(2011.08.13)二叉树实例

　　始终对二叉树的应用有点模糊，从网上找了一个实例，在这里保存一下。

#include <iostream>#include <vector>#include <string>#include <math.h>#include <iomanip>#include <stdlib.h>#include <algorithm>using namespace std;#define HeadSTUDENT int//以下是数据类型的定义enum  Status{OK, ERROR};typedef struct{    char            number[10];    char            name[8];    char            sex[3];    int                age;    char            place[20];}STUDENT;typedef struct BinaryTreeNode{        STUDENT         data;    BinaryTreeNode    *LChild;    BinaryTreeNode    *RChild;} BinaryTree;typedef struct {    BinaryTreeNode    *ptr;    bool        B; //true代表左子树，false代表右子树} SType;typedef struct //StackElement{        SType            *element;    int            top;    int            MaxSize;} Stack;void DigitalToString(char str[],int n){    char    temp;    char    k=1;    int    i=0;    while (n && i<80)    {        k=n%10+48;        n=n/10;        str[i]=k;        i++;    }    str[i]='\0';    int len=strlen(str);    for (i=0;i<len/2;i++)    {        temp=str[i];        str[i]=str[len-i-1];        str[len-i-1]=temp;    }}void OutputLevelOrderTL(BinaryTreeNode *BT){// 从左至右，从上至下按层次输出一棵二叉树    typedef struct     {        BinaryTreeNode    *ptr;    } Node_Ptr;    Node_Ptr        temp,*element;    BinaryTreeNode     *p;    int        MaxSize=50;     int        pagewidth=80;    int        node_last_position;    int        High;    element = new Node_Ptr [MaxSize+1];        //定义一个用于存放二叉树结点指针的数组    for (int i=1;i<MaxSize;i++)                //对指针数组初始化，初值设为NULL        element[i].ptr=NULL;    p = BT;    temp.ptr = p;    if (p) element[1]=temp;            for (int i=1;i<MaxSize/2;i++)    //将二叉树中的每个结点指针以顺序存储结构存放到数组中，并同时求取最大结点的编号    {        p=element[i].ptr;        if (p)        {            if (p->LChild)                 {                temp.ptr = p->LChild;                element[2*i]=temp;                node_last_position=2*i;            }            if (p->RChild)                 {                temp.ptr = p->RChild;                element[2*i+1]=temp;                node_last_position=2*i+1;            }        }    }    cout<<endl;    int position_data[32]={0,        40,          20,                40,          10,        20,        20,        20,          6,  10,  10, 10,  10,  10, 10,  10,          3,5,5,5, 5,5,5,5, 5,5, 5,5, 5,5, 5,5};    int        kk,k;    int        startnum,endnum;    int        startnum1,endnum1;    int        len, curlenharf,prelenharf,templen,lenharf;    int        num_space;    char    str[80];    char    emptystr[42]={""};    char    space[2]=" ";    char    line[3]="─";    char    prechar[42];                    //prechar中记载当前输入出项的字符串    char    prespace[42];                    //prespace中记载当前输入出项前面的空格串    char    postspace[42];                    //postspace中记载当前输入出项后面的空格串    cout<<"                                 "<<"根结点BT"<<endl;    cout<<"                                   "<<"  ↘"<<endl;    High=log((double)node_last_position)/log(2.0)+1;    startnum=1;                                //startnum中记载当前层中起始结点编号    startnum1=2;                            //startnum中记载当前层中起始结点编号    for (int i=1;i<=High;i++)    {        endnum=pow(2.0,i)-1;                    //endnum中记载当前层中最大结点编号        if (endnum>node_last_position)            endnum=node_last_position;        prelenharf=0;        //输出第一个数据项        for(k=startnum;k<=endnum;k++)        {            templen=1;                p=element[k].ptr;            if (p)            {                DigitalToString(str, p->data.age);                len=strlen(str);                curlenharf=len/2;                if (!(len%2) && (prelenharf%2)==(curlenharf%2)&&(k%2))                    templen-=2;                if ((prelenharf%2)!=(curlenharf%2)&&(k%2))                    templen--;                num_space=position_data[k]-curlenharf-prelenharf-templen;            }            else                num_space=position_data[k]-templen-2;            strcpy(prechar,emptystr);                        //前导空格串的初值为空串                        for (kk=1;kk<=num_space;kk++)                    //用字符串联接方式生成前导空格串prechar                strcat(prechar,space);            prelenharf=curlenharf;            if (p)                 cout<<prechar<<p->data.age;            else                cout<<prechar<<"   ";                        //" 0 "        }        cout<<endl;        //输出第二个数据项        prelenharf=0;        for(k=startnum;k<=endnum;k++)        {            templen=1;                p=element[k].ptr;            if (p)            {                len=strlen(p->data.name);                curlenharf=len/2;                if (!(len%2) && (prelenharf%2)==(curlenharf%2)&&(k%2))                    templen-=2;                if ((prelenharf%2)!=(curlenharf%2)&&(k%2))                    templen--;                num_space=position_data[k]-curlenharf-prelenharf-templen;            }            else                num_space=position_data[k]-templen-2;            strcpy(prechar,emptystr);                        //前导空格串的初值为空串            for (kk=1;kk<=num_space;kk++)                    //用字符串联接方式生成前导空格串prechar                strcat(prechar,space);            prelenharf=curlenharf;            if (p)                 cout<<prechar<<p->data.name ;            else                cout<<prechar<<"   ";                        //" ^ "        }        startnum=endnum+1;        cout<<endl;        //以下程序是完成分支结的输出        int position_line[32]={0,            20,              19,                     19,              9,        9,            18,          9,              5,    3,    10,      3,  10,  3,  10,  3,              2,1,  4,1,4,1,  4,1,    4, 1,4,1, 4,1,4,1};        if (i<High)        {            endnum1=pow(2.0,i+1)-1;                        //endnum中记载第i层下面的分枝线层中最大结点编号            for(k=startnum1;k<=endnum1;k++)            {                strcpy(prechar,emptystr);                //前导空格串的初值为空串                            for (kk=1;kk<=position_line[k];kk++)    //用字符串联接方式生成前导空格串prechar==startnum1                    if (!(k%2))                        strcat(prechar,space);            //形成当前中第偶数个结点前的空格串                    else                        strcat(prechar,line);            //形成当前中第奇数个结点前的"─"串                if (!(k%2))                     cout<<prechar;                        //当前中第偶数个结点前输出空格串                else                 {                    len=strlen(prechar);                    lenharf=len/2;                    if ((element[k-1].ptr && element[k].ptr))        //当前分支左右均有结点                    {                        prechar[lenharf]='┴';                        cout<<"┌"<<prechar<<"┐";                    }                    if ((element[k-1].ptr && !element[k].ptr))        //当前分支左边有结点，右边无结点                    {                        prechar[lenharf-1]='\0';                        cout<<"┌"<<prechar<<"┘";                        strcpy(postspace,emptystr);                        for (kk=1;kk<=lenharf+1;kk++)                            strcat(postspace,space);                        cout<<postspace;                    }                    if ((!element[k-1].ptr && element[k].ptr))        //当前分支右边有结点，左边无结点                    {                        strcpy(prespace,emptystr);                        for (kk=1;kk<=lenharf+1;kk++)                            strcat(prespace,space);                        prechar[lenharf-1]='\0';                        cout<<prespace<<"└"<<prechar<<"┐";                    }                    if ((!element[k-1].ptr && !element[k].ptr))        //当前分支左右均无结点                    {                        strcpy(prespace,emptystr);                        for (kk=1;kk<=len;kk++)                            strcat(prespace,space);                        cout<<prespace<<"    ";                    }                }            }            cout<<endl;            startnum1=endnum1+1;        }    }    cout<<endl<<endl<<endl;}void CreatStack(Stack &S, int MaxStackSize){// 构造一个最大容量为MaxStackSize 的堆栈    S.MaxSize = MaxStackSize;    S.element = new SType[S.MaxSize];    S.top =-1;}bool IsEmpty(Stack &S){// 判断堆栈S是否为空    if (S.top == -1)   return true;    return  false;}bool IsFull(Stack &S){// 判断堆栈S是否为满    if (S.top >= S.MaxSize-1)   return true;    return  false;}Status Push(Stack &S , SType &x){// x进s栈，返回进栈后的状态值    if (IsFull(S))   return ERROR;    S.top++;    S.element[S.top] = x;    return OK;}Status Pop(Stack &S , SType &x){// 将s栈顶的值取至x中，返回出栈后的状态值    if (IsEmpty(S))   return ERROR;    x = S.element[S.top];    S.top--;    return OK;}BinaryTreeNode   *MakeNode(STUDENT &x)    {//构造结点      BinaryTreeNode* newtree=new BinaryTreeNode;      newtree->data=x;      return newtree;}void MakeBinaryTree(BinaryTreeNode *root, BinaryTreeNode *left, BinaryTreeNode *right){// 联接root，left, right所指的结点指针为二叉树    root->LChild=left;     root->RChild=right;     }int  BinaryHeight(BinaryTreeNode  *BT) {// 返回二叉树的高度    if (BT==NULL) return 0;    int HighL = BinaryHeight(BT ->LChild);    int HighR = BinaryHeight(BT ->RChild);     if (HighL > HighR)          return ++HighL;    else         return ++HighR;}void PreOrderN(BinaryTreeNode *BT){//二叉树的前序遍历非递归算法    Stack            S;    SType            temp;    BinaryTreeNode    *p = BT;    int MaxStackSize=50;    CreatStack(S ,MaxStackSize);            //产生一个空栈，这一过程函数可以不在这里进行    while (p!=NULL || !IsEmpty(S))    {        while (p!=NULL)             //遍历左子树        {            temp.ptr=p;            Push(S,temp);            cout<<p->data.name<<" ";            p=p->LChild;          }        if (!IsEmpty(S))         //通过下一次循环中的内嵌while实现右子树遍历        {            Pop(S,temp);            p=temp.ptr->RChild;                }    }     cout<<endl;}void InOrderN(BinaryTreeNode *BT) {//二叉树的中序遍历非递归算法    Stack            S;    SType            temp;    BinaryTreeNode    *p = BT;    int MaxStackSize=50;    CreatStack (S , MaxStackSize);                //产生一个空栈，这一过程函数可以不在这里进行    while (p!=NULL || !IsEmpty(S))    {        while (p!=NULL)             //遍历左子树        {            temp.ptr=p;            Push(S,temp);            p=p->LChild;        }        if (!IsEmpty(S))        {            Pop(S,temp);            cout<<temp.ptr->data.name<<" ";            p=temp.ptr->RChild;;            //通过下一次循环实现右子树遍历        }      }   cout<<endl;}void PostOrderN(BinaryTreeNode *BT) {//二叉树的后序遍历非递归算法    SType            temp;    Stack            S;    BinaryTreeNode    *p = BT;    int MaxStackSize=50;    CreatStack (S , MaxStackSize);    //产生一个空栈，这一过程函数可以不在这里进行    do     {        while (p!=NULL)        //遍历左子树        {            temp.ptr = p;             temp.B = false;         //标记为左子树            Push(S,temp);            p=p->LChild;        }        while (!IsEmpty(S) && S.element[S.top].B==true)          {            Pop(S,temp);            p = temp.ptr;            cout<<temp.ptr->data.name<<" ";   //tag为R，表示右子树访问完毕，故访问根结点               }        if (!IsEmpty(S))        {            S.element[S.top].B =true;     //遍历右子树            p=S.element[S.top].ptr->RChild;                }        }while (!IsEmpty(S));cout<<endl;} //下面是主程序int main(){    BinaryTreeNode  *BT,*p=NULL,*pp[10];    STUDENT        x;    int        High;    char    n[][8]={"    ","AAA","BBB","CCC","DDD","EEE","FFF","GGG","HHH"};    for(int i=1;i<9;i++)    {        strcpy(x.number,"7777777");        strcpy(x.name,n[i]);        if (i>4)            strcpy(x.sex,"男");        else             strcpy(x.sex,"女");        x.age=500+i;        strcpy(x.place,"WWWWW");        pp[i]=MakeNode(x);        p=pp[i];    }    MakeBinaryTree(pp[1], pp[2], pp[3]);    MakeBinaryTree(pp[2], pp[4], NULL);    MakeBinaryTree(pp[3], pp[5], pp[6]);    MakeBinaryTree(pp[4], NULL, pp[7]);    MakeBinaryTree(pp[5], pp[8], NULL);     BT=pp[1];    pp[7]->LChild=NULL;    pp[7]->RChild=NULL;    pp[8]->LChild=NULL;    pp[8]->RChild=NULL;    pp[6]->LChild=NULL;    pp[6]->RChild=NULL;    High=BinaryHeight(BT) ;    cout<<"树高="<<High<<endl<<endl;    OutputLevelOrderTL(BT);    cout<<"先序遍历的顺序为："<<endl;    PreOrderN(BT);    cout<<"中序遍历的顺序为："<<endl;    InOrderN(BT);    cout<<"后序遍历的顺序为："<<endl;    PostOrderN(BT);    return 0;}

http://www.cppblog.com/hunter/archive/2008/11/22/67579.html