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二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)

費了兩天時間寫的,包括前中后序遍歷的遞歸和非遞歸算法,還有層序遍歷總共2*3 + 1 = 7中遍歷二叉樹的算法,感覺其中后序遍歷的非遞歸算法比較困難,想了很久最后的實現還是不夠優雅,請大家指正~~

總共三個文件,一個頭文件,一個對應的cpp文件,還有一個用于測試的文件.

頭文件:
/********************************************************************
????created:????2006/07/04
????filename:?????BinaryTree.h
????author:????????李創
????????????????http://www.shnenglu.com/converse/

????purpose:????演示二叉樹的算法
*********************************************************************/

#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????????????//?層序
????};

????BinaryTree(Item?Array[],?int?nLength);
????~BinaryTree();

????PTreeNode?GetRoot()
????{
????????return?m_pRoot;
????}

????//?遍歷樹的對外接口
????//?指定遍歷類型和是否是非遞歸遍歷,默認是遞歸遍歷
????void?Traverse(TraverseType?traversetype,?bool?bRec?=?true);

private:
????PTreeNode???CreateTreeImpl(Item?Array[],?int?nLength);
????void????????DetroyTreeImpl(PTreeNode?pTreenode);

????void????????PreTraverseImpl(PTreeNode?pTreenode);????????//?遞歸前序遍歷樹
????void????????InTraverseImpl(PTreeNode?pTreenode);????????//?遞歸中序遍歷樹
????void????????PostTraverseImpl(PTreeNode?pTreenode);????????//?遞歸后序遍歷樹

????void????????NoRecPreTraverseImpl(PTreeNode?pTreenode);????//?非遞歸前序遍歷樹
????void????????NoRecInTraverseImpl(PTreeNode?pTreenode);????//?非遞歸中序遍歷樹
????void????????NoRecPostTraverseImpl(PTreeNode?pTreenode);????//?非遞歸后序遍歷樹

????void????????LevelTraverseImpl(PTreeNode?pTreenode);

????PTreeNode???m_pRoot;????????//?根結點

????//?采用STL里面的stack作為模擬保存鏈表結點的stack容器
????typedef?std::stack<BinaryTree::PTreeNode>?TreeNodeStack;
};

#endif


實現文件:
/********************************************************************
????created:????2006/07/04
????filename:?????BinaryTree.cpp
????author:????????李創
????????????????http://www.shnenglu.com/converse/

????purpose:????演示二叉樹的算法
*********************************************************************/

#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);
}

//?按照中序遞歸創建樹
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;
}

//?遍歷樹的對外接口
//?指定遍歷類型和是否是非遞歸遍歷,默認是遞歸遍歷
void?BinaryTree::Traverse(TraverseType?traversetype,?bool?bRec?/*=?true*/)
{
????switch?(traversetype)
????{
????case?PREORDER:????//?前序
????????{????????????
????????????if?(true?==?bRec)
????????????{
????????????????std::cout?<<?"遞歸前序遍歷樹\n";
????????????????PreTraverseImpl(m_pRoot);
????????????}
????????????else
????????????{
????????????????std::cout?<<?"非遞歸前序遍歷樹\n";
????????????????NoRecPreTraverseImpl(m_pRoot);
????????????}
????????}
????????break;

????case?INORDER:????//?中序
????????{????????????
????????????if?(true?==?bRec)
????????????{
????????????????std::cout?<<?"遞歸中序遍歷樹\n";
????????????????InTraverseImpl(m_pRoot);
????????????}
????????????else
????????????{
????????????????std::cout?<<?"非遞歸中序遍歷樹\n";
????????????????NoRecInTraverseImpl(m_pRoot);
????????????}
????????}
????????break;

????case?POSTORDER:????//?后序
????????{????????????
????????????if?(true?==?bRec)
????????????{
????????????????std::cout?<<?"遞歸后序遍歷樹\n";
????????????????PostTraverseImpl(m_pRoot);
????????????}
????????????else
????????????{
????????????????std::cout?<<?"非遞歸后序遍歷樹\n";
????????????????NoRecPostTraverseImpl(m_pRoot);
????????????}
????????}
????????break;

????case?LEVELORDER:????//?層序
????????{
????????????std::cout?<<?"層序遍歷樹\n";
????????????LevelTraverseImpl(m_pRoot);
????????}
????}

????std::cout?<<?std::endl;
}

//?遞歸前序遍歷樹
void?BinaryTree::PreTraverseImpl(PTreeNode?pTreenode)
{
????if?(NULL?==?pTreenode)
????????return;

????std::cout?<<?"Item?=?"?<<?pTreenode->Node?<<?std::endl;

????PreTraverseImpl(pTreenode->pLeft);

????PreTraverseImpl(pTreenode->pRight);
}

//?非遞歸前序遍歷樹
void?BinaryTree::NoRecPreTraverseImpl(PTreeNode?pTreenode)
{
????if?(NULL?==?pTreenode)
????????return;

????TreeNodeStack?NodeStack;
????PTreeNode?pNode;
????NodeStack.push(pTreenode);

????while?(!NodeStack.empty())
????{
????????while?(NULL?!=?(pNode?=?NodeStack.top()))????//?向左走到盡頭
????????{
????????????std::cout?<<?"Item?=?"?<<?pNode->Node?<<?std::endl;????//?訪問當前結點
????????????NodeStack.push(pNode->pLeft);????????????????????//?左子樹根結點入棧
????????}
????????NodeStack.pop();????????????????????????????????????//?左子樹根結點退棧
????????if?(!NodeStack.empty())
????????{
????????????pNode?=?NodeStack.top();
????????????NodeStack.pop();????????????????????????????????//?當前結點退棧
????????????NodeStack.push(pNode->pRight);????????????????//?當前結點的右子樹根結點入棧
????????}
????}
}

//?中序遍歷樹
//?中序遍歷輸出的結果應該和用來初始化樹的數組的排列順序一致
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);
????}
}

//?非遞歸中序遍歷樹
void?BinaryTree::NoRecInTraverseImpl(PTreeNode?pTreenode)
{
????if?(NULL?==?pTreenode)
????????return;

????TreeNodeStack?NodeStack;
????PTreeNode?pNode;
????NodeStack.push(pTreenode);

????while?(!NodeStack.empty())
????{
????????while?(NULL?!=?(pNode?=?NodeStack.top()))????//?向左走到盡頭
????????{
????????????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);
????????}
????}
}

//?后序遍歷樹
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;
}

//?非遞歸后序遍歷樹
void?BinaryTree::NoRecPostTraverseImpl(PTreeNode?pTreenode)
{
????if?(NULL?==?pTreenode)
????????return;

????TreeNodeStack?NodeStack;
????PTreeNode?pNode1,?pNode2;
????NodeStack.push(pTreenode);
????pNode1?=?pTreenode->pLeft;
????
????bool?bVisitRoot?=?false;????????????//?標志位,是否訪問過根結點
????while?(!NodeStack.empty())
????{
????????while?(NULL?!=?pNode1)????????????//?向左走到盡頭
????????{
????????????NodeStack.push(pNode1);
????????????pNode1?=?pNode1->pLeft;
????????}

????????pNode1?=?NodeStack.top();
????????NodeStack.pop();

????????if?(NULL?==?pNode1->pRight)????????????//?如果沒有右子樹就是葉子結點
????????{
????????????std::cout?<<?"Item?=?"?<<?pNode1->Node?<<?std::endl;
????????????pNode2?=?pNode1;
????????????pNode1?=?NodeStack.top();

????????????if?(pNode2?==?pNode1->pRight)????//?如果這個葉子結點是右子樹
????????????{
????????????????std::cout?<<?"Item?=?"?<<?pNode1->Node?<<?std::endl;
????????????????NodeStack.pop();
????????????????pNode1?=?NULL;
????????????}
????????????else????????????????????????????//?否則訪問右子樹
????????????{
????????????????pNode1?=?pNode1->pRight;
????????????}
????????}
????????else????????????????????????????????//?訪問右子樹
????????{
????????????if?(pNode1?==?pTreenode?&&?true?==?bVisitRoot)????//?如果已經訪問過右子樹那么就退出
????????????{
????????????????std::cout?<<?"Item?=?"?<<?pNode1->Node?<<?std::endl;
????????????????return;
????????????}
????????????else
????????????{
????????????????if?(pNode1?==?pTreenode)
????????????????{
????????????????????bVisitRoot?=?true;
????????????????}

????????????????NodeStack.push(pNode1);
????????????????pNode1?=?pNode1->pRight;
????????????}
????????}
????}
}

//?按照樹的層次從左到右訪問樹的結點
void?BinaryTree::LevelTraverseImpl(PTreeNode?pTreenode)
{
????if?(NULL?==?pTreenode)
????????return;

????//?層序遍歷用于保存結點的容器是隊列
????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);
????????}????
????}
}
測試文件:
/********************************************************************
????created:????2006/07/04
????filename:?????main.cpp
????author:????????李創
????????????????http://www.shnenglu.com/converse/

????purpose:????測試二叉樹的算法
*********************************************************************/

#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));

????//?創建數組
????CreateNewArray(array,?10);
????DisplayArray(array,?10);

????BinaryTree?*pTree?=?new?BinaryTree(array,?10);

????//?測試前序遍歷
????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);
????
????//?測試中序遍歷
????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);
????//?測試后序遍歷
????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);
????//?測試層序遍歷
????pTree->Traverse(BinaryTree::LEVELORDER);

????system("pause");
????
????delete?pTree;

????return?0;
}

posted on 2006-07-08 15:21 那誰 閱讀(20260) 評論(9)  編輯 收藏 引用 所屬分類: 算法與數據結構

評論

# re: 二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)  回復  更多評論   

good
2007-06-16 18:04 | superdaxia

# re: 二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)  回復  更多評論   

你好,我是新手,在用VC調試時發現錯誤
f:\hwh\二叉樹\binarytree.h(64) : error C2027: use of undefined type 'BinaryTree'
f:\hwh\二叉樹\binarytree.h(8) : see declaration of 'BinaryTree'
main.cpp
f:\hwh\二叉樹\binarytree.h(64) : error C2027: use of undefined type 'BinaryTree'
f:\hwh\二叉樹\binarytree.h(8) : see declaration of 'BinaryTree'
執行 cl.exe 時出錯.

二叉樹.exe - 1 error(s), 0 warning(s)
為什么呢?
2007-12-25 11:37 | tomy

# re: 二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)  回復  更多評論   

@tomy
你用的什么編譯器?我用的VS2003,其次,你的工程里面有幾個文件?這里一共有三個文件:binarytree.h,binarytree.cpp,main.cpp
2007-12-26 11:18 | 創系

# re: 二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)[未登錄]  回復  更多評論   

我用DEV C++編譯后報以下信息,請指教:

C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp/cceIaaaa.o(.text+0x52d):main.cpp: undefined reference to `BinaryTree::Traverse(BinaryTree::TraverseType, bool)'
C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp/cceIaaaa.o(.text+0x62f):main.cpp: more undefined references to `BinaryTree::Traverse(BinaryTree::TraverseType, bool)' follow
C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp/cceIaaaa.o(.text+0x676):main.cpp: undefined reference to `BinaryTree::~BinaryTree()'
collect2: ld returned 1 exit status
2008-01-06 01:10 | ben

# re: 二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)  回復  更多評論   

樓上的錯誤是DEV C++的工程文件/配置文件的問題吧?

# re: 二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)[未登錄]  回復  更多評論   

已經解決了,謝謝指點!
2008-01-06 15:19 | ben

# re: 二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)  回復  更多評論   

請問，為什么我的窗口上什么都米有？只有一個“請按任意鍵繼續”，用的是VC++ 2008
2008-07-09 07:03 | liuyu

# re: 二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)  回復  更多評論   

其實如果不用 Stack 而改用 List 的話，三種非遞歸遍歷將變得更加簡單一致，一個 While 就夠了

typedef std::list<BinaryTree::PTreeNode> TreeNodeList;

typedef struct TreeNode
{
Item Node;
TreeNode* pRight;
TreeNode* pLeft;
bool bVisited; // 關鍵

TreeNode(Item node = 0, TreeNode* pright = NULL, TreeNode* pleft = NULL)
: Node(node)
, pRight(pright)
, pLeft(pleft)
, bVisited(false)
{
}

}TreeNode, *PTreeNode;




// 非遞歸前序遍歷樹
void BinaryTree::NoRecPreTraverseImpl(PTreeNode pTreenode)
{
if (NULL == pTreenode)
return;

TreeNodeList NodeList;
PTreeNode pNode;
NodeList.push_front(pTreenode);

while (!NodeList.empty())
{
pNode = NodeList.front();
NodeList.pop_front();

std::cout << "Item = " << pNode->Node << std::endl;

if(pNode->pRight != NULL) NodeList.push_front(pNode->pRight);
if(pNode->pLeft != NULL) NodeList.push_front(pNode->pLeft);
}
}


// 非遞歸中序遍歷樹
void BinaryTree::NoRecInTraverseImpl(PTreeNode pTreenode)
{
if (NULL == pTreenode)
return;

TreeNodeList NodeList;
PTreeNode pNode;
NodeList.push_front(pTreenode);

while (!NodeList.empty())
{
pNode = NodeList.front();

if(pNode->bVisited)
{
NodeList.pop_front();
pNode->bVisited = false; // 為下一次遍歷做準備

std::cout << "Item = " << pNode->Node << std::endl;

if(pNode->pRight != NULL) NodeList.push_front(pNode->pRight);
}
else
{
if(pNode->pLeft != NULL) NodeList.push_front(pNode->pLeft);
pNode->bVisited = true;
}

}
}

// 非遞歸后序遍歷樹
void BinaryTree::NoRecPostTraverseImpl(PTreeNode pTreenode)
{
if (NULL == pTreenode)
return;

TreeNodeList NodeList;
PTreeNode pNode;
NodeList.push_front(pTreenode);

while (!NodeList.empty())
{
pNode = NodeList.front();

if(pNode->bVisited)
{
NodeList.pop_front();
pNode->bVisited = false; // 為下一次遍歷做準備

std::cout << "Item = " << pNode->Node << std::endl;
}
else
{
if(pNode->pRight != NULL) NodeList.push_front(pNode->pRight);
if(pNode->pLeft != NULL) NodeList.push_front(pNode->pLeft);
pNode->bVisited = true;
}

}
}


2008-09-08 22:58 | Godspeed

# re: 二叉樹遍歷算法集合(前中后序遍歷的遞歸和非遞歸算法,層序遍歷算法)[未登錄]  回復  更多評論   

非遞歸后續遍歷修改為：
public static void iterativePostorder(BinaryTree boot) {
Stack<BinaryTree> stack = new Stack<BinaryTree>();
BinaryTree current, pointer=boot;
boolean bVisitRoot = false;//標志是否訪問過根節點
if (boot == null) {
return;
}
stack.push(boot);
current = boot.leftpoiter;
while (!stack.empty()) {
while (current != null) {//向左走到盡頭
stack.push(current);
current = current.leftpoiter;
}
current = stack.peek();
stack.pop();
if ((current.rightpoiter == null)||(pointer == current.rightpoiter)) {
visit(current);
pointer = current;
current = stack.peek();
if (pointer == current.rightpoiter) {
visit(current);
stack.pop();
pointer=current;
current = null;
} else {
current = current.rightpoiter;
}
} else {
if (current == boot && (bVisitRoot == true)) {
visit(current);
return;
} else {
if (current == boot) {
bVisitRoot = true;
}
stack.push(current);
current = current.rightpoiter;
}
}

}

}
2011-07-07 11:12 | hepeng
青青草原综合久久大伊人导航_色综合久久天天综合_日日噜噜夜夜狠狠久久丁香五月_热久久这里只有精品

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