创的技术博客
二叉树遍历算法集合(前中后序遍历的递归和非递归算法,层序遍历算法)
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)