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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;
}
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