二叉树的各种遍历

 

费了两天时间写的,包括前中后序遍历的递归和非递归算法,还有层序遍历总共2*3 + 1 = 7中遍历二叉树的算法,感觉其中后序遍历的非递归算法比较困难,想了很久最后的实现还是不够优雅,请大家指正~~

总共三个文件,一个头文件,一个对应的cpp文件,还有一个用于测试的文件.

头文件:
/**//********************************************************************
    created:    2006/07/04
    filename:     BinaryTree.h
    author:        李创
 http://www.cppblog.com/converse/
 
   purpose:    演示二叉树的算法
*********************************************************************/

#ifndef BinaryTree_H
#define BinaryTree_H

#include <stdlib.h>
#include <stack>

class BinaryTree
{
private:
    typedef int Item;
    typedef struct TreeNode
    {
        Item        Node;
        TreeNode*   pRight;
        TreeNode*   pLeft;
  
        TreeNode(Item node = 0, TreeNode* pright = NULL, TreeNode* pleft = NULL)
            : Node(node)
            , pRight(pright)
            , pLeft(pleft)
        {
        }
  
    }TreeNode, *PTreeNode;
 
public:
    enum TraverseType
    {
        PREORDER    = 0,        // 前序
   INORDER        = 1,        // 中序
   POSTORDER    = 2,        // 后序
   LEVELORDER    = 3            // 层序
    };
 
    BinaryTree(Item Array[], int nLength);
    ~BinaryTree();
 
    PTreeNode GetRoot()
    {
        return m_pRoot;
    }
 
    // 遍历树的对外接口
    // 指定遍历类型和是否是非递归遍历,默认是递归遍历
    void Traverse(TraverseType traversetype, bool bRec = true);
 
private:
    PTreeNode   CreateTreeImpl(Item Array[], int nLength);
    void        DetroyTreeImpl(PTreeNode pTreenode);
 
    void        PreTraverseImpl(PTreeNode pTreenode);        // 递归前序遍历树
    void        InTraverseImpl(PTreeNode pTreenode);        // 递归中序遍历树
    void        PostTraverseImpl(PTreeNode pTreenode);        // 递归后序遍历树
 
    void        NoRecPreTraverseImpl(PTreeNode pTreenode);    // 非递归前序遍历树
    void        NoRecInTraverseImpl(PTreeNode pTreenode);    // 非递归中序遍历树
    void        NoRecPostTraverseImpl(PTreeNode pTreenode);    // 非递归后序遍历树
 
    void        LevelTraverseImpl(PTreeNode pTreenode);
 
    PTreeNode   m_pRoot;        // 根结点
 
    // 采用STL里面的stack作为模拟保存链表结点的stack容器
    typedef std::stack<BinaryTree::PTreeNode> TreeNodeStack;
};

#endif

实现文件:
/**//********************************************************************
    created:    2006/07/04
    filename:     BinaryTree.cpp
    author:        李创
 http://www.cppblog.com/converse/
 
   purpose:    演示二叉树的算法
*********************************************************************/

#include <iostream>
#include <assert.h>
#include <queue>
#include "BinaryTree.h"

BinaryTree::BinaryTree(Item Array[], int nLength)
: m_pRoot(NULL)
{
    assert(NULL != Array);
    assert(nLength > 0);
 
    m_pRoot = CreateTreeImpl(Array, nLength);
}

BinaryTree::~BinaryTree()
{
    DetroyTreeImpl(m_pRoot);
}

// 按照中序递归创建树
BinaryTree::PTreeNode BinaryTree::CreateTreeImpl(Item Array[], int nLength)
{
    int mid = nLength / 2;
    PTreeNode p = new TreeNode(Array[mid]);
 
    if (nLength > 1)
    {
        p->pLeft    = CreateTreeImpl(Array, nLength / 2);
        p->pRight   = CreateTreeImpl(Array + mid + 1, nLength / 2 - 1);
    }
 
    return p;
}

void BinaryTree::DetroyTreeImpl(PTreeNode pTreenode)
{
    if (NULL != pTreenode->pLeft)
    {
        DetroyTreeImpl(pTreenode->pLeft);
    }
    if (NULL != pTreenode->pRight)
    {
        DetroyTreeImpl(pTreenode->pRight);
    }
 
    delete pTreenode;
    pTreenode = NULL;
}

// 遍历树的对外接口
// 指定遍历类型和是否是非递归遍历,默认是递归遍历
void BinaryTree::Traverse(TraverseType traversetype, bool bRec /**//*= true*/)
{
    switch (traversetype)
    {
    case PREORDER:    // 前序
        {           
            if (true == bRec)
            {
                std::cout << "递归前序遍历树\n";
                PreTraverseImpl(m_pRoot);
            }
            else
            {
                std::cout << "非递归前序遍历树\n";
                NoRecPreTraverseImpl(m_pRoot);
            }
        }
        break;
  
    case INORDER:    // 中序
        {           
            if (true == bRec)
            {
                std::cout << "递归中序遍历树\n";
                InTraverseImpl(m_pRoot);
            }
            else
            {
                std::cout << "非递归中序遍历树\n";
                NoRecInTraverseImpl(m_pRoot);
            }
        }
        break;
  
    case POSTORDER:    // 后序
        {           
            if (true == bRec)
            {
                std::cout << "递归后序遍历树\n";
                PostTraverseImpl(m_pRoot);
            }
            else
            {
                std::cout << "非递归后序遍历树\n";
                NoRecPostTraverseImpl(m_pRoot);
            }
        }
        break;
  
    case LEVELORDER:    // 层序
        {
            std::cout << "层序遍历树\n";
            LevelTraverseImpl(m_pRoot);
        }
    }
 
    std::cout << std::endl;
}

// 递归前序遍历树
void BinaryTree::PreTraverseImpl(PTreeNode pTreenode)
{
    if (NULL == pTreenode)
        return;
 
    std::cout << "Item = " << pTreenode->Node << std::endl;
 
    PreTraverseImpl(pTreenode->pLeft);
 
    PreTraverseImpl(pTreenode->pRight);
}

// 非递归前序遍历树
void BinaryTree::NoRecPreTraverseImpl(PTreeNode pTreenode)
{
    if (NULL == pTreenode)
        return;
 
    TreeNodeStack NodeStack;
    PTreeNode pNode;
    NodeStack.push(pTreenode);
 
    while (!NodeStack.empty())
    {
        while (NULL != (pNode = NodeStack.top()))    // 向左走到尽头
        {
            std::cout << "Item = " << pNode->Node << std::endl;    // 访问当前结点
            NodeStack.push(pNode->pLeft);                    // 左子树根结点入栈
        }
        NodeStack.pop();                                    // 左子树根结点退栈
        if (!NodeStack.empty())
        {
            pNode = NodeStack.top();
            NodeStack.pop();                                // 当前结点退栈
            NodeStack.push(pNode->pRight);                // 当前结点的右子树根结点入栈
        }
    }
}

// 中序遍历树
// 中序遍历输出的结果应该和用来初始化树的数组的排列顺序一致
void BinaryTree::InTraverseImpl(PTreeNode pTreenode)
{
    if (NULL == pTreenode)
        return;
 
    if (NULL != pTreenode->pLeft)
    {
        InTraverseImpl(pTreenode->pLeft);
    }
 
    std::cout << "Item = " << pTreenode->Node << std::endl;
 
    if (NULL != pTreenode->pRight)
    {
        InTraverseImpl(pTreenode->pRight);
    }
}

// 非递归中序遍历树
void BinaryTree::NoRecInTraverseImpl(PTreeNode pTreenode)
{
    if (NULL == pTreenode)
        return;
 
    TreeNodeStack NodeStack;
    PTreeNode pNode;
    NodeStack.push(pTreenode);
 
    while (!NodeStack.empty())
    {
        while (NULL != (pNode = NodeStack.top()))    // 向左走到尽头
        {
            NodeStack.push(pNode->pLeft);
        }
  
        NodeStack.pop();
  
        if (!NodeStack.empty() && NULL != (pNode = NodeStack.top()))
        {
            std::cout << "Item = " << pNode->Node << std::endl;
            NodeStack.pop();
            NodeStack.push(pNode->pRight);
        }
    }
}

// 后序遍历树
void BinaryTree::PostTraverseImpl(PTreeNode pTreenode)
{
    if (NULL == pTreenode)
        return;
 
    if (NULL != pTreenode->pLeft)
    {
        PostTraverseImpl(pTreenode->pLeft);
    }
 
    if (NULL != pTreenode->pRight)
    {
        PostTraverseImpl(pTreenode->pRight);
    }
 
    std::cout << "Item = " << pTreenode->Node << std::endl;
}

// 非递归后序遍历树
void BinaryTree::NoRecPostTraverseImpl(PTreeNode pTreenode)
{
    if (NULL == pTreenode)
        return;
 
    TreeNodeStack NodeStack;
    PTreeNode pNode1, pNode2;
    NodeStack.push(pTreenode);
    pNode1 = pTreenode->pLeft;
   
    bool bVisitRoot = false;            // 标志位,是否访问过根结点
    while (!NodeStack.empty())
    {
        while (NULL != pNode1)            // 向左走到尽头
        {
            NodeStack.push(pNode1);
            pNode1 = pNode1->pLeft;
        }
  
        pNode1 = NodeStack.top();
        NodeStack.pop();
  
        if (NULL == pNode1->pRight)            // 如果没有右子树就是叶子结点
        {
            std::cout << "Item = " << pNode1->Node << std::endl;
            pNode2 = pNode1;
            pNode1 = NodeStack.top();
   
            if (pNode2 == pNode1->pRight)    // 如果这个叶子结点是右子树
            {
                std::cout << "Item = " << pNode1->Node << std::endl;
                NodeStack.pop();
                pNode1 = NULL;
            }
            else                            // 否则访问右子树
            {
                pNode1 = pNode1->pRight;
            }
        }
        else                                // 访问右子树
        {
            if (pNode1 == pTreenode && true == bVisitRoot)    // 如果已经访问过右子树那么就退出
            {
                std::cout << "Item = " << pNode1->Node << std::endl;
                return;
            }
            else
            {
                if (pNode1 == pTreenode)
                {
                    bVisitRoot = true;
                }
    
                NodeStack.push(pNode1);
                pNode1 = pNode1->pRight;
            }
        }
    }
}

// 按照树的层次从左到右访问树的结点
void BinaryTree::LevelTraverseImpl(PTreeNode pTreenode)
{
    if (NULL == pTreenode)
        return;
 
    // 层序遍历用于保存结点的容器是队列
    std::queue<PTreeNode> NodeQueue;
    PTreeNode pNode;
    NodeQueue.push(pTreenode);
 
    while (!NodeQueue.empty())
    {
        pNode = NodeQueue.front();
        NodeQueue.pop();
        std::cout << "Item = " << pNode->Node << std::endl;
  
        if (NULL != pNode->pLeft)
        {
            NodeQueue.push(pNode->pLeft);   
        }
        if (NULL != pNode->pRight)
        {
            NodeQueue.push(pNode->pRight);
        }   
    }
}
测试文件:
/**//********************************************************************
    created:    2006/07/04
    filename:     main.cpp
    author:        李创
 http://www.cppblog.com/converse/
 
   purpose:    测试二叉树的算法
*********************************************************************/

#include "BinaryTree.h"

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <iostream>

void DisplayArray(int array[], int length)
{
    int i;
 
    for (i = 0; i < length; i++)
    {
        printf("array[%d] = %d\n", i, array[i]);
    }
}

void CreateNewArray(int array[], int length)
{
    for (int i = 0; i < length; i++)
    {
        array[i] = rand() % 256 + i;
    }
}

int main()
{
    int array[10];
    srand(time(NULL));
 
    // 创建数组
    CreateNewArray(array, 10);
    DisplayArray(array, 10);
 
    BinaryTree *pTree = new BinaryTree(array, 10);
 
    // 测试前序遍历
    pTree->Traverse(BinaryTree::PREORDER);
    std::cout << "root = " << pTree->GetRoot()->Node << std::endl;
    std::cout << "root->left = " << pTree->GetRoot()->pLeft->Node << std::endl;
    std::cout << "root->right = " << pTree->GetRoot()->pRight->Node << std::endl;
    pTree->Traverse(BinaryTree::PREORDER, false);
   
    // 测试中序遍历
    pTree->Traverse(BinaryTree::INORDER);
    std::cout << "root = " << pTree->GetRoot()->Node << std::endl;
    std::cout << "root->left = " << pTree->GetRoot()->pLeft->Node << std::endl;
    std::cout << "root->right = " << pTree->GetRoot()->pRight->Node << std::endl;
    pTree->Traverse(BinaryTree::INORDER, false);
    // 测试后序遍历
    pTree->Traverse(BinaryTree::POSTORDER);
    std::cout << "root = " << pTree->GetRoot()->Node << std::endl;
    std::cout << "root->left = " << pTree->GetRoot()->pLeft->Node << std::endl;
    std::cout << "root->right = " << pTree->GetRoot()->pRight->Node << std::endl;
    pTree->Traverse(BinaryTree::POSTORDER, false);
    // 测试层序遍历
    pTree->Traverse(BinaryTree::LEVELORDER);
 
    system("pause");
   
    delete pTree;
 
    return 0;
}