二叉树的深度优先和广度优先遍历

http://steven-hong.javaeye.com/blog/493665

图的深度优先搜索法是树的先根遍历的推广，它的基本思想是：从图G的某个顶点v0出发，访问v0，然后选择一个与v0相邻且没被访问过的顶点vi访问，再 从vi出发选择一个与vi相邻且未被访问的顶点vj进行访问，依次继续。如果当前被访问过的顶点的所有邻接顶点都已被访问，则退回到已被访问的顶点序列中 最后一个拥有未被访问的相邻顶点的顶点w，从w出发按同样的方法向前遍历，直到图中所有顶点都被访问。

图的广度优先搜索是树的按层次遍历的推广，它的基本思想是：首先访问初始点vi，并将其标记为已访问过，接着访问vi的所有未被访问过的邻接点 vi1,vi2, …, vi t，并均标记已访问过，然后再按照vi1,vi2, …, vi t的次序，访问每一个顶点的所有未被访问过的邻接点，并均标记为已访问过，依次类推，直到图中所有和初始点vi有路径相通的顶点都被访问过为止。

二叉树的深度优先遍历的非递归的通用做法是采用栈，广度优先遍历的非递归的通用做法是采用队列。

为了方便程序验证，首先构造一个如图所示的二叉树。

 

源码：

/*************************** bintree.h文件 *****************************/

#ifndef _BINTREE_H

#define _BINTREE_H

 

template <class T>

class CBintree

{

public:

       CBintree();

       bool Depth_RF();//先根深度遍历

       bool Depth_RM();//中根深度遍历

       bool WidthFS(); //层次遍历

protected:

private:  

       struct TreeNode

       {

              T va;

              TreeNode *plchild;

              TreeNode *prchild;

       };

       TreeNode *m_pBintree;

};

#endif

 

template <class T>

CBintree<T>::CBintree()

{

       m_pBintree = new TreeNode;     

       TreeNode *pNode2 = new TreeNode;

       TreeNode *pNode3 = new TreeNode;

    TreeNode *pNode4 = new TreeNode;

       TreeNode *pNode5 = new TreeNode;

       TreeNode *pNode6 = new TreeNode;

       TreeNode *pNode7 = new TreeNode;

     

       m_pBintree->va = (T)1;

       m_pBintree->plchild = pNode2;

       m_pBintree->prchild = pNode3;

     

    pNode2->va = (T)2;

       pNode2->plchild = pNode4;

    pNode2->prchild = pNode5;

     

       pNode3->va = (T)3;

       pNode3->plchild = NULL;

       pNode3->prchild = pNode6;

     

       pNode4->va = (T)4;

       pNode4->plchild = NULL;

       pNode4->prchild = NULL;

     

       pNode5->va = (T)5;

       pNode5->plchild = pNode7;

       pNode5->prchild = NULL;

     

       pNode6->va = (T)6;

       pNode6->plchild = NULL;

       pNode6->prchild = NULL;

     

       pNode7->va = (T)7;

       pNode7->plchild = NULL;

       pNode7->prchild = NULL;

}

 

template <class T>

bool CBintree<T>::Depth_RF() //先根深度遍历

{

       cout << "先根遍历序列:\n";

       stack <TreeNode> s;   

       s.push(*m_pBintree);

       while (!s.empty())

       {

              TreeNode node_s = s.top();

              cout << node_s.va << "\n";

              s.pop();

              if (node_s.prchild != NULL)

              {

                     s.push(*node_s.prchild);

              }

              if (node_s.plchild != NULL)

              {

                     s.push(*node_s.plchild);

              }

            

       }

 

       return true;

}

 

template <class T>

bool CBintree<T>::Depth_RM() //中根深度遍历

{

       cout << "中根遍历序列:\n";

       stack <TreeNode> s;   

    TreeNode *pNode = m_pBintree;

       while (pNode != NULL || !s.empty())

       {

              while (pNode != NULL)

              {

                     s.push(*pNode);

                     pNode = pNode->plchild;

              }

            

              if (!s.empty())

              {

                     TreeNode node_s = s.top();

                     cout << node_s.va << "\n";

                     s.pop();

                     pNode = node_s.prchild;

              }

       }   

       return true;

}

 

template <class T>

bool CBintree<T>::WidthFS() //层次遍历

{

       cout << "层次遍历序列:\n";

       queue <TreeNode> q;

       q.push(*m_pBintree);

       while (!q.empty())

       {

              TreeNode *pNode = &q.front();

              cout << pNode->va << "\n";

              if (pNode->plchild != NULL)

              {

                     q.push(*pNode->plchild);

              }

              if (pNode->prchild != NULL)

              {

                     q.push(*pNode->prchild);

              }

              q.pop(); 

       }

 

       return true;

}

 

/************************ main.cpp 文件 ****************************/

#include <iostream>

#include <stack>

#include <queue>

using namespace std;

 

#include "bintree.h"

 

int main()

{

       CBintree <int> bt;

       bt.Depth_RF();

       bt.Depth_RM();

       bt.WidthFS();

       return 0;

}

/***************** 教科书标准算法及优化算法（转）*******************/
1.先序遍历非递归算法
void PreOrderUnrec(Bitree *t)
{
    Stack s;
    StackInit(s);
    Bitree *p=t;
  
    while (p!=NULL || !StackEmpty(s))
    {
        while (p!=NULL)             //遍历左子树
        {
            visite(p->data);
            push(s,p);
            p=p->lchild; 
        }
       
        if (!StackEmpty(s))         //通过下一次循环中的内嵌while实现右子树遍历
        {
            p=pop(s);
            p=p->rchild;       
        }//endif
              
    }//endwhile
}


2.中序遍历非递归算法
void InOrderUnrec(Bitree *t)
{
    Stack s;
    StackInit(s);
    Bitree *p=t;

    while (p!=NULL || !StackEmpty(s))
    {
        while (p!=NULL)             //遍历左子树
        {
            push(s,p);
            p=p->lchild;
        }
       
        if (!StackEmpty(s))
        {
            p=pop(s);
            visite(p->data);        //访问根结点
            p=p->rchild;            //通过下一次循环实现右子树遍历
        }//endif  
  
    }//endwhile
}

3.后序遍历非递归算法
typedef enum{L,R} tagtype;
typedef struct
{
    Bitree ptr;
    tagtype tag;
}stacknode;

typedef struct
{
    stacknode Elem[maxsize];
    int top;
}SqStack;

void PostOrderUnrec(Bitree t)
{
    SqStack s;
    stacknode x;
    StackInit(s);
    p=t;
  
    do
    {
        while (p!=null)        //遍历左子树
        {
            x.ptr = p;
            x.tag = L;         //标记为左子树
            push(s,x);
            p=p->lchild;
        }
  
        while (!StackEmpty(s) && s.Elem[s.top].tag==R) 
        {
            x = pop(s);
            p = x.ptr;
            visite(p->data);   //tag为R，表示右子树访问完毕，故访问根结点     
        }
       
        if (!StackEmpty(s))
        {
            s.Elem[s.top].tag =R;     //遍历右子树
            p=s.Elem[s.top].ptr->rchild;       
        }  
    }while (!StackEmpty(s));
}//PostOrderUnrec

 

4.前序最简洁非递归算法

void PreOrderUnrec(Bitree *t)

{

       Bitree *p;

       Stack s;

       s.push(t);

     

       while (!s.IsEmpty())

       {

              s.pop(p);

              visit(p->data);

              if (p->rchild != NULL) s.push(p->rchild);

              if (p->lchild != NULL) s.push(p->lchild);

       }

}

 

5.后序算法之二

void BT_PostOrderNoRec(pTreeT root)

{

       stack<treeT *> s;

       pTreeT pre=NULL;

     

       while ((NULL != root) || !s.empty())

       {

              if (NULL != root)

              {

                     s.push(root);

                     root = root->left;

              }

              else

              {

                     root = s.top();

                     if (root->right!=NULL && pre!=root->right){

                            root=root->right;

                     }

                     else{

                            root=pre=s.top();

                            visit(root);

                            s.pop();

                            root=NULL;

                     }

              }

       }

}