数据结构开发(21):树中属性操作与层次遍历

0.目录

1.树中属性操作的实现

2.树形结构的层次遍历

3.小结

1.树中属性操作的实现

树中结点的数目:

  • 定义功能:count(node)
    1. node 为根结点的树中统计结点数目

树结点数目的计算示例:

  • count(A) = count(B) + count(C) + count(D) + 1

在GTree.h中实现统计结点数目:

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

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

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

        return ret;
    }
public:
    int count() const
    {
        return count(root());
    }

树的高度:

  • 定义功能:height(node)
    1. 获取 node 为根结点的树的高度

树的高度计算示例:

  • height(A) = MAX{ height(B), height(C), height(D) } + 1

在GTree.h中实现获取树的高度:

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

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

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

            ret = ret + 1;
        }

        return ret;
    }
public:
    int height() const
    {
        return height(root());
    }

树的度数:

  • 定义功能:degree(node)
    1. 获取 node 为根结点的树的度数

树的度计算示例:

  • degree(A) = MAX{ degree(B), degree(C), degree(D), 3 }

在GTree.h中实现获取树的度数:

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

        if( node != NULL )
        {
            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;
    }
public:
    int degree() const
    {
        return degree(root());
    }

统一mian.cpp测试:

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

using namespace std;
using namespace StLib;

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

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

    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);

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

    return 0;
}

运行结果为:

13
4
3

2.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* )
  • 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
  • 通过结点中的 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。

层次遍历算法:

  • 原料:class LinkQueue<T>;
  • 游标:LinkQueue<T>: :front();
  • 思想:
    1. begin() → 将根结点压入队列中
    2. current() → 访问队头元素指向的数据元素
    3. next() → 队头元素弹出,将队头元素的孩子压入队列中 ( 核心 )
    4. end() → 判断队列是否为空

层次遍历算法示例:

在GTree.h中实现树形结构的层次遍历:

protected:
    LinkQueue<GTreeNode<T>*> m_queue;
public:
    bool begin()
    {
        bool ret = (root() != NULL);

        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(InvalidOperationException, "No value at current position ...");
        }
    }

然后在其他地方加入对应的清空队列的代码:

public:
    SharedPointer< Tree<T> > remove(const T& value)
    {
        GTree<T>* ret = NULL;
        GTreeNode<T>* node = find(value);

        if( node == NULL )
        {
            THROW_EXCEPTION(InvalidParameterException, "Can not find the node via parameter value ...");
        }
        else
        {
            remove(node, ret);

            m_queue.clear();
        }

        return ret;
    }

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

        node = find(node);

        if( node == NULL )
        {
            THROW_EXCEPTION(InvalidParameterException, "Parameter node is invalid ...");
        }
        else
        {
            remove(dynamic_cast<GTreeNode<T>*>(node), ret);

            m_queue.clear();
        }

        return ret;
    }

最后把GTree和GTreeNode类的拷贝构造和赋值操作都声明为保护成员函数:
GTree.h

protected:
    GTree(const GTree<T>&);
    GTree<T>& operator = (const GTree<T>&);
public:
    GTree()
    {

    }

GTreeNode.h

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

最终main.cpp测试

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

using namespace std;
using namespace StLib;

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

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

    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;
}

运行结果为:

ABCDEFGHIJKLM

3.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
  • 遍历算法的核心为队列的使用

最终的GTree.h代码:

#ifndef GTREE_H
#define GTREE_H

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

namespace StLib
{

template <typename T>
class GTree : public Tree<T>
{
protected:
    LinkQueue<GTreeNode<T>*> m_queue;

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

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

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

        return ret;
    }

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

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

        return ret;
    }

    void free(GTreeNode<T>* node)
    {
        if( node != NULL )
        {
            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 == NULL )
        {
            THROW_EXCEPTION(NoEnoughMemoryException, "No memory to create new tree ...");
        }
        else
        {
            if( root() == node )
            {
                this->m_root = NULL;
            }
            else
            {
                LinkList<GTreeNode<T>*>& child = dynamic_cast<GTreeNode<T>*>(node->parent)->child;

                child.remove(child.find(node));

                node->parent = NULL;
            }

            ret->m_root = node;
        }
    }

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

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

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

            ret = ret + 1;
        }

        return ret;
    }

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

        if( node != NULL )
        {
            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;
    }
public:
    GTree()
    {

    }

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

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

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

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

        return ret;
    }

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

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

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

        return ret;
    }

    SharedPointer< Tree<T> > remove(const T& value)
    {
        GTree<T>* ret = NULL;
        GTreeNode<T>* node = find(value);

        if( node == NULL )
        {
            THROW_EXCEPTION(InvalidParameterException, "Can not find the node via parameter value ...");
        }
        else
        {
            remove(node, ret);

            m_queue.clear();
        }

        return ret;
    }

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

        node = find(node);

        if( node == NULL )
        {
            THROW_EXCEPTION(InvalidParameterException, "Parameter node is invalid ...");
        }
        else
        {
            remove(dynamic_cast<GTreeNode<T>*>(node), ret);

            m_queue.clear();
        }

        return ret;
    }

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

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

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

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

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

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

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

        this->m_root = NULL;

        m_queue.clear();
    }

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

        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(InvalidOperationException, "No value at current position ...");
        }
    }

    ~GTree()
    {
        clear();
    }
};

}

#endif // GTREE_H
posted @ 2018-12-21 22:09  PyLearn  阅读(462)  评论(0编辑  收藏  举报