数据结构 实验三 树与二叉树的常见操作

数据结构 实验三  树与二叉树的常见操作

实验内容：

    1．输入字符序列，建立二叉链表。

    2．中序遍历二叉树:递归算法。

    3．中序遍历二叉树:非递归算法。（最好也能实现先序，后序非递归算法）

    4．求二叉树的高度 。

    5．求二叉树的叶子个数。

   *6．将二叉链表视为森林的孩子兄弟链表，计算森林中叶子个数。

   *7．建立中序线索二叉树，并实现中序遍历。

   8．借助队列实现二叉树的层次遍历。 

   9．在主函数中设计一个简单的菜单，分别调试上述算法。

  *10．综合训练：为N个权值设计哈夫曼编码。

代码实现：

#include <iostream>
#include <stdio.h>
#include <stdlib.h>

#define Size 100

using namespace std;

typedef char ElemType;

typedef struct BiNode
{
    ElemType data;
    struct BiNode*lchild,*rchild;
} BiNode,*BiTree;

void CreateBiTree1(BiTree *t)  ///指针实现创建一棵二叉树
{
    char ch;
    ch=getchar();
    if(ch==' ')
        *t=NULL;
    else
    {
        (*t)=new BiNode;
        (*t)->data = ch;
        CreateBiTree1(&((*t)->lchild));
        CreateBiTree1(&((*t)->rchild));
    }
}

void CreateBiTree2(BiTree &t)  ///引用实现创建一棵二叉树
{
    char ch;
    scanf("%c",&ch);
    if(ch==' ')
        t=NULL;
    else
    {
        t=(BiTree)malloc(sizeof(BiNode));
        t->data=ch;
        CreateBiTree2(t->lchild);
        CreateBiTree2(t->rchild);
    }
}

BiTree CreateBiTree3()  ///返回值为一棵二叉树指针
{
    BiTree t;
    char ch;
    ch=getchar();
    if(ch!=' ')
    {
        t=new BiNode;
        t->data=ch;
        t->lchild=CreateBiTree3();
        t->rchild=CreateBiTree3();
    }
    else t=NULL;
    return t;
}

void PreOrder(BiTree t) ///递归先序遍历一棵二叉树
{
    if(t!=NULL)
    {
        printf("%c ",t->data);
        PreOrder(t->lchild);
        PreOrder(t->rchild);
    }
}

void InOrder(BiTree t) ///递归中序遍历一棵二叉树
{
    if(t!=NULL)
    {
        InOrder(t->lchild);
        printf("%c ",t->data);
        InOrder(t->rchild);
    }
}

void PasOrder(BiTree t) ///递归后序遍历一棵二叉树
{
    if(t!=NULL)
    {
        PasOrder(t->lchild);
        PasOrder(t->rchild);
        printf("%c ",t->data);
    }
}

void PreOrderfi(BiTree t) ///非递归先序遍历一个二叉树
{
    BiTree S[Size];
    int top=-1;
    BiTree p=t;
    while(p!=NULL || top>-1)
    {
        while(p!=NULL)
        {
            cout<<p->data<<" ";
            top++;
            S[top]=p;
            p=p->lchild;
        }
        if(top>-1)
        {
            p=S[top];
            top--;
            p=p->rchild;
        }
    }
}

void InOrderfi(BiTree t) ///非递归中序遍历一棵二叉树
{
    BiTree s[Size];
    int top=-1;
    BiTree current;
    current=t;
    while(current!=NULL || top>-1)
    {
        while(current!=NULL)
        {
            top++;
            s[top]=current;
            current=current->lchild;
        }
        if(top>-1)
        {
            current=s[top];
            cout<<current->data<<" ";
            top--;
            current=current->rchild;
        }
    }
}

void PasOrderfi(BiTree t)  ///非递归后序遍历一棵二叉树
{
    struct
    {
        BiTree pp;///*模拟三次相遇，tag==0，表示第一次相遇，tag==1，表示第二次相遇（即把其置1），第三次即判断tag的值是否为1，若为1，则表示第三次相遇*///
        int tag;
    } SS[Size];
    int top;
    BiTree p;
    top=0;
    p=t;
    while(p || top>0)
    {
        while(p)
        {
            top++;
            SS[top].tag=0;
            SS[top].pp=p;
            p=p->lchild;
        }
        if(top>0)
        {
            if(SS[top].tag==0)
            {
                SS[top].tag=1;
                p=SS[top].pp;
                p=p->rchild;
            }
            else
            {
                p=SS[top].pp;
                cout<<p->data<<" ";
                top--;
                p=NULL;
            }
        }
    }
}

int Depth(BiTree t)///计算树的深度
{
    int l,r;
    if(t==NULL) return 0;
    else
    {
        l=Depth(t->lchild);
        r=Depth(t->rchild);
        if(l>r)
            return l+1;
        else return r+1;
    }
}

void PreOrderYezi(BiTree t,int & yezinum) ///先序实现计算叶子节点数
{
    if(t!=NULL)
    {
        if( t->lchild ==NULL && t->rchild==NULL)
        {
            yezinum++;
        }
        PreOrderYezi(t->lchild,yezinum);
        PreOrderYezi(t->rchild,yezinum);
    }
}

void Menu()
{
    cout<<"WELCOME!"<<endl;
    cout<<"0.Break!"<<endl;
    cout<<"1.Create BiTree by Method1."<<endl;
    cout<<"2.Create BiTree by Method2."<<endl;
    cout<<"3.Create BiTree by Method3."<<endl;
    cout<<"4.Digui PreOrder Travel."<<endl;
    cout<<"5.Digui InOrder Travel."<<endl;
    cout<<"6.Digui PasOrder Travel."<<endl;
    cout<<"7.FiDigui PreOrder Travel."<<endl;
    cout<<"8.FiDigui InOrder Travel."<<endl;
    cout<<"9.FiDigui PasOrder Travel."<<endl;
    cout<<"10.The Depth."<<endl;
    cout<<"11.The leaf number."<<endl;
}

int main()
{
    BiTree T;
    int high,yezinum;
    int casenum;
    Menu();
    cin>>casenum;
    while(casenum!=0)
    {
        switch(casenum)
        {
        case 1:
            getchar();
            cout<<"Create BiTree Method 1:"<<endl;
            CreateBiTree1(&T);
            cout<<"Create Over!"<<endl;
            cin>>casenum;
            break;

        case 2:
            getchar();
            cout<<"Create BiTree Method 2:"<<endl;
            CreateBiTree2(T);
            cout<<"Create Over!"<<endl;
            cin>>casenum;
            break;

        case 3:
            getchar();
            cout<<"Create BiTree Method 3:"<<endl;
            T=CreateBiTree3();
            cout<<"Create Over!"<<endl;
            cin>>casenum;
            break;

        case 4:
            getchar();
            cout<<"DI GUI XIAN XU: "<<endl;
            PreOrder(T);
            cout<<endl;
            cin>>casenum;
            break;

        case 5:
            getchar();
            cout<<"DI GUI ZHONG XU: "<<endl;
            InOrder(T);
            cout<<endl;
            cin>>casenum;
            break;

        case 6:
            getchar();
            cout<<"DI GUI HOU XU: "<<endl;
            PasOrder(T);
            cout<<endl;
            cin>>casenum;
            break;

        case 7:
            getchar();
            cout<<"FEI DI GUI XIAN XU: "<<endl;
            PreOrderfi(T);
            cout<<endl;
            cin>>casenum;
            break;

        case 8:
            getchar();
            cout<<"FEI DI GUI ZHONG XU: "<<endl;
            InOrderfi(T);
            cout<<endl;
            cin>>casenum;
            break;

        case 9:
            getchar();
            cout<<"FEI DI GUI HOU XU: "<<endl;
            PasOrderfi(T);
            cout<<endl;
            cin>>casenum;
            break;

        case 10:
            getchar();
            high=Depth(T);
            cout<<"THE TREE's HIGHTH IS: "<<high<<endl;
            cin>>casenum;
            break;

        case 11:
            getchar();
            yezinum=0;
            PreOrderYezi(T,yezinum);
            cout<<"THE TREE's YEZI IS: "<<yezinum<<endl;
            cin>>casenum;
            break;

        default :cin>>casenum;
            break;
        }
    }
    return 0;
}