【数据结构】58_树形结构的层次遍历

问题

如何按层次遍历通用树结构中的每一个数据元素？

---

当前的事实：树是非线性的数据结构，树的结点没有固定的编号方式
新的需求：为通用树结构提供新的方法，快速遍历每一个结点

设计思路（游标）

• 在树中定义一个游标 (GTreeNode<T> *)
• 遍历开始前将游标指向根结点 (root())
• 获取游标指向的数据元素
• 通过结点的 child 成员移动游标

提供一组遍历相关的函数，按层次访问树中的数据元素

函数	功能说明
begin()	初始化，准备进行遍历访问
next()	移动游标，指向下一个结点
current()	获取游标所指向的数据元素
end()	判断游标是否到达尾部

层次遍历算法

• 原料：class LinkQueue<T>;
• 游标：LinkQueue<T>::front();

• 思想：

  • begin() → 将根结点压入队列中
  • current() → 访问队头元素指向的数据元素
  • next() → 队头元素弹出，将队头元素的孩子压入队列中
  • end() → 判断队列是否为空

层次遍历算法示例

编程实验：通用树结构的层次遍历

文件：GTreeNode.h

#ifndef GTREENODE_H
#define GTREENODE_H

#include "TreeNode.h"
#include "LinkList.h"

namespace DTLib
{

template <typename T>
class GTreeNode : public TreeNode<T>
{
public:
    LinkList<GTreeNode<T>*> child;

    GTreeNode() = default;

    bool flag()
    {
        return m_flag;
    }

    static GTreeNode<T>* NewNode()
    {
        GTreeNode<T> *ret = new GTreeNode<T>();

        if (ret != nullptr)
        {
            ret->m_flag = true;
        }

        return ret;
    }

protected:
    bool m_flag = false;

    GTreeNode(const GTreeNode<T>&) = default;
    GTreeNode<T>& operator = (const GTreeNode<T>&) = default;

    void *operator new (unsigned int size) noexcept(true)
    {
        return Object::operator new(size);
    }
};

}

#endif // GTREENODE_H

文件：GTree.h

#ifndef GTREE_H
#define GTREE_H

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

namespace DTLib
{

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

    bool insert(TreeNode<T> *node) override
    {
        bool ret = true;

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

                if (np != nullptr)
                {
                    GTreeNode<T> *n = dynamic_cast<GTreeNode<T>*>(node);

                    if (np->child.find(n) < 0)
                    {
                        np->child.insert(n);
                    }
                }
                else
                {
                    THROW_EXCEPTION(InvalidOpertionExcetion, "Invalid partent tree node ...");
                }
            }
        }
        else
        {
            THROW_EXCEPTION(InvalidParameterExcetion, "Parameter node cannot be NULL ...");
        }

        return ret;
    }

    bool insert(const T &value, TreeNode<T> *parent) override
    {
        bool ret = true;

        GTreeNode<T> *node = GTreeNode<T>::NewNode();

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

            insert(node);
        }
        else
        {
            THROW_EXCEPTION(NoEnoughMemoryException, "No enough memory to create node ...");
        }

        return ret;
    }

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

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

        if (node != nullptr)
        {
            remove(node, ret);

            m_queue.clear();
        }
        else
        {
            THROW_EXCEPTION(InvalidParameterExcetion, "can not find the node ...");
        }

        return ret;
    }

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

        node = find(node);

        if (node != nullptr)
        {
            remove(dynamic_cast<GTreeNode<T>*>(node), ret);

            m_queue.clear();
        }
        else
        {
            THROW_EXCEPTION(InvalidParameterExcetion, "Parameter node is invalid ...");
        }

        return ret;
    }

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

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

    GTreeNode<T>* root() const override
    {
        return dynamic_cast<GTreeNode<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;

        m_queue.clear();
    }

    bool begin()
    {
        bool ret = (root() != nullptr);

        if (ret)
        {
            m_queue.clear();
            m_queue.add(root());
        }

        return ret;
    }

    bool end()
    {
        return (m_queue.length() == 0);
    }

    bool next()
    {
        bool ret = (m_queue.length() > 0);

        if (ret)
        {
            GTreeNode<T> *node = m_queue.front();

            m_queue.remove();

            for (node->child.move(0); !node->child.end(); node->child.next())
            {
                m_queue.add(node->child.current());
            }
        }

        return ret;
    }

    T current()
    {
        if (!end())
        {
            return m_queue.front()->value;
        }
        else
        {
            THROW_EXCEPTION(InvalidOpertionExcetion, "No value at current position ...");
        }
    }

    ~GTree()
    {
        clear();
    }

protected:
    LinkQueue<GTreeNode<T>*> m_queue;

    GTree(const GTree<T>&) = default;
    GTree<T>& operator = (const GTree<T>&) = default;

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

        if (node != nullptr)
        {
            if (node->value == value)
            {
                return node;
            }
            else
            {
                for (node->child.move(0); !node->child.end() && (ret == nullptr); node->child.next())
                {
                    ret = find(node->child.current(), value);
                }
            }
        }

        return ret;
    }

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

        if (node == obj)
        {
            return node;
        }
        else
        {
            if (node != nullptr)
            {
                for (node->child.move(0); !node->child.end() && (ret == nullptr); node->child.next())
                {
                    ret = find(node->child.current(), obj);
                }
            }
        }

        return ret;
    }

    void free(GTreeNode<T> *node)
    {
        if (node != nullptr)
        {
            for (node->child.move(0); !node->child.end(); node->child.next())
            {
                free(node->child.current());
            }

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

    void remove(GTreeNode<T> *node, GTree<T> *&ret)
    {
        ret = new GTree<T>();

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

                parent->child.remove(parent->child.find(node));

                node->parent = nullptr;
            }

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

    int count(GTreeNode<T> *node) const
    {
        int ret = 0;

        if (node != nullptr)
        {
            ret = 1;

            for (node->child.move(0); !node->child.end(); node->child.next())
            {
                ret += count(node->child.current());
            }
        }

        return ret;
    }

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

        if (node != nullptr)
        {
            for (node->child.move(0); !node->child.end(); node->child.next())
            {
                int h = height(node->child.current());

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

            ret += 1;
        }

        return ret;
    }

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

        if (node != nullptr)
        {
            ret = node->child.length();

            for (node->child.move(0); !node->child.end(); node->child.next())
            {
                int d = degree(node->child.current());

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

        return ret;
    }
};

}

#endif // GTREE_H

文件：main.cpp

#include <iostream>
#include "GTree.h"

using namespace std;
using namespace DTLib;

int main()
{
    GTree<char> t;
    GTreeNode<char> *node = nullptr;

    GTreeNode<char> root;

    root.value = 'A';
    root.parent = nullptr;

    t.insert(&root);

    node = t.find('A');
    t.insert('B', node);
    t.insert('C', node);
    t.insert('D', node);

    node = t.find('B');
    t.insert('E', node);
    t.insert('F', node);

    node = t.find('E');
    t.insert('K', node);
    t.insert('L', node);

    node = t.find('C');
    t.insert('G', node);

    node = t.find('D');
    t.insert('H', node);
    t.insert('I', node);
    t.insert('J', node);

    node = t.find('H');
    t.insert('M', node);

    for (t.begin(); !t.end(); t.next())
    {
        cout << t.current() << " ";
    }

    cout << endl;

    return 0;
}

输出：

A B C D E F G H I J K L M

小结

• 树的结点没有固定的编号方式
• 可以按照层次关系对树中的结点进行遍历
• 通过游标的思想设计遍历成员函数
• 遍历成员函数是相互依赖，相互配合的关系
• 遍历算法的核心是队列的使用

以上内容整理于狄泰软件学院系列课程，请大家保护原创！