉树的度数

编程实验：二叉树的度数

int degree(BTreeNode<T> *node) const
{
    int ret = 0;

    if (node != nullptr)
    {
        BTreeNode<T> *child[] = {node->left, node->right};
        ret = !!node->left + !!node->left;

        for (int i=0; (i<2) && (ret<2); ++i)
        {
            int d = degree(child[i]);

            if (ret < d)
            {
                ret = d;
            }
        }
    }

    return ret;
}

int degree() const override
{
    return degree(root());
}

---

文件：BTree.h

#ifndef BTREE_H
#define BTREE_H

#include "Tree.h"
#include "BTreeNode.h"
#include "Exception.h"
#include "LinkQueue.h"

namespace DTLib
{

template <typename T>
class BTree : public Tree<T>
{
public:
    BTree() = default;

    bool insert(TreeNode<T> *node) override
    {
        return insert(node, ANY);
    }

    virtual bool insert(TreeNode<T> *node, BTNodePos pos)
    {
        bool ret = true;

        if (node != nullptr)
        {
            if (this->m_root == nullptr)
            {
                node->parent = nullptr;
                this->m_root = node;
            }
            else
            {
                BTreeNode<T> *np = find(node->parent);

                if (np != nullptr)
                {
                    ret = insert(dynamic_cast<BTreeNode<T>*>(node), np, pos);
                }
                else
                {
                    THROW_EXCEPTION(InvalidParameterExcetion, "Invalid parent tree node ...");
                }
            }
        }
        else
        {
            THROW_EXCEPTION(InvalidParameterExcetion, "Parameter can not be null ...");
        }

        return ret;
    }

    bool insert(const T &value, TreeNode<T> *parent) override
    {
        return insert(value, parent, ANY);
    }

    virtual bool insert(const T &value, TreeNode<T> *parent, BTNodePos pos)
    {
        bool ret = true;
        BTreeNode<T> *node = BTreeNode<T>::NewNode();

        if (node != nullptr)
        {
            node->value = value;
            node->parent = parent;

            ret = insert(node, pos);

            if (!ret)
            {
                delete node;
            }
        }
        else
        {
            THROW_EXCEPTION(NoEnoughMemoryException, "No enough memory to create node ...");
        }

        return ret;
    }

    SharedPointer<Tree<T>> remove(const T &value) override
    {
        BTree<T> *ret = nullptr;

        BTreeNode<T> *node = find(value);

        if (node != nullptr)
        {
            remove(node, ret);
        }
        else
        {
            THROW_EXCEPTION(InvalidParameterExcetion, "Can not find the tree node via value ...");
        }

        return ret;
    }

    SharedPointer<Tree<T>> remove(TreeNode<T> *node) override
    {
        BTree<T> *ret = nullptr;

        node = find(node);

        if (node != nullptr)
        {
            remove(dynamic_cast<BTreeNode<T>*>(node), ret);
        }
        else
        {
            THROW_EXCEPTION(InvalidParameterExcetion, "Parameter node is invalid ...");
        }

        return ret;
    }

    BTreeNode<T>* find(const T &value) const override
    {
        return find(root(), value);
    }

    BTreeNode<T>* find(TreeNode<T> *node) const override
    {
        return find(root(), dynamic_cast<BTreeNode<T>*>(node));
    }

    BTreeNode<T>* root() const override
    {
        return dynamic_cast<BTreeNode<T>*>(this->m_root);
    }

    int degree() const override
    {
        return degree(root());
    }

    int count() const override
    {
        return count(root());
    }

    int height() const override
    {
        return height(root());
    }

    void clear() override
    {
        free(root());

        this->m_root = nullptr;
    }

    ~BTree()
    {
        clear();
    }

protected:
    BTree(const BTree<T>&) = default;
    BTree<T>& operator = (const BTree<T>&) = default;

    virtual BTreeNode<T>* find(BTreeNode<T> *node, const T &value) const
    {
        BTreeNode<T> *ret = nullptr;

        if (node != nullptr)
        {
            if (node->value == value)
            {
                ret = node;
            }
            else
            {
                if (ret == nullptr)
                {
                    ret = find(node->left, value);
                }

                if (ret == nullptr)
                {
                    ret = find(node->right, value);
                }
            }
        }

        return ret;
    }

    virtual BTreeNode<T>* find(BTreeNode<T> *node, BTreeNode<T> *obj) const
    {
        BTreeNode<T> *ret = nullptr;

        if (node == obj)
        {
            ret = node;
        }
        else
        {
            if (node != nullptr)
            {
                if (ret == nullptr)
                {
                    ret = find(node->left, obj);
                }

                if (ret == nullptr)
                {
                    ret = find(node->right, obj);
                }
            }
        }

        return ret;
    }

    virtual bool insert(BTreeNode<T> *node, BTreeNode<T> *np, BTNodePos pos)
    {
        bool ret = true;

        if (pos == ANY)
        {
            if (np->left == nullptr)
            {
                np->left = node;
            }
            else if (np->right == nullptr)
            {
                np->right = node;
            }
            else
            {
                ret = false;
            }
        }
        else if (pos == LEFT)
        {
            if (np->left == nullptr)
            {
                np->left = node;
            }
            else
            {
                ret = false;
            }
        }
        else if (pos == RIGHT)
        {
            if (np->right == nullptr)
            {
                np->right = node;
            }
            else
            {
                ret = false;
            }
        }

        return ret;
    }

    virtual void remove(BTreeNode<T> *node, BTree<T> *&ret)
    {
        ret = new BTree<T>();

        if (ret != nullptr)
        {
            if (root() == node)
            {
                this->m_root = nullptr;
            }
            else
            {
                BTreeNode<T> *parent = dynamic_cast<BTreeNode<T>*>(node->parent);

                if (node == parent->left)
                {
                    parent->left = nullptr;
                }
                else if (node == parent->right)
                {
                    parent->right = nullptr;
                }

                node->parent = nullptr;
            }

            ret->m_root = node;
        }
        else
        {
            THROW_EXCEPTION(NoEnoughMemoryException, "No memory to create btree ...");
        }
    }

    virtual void free(BTreeNode<T> *node)
    {
        if (node != nullptr)
        {
            free(node->left);
            free(node->right);

            if (node->flag())
            {
                delete node;
            }
        }
    }

    int count(BTreeNode<T> *node) const
    {
        return (node != nullptr) ? (count(node->left) + count(node->right) + 1) : 0;
    }

    int height(BTreeNode<T> *node) const
    {
        int ret = 0;

        if (node != nullptr)
        {
            int lh = height(node->left);
            int rh = height(node->right);

            ret = ((lh > rh) ? lh : rh) + 1;
        }

        return ret;
    }

    int degree(BTreeNode<T> *node) const
    {
        int ret = 0;

        if (node != nullptr)
        {
            BTreeNode<T> *child[] = {node->left, node->right};
            ret = !!node->left + !!node->left;

            for (int i=0; (i<2) && (ret<2); ++i)
            {
                int d = degree(child[i]);

                if (ret < d)
                {
                    ret = d;
                }
            }
        }

        return ret;
    }
};

}

#endif // BTREE_H

文件：main.cpp

#include <iostream>
#include "BTreeNode.h"
#include "BTree.h"

using namespace std;
using namespace DTLib;

int main()
{
    BTree<int> bt;
    BTreeNode<int> *n = nullptr;

    bt.insert(1, nullptr);

    n = bt.find(1);
    bt.insert(2, n);
    bt.insert(3, n);

    n = bt.find(2);
    bt.insert(4, n);
    bt.insert(5, n);

    n = bt.find(4);
    bt.insert(8, n);
    bt.insert(9, n);

    n = bt.find(5);
    bt.insert(10, n);

    n = bt.find(3);
    bt.insert(6, n);
    bt.insert(7, n);

    cout << bt.count() << endl;
    cout << bt.height() << endl;
    cout << bt.degree() << endl;

    bt.clear();

    cout << bt.count() << endl;
    cout << bt.height() << endl;
    cout << bt.degree() << endl;

    return 0;
}

输出：

10
4
2
0
0
0

To be continued

思考： 如何遍历 BTree （二叉树结构） 的每一个结点？