第十一周项目1—二叉树算法验证

（1）层次遍历算法的验证

#include <stdio.h>#include "btree.h"void LevelOrder(BTNode *b){    BTNode *p;    BTNode *qu[MaxSize];    //定义环形队列,存放节点指针    int front,rear; //定义队头和队尾指针    front=rear=-1;      //置队列为空队列    rear++;    qu[rear]=b;     //根节点指针进入队列    while (front!=rear) //队列不为空    {        front=(front+1)%MaxSize;        p=qu[front];        //队头出队列        printf("%c ",p->data);  //访问节点        if (p->lchild!=NULL)    //有左孩子时将其进队        {            rear=(rear+1)%MaxSize;            qu[rear]=p->lchild;        }        if (p->rchild!=NULL)    //有右孩子时将其进队        {            rear=(rear+1)%MaxSize;            qu[rear]=p->rchild;        }    }}int main(){    BTNode *b;    CreateBTNode(b,"A(B(D,E(H(J,K(L,M(,N))))),C(F,G(,I)))");    printf("二叉树b: ");    DispBTNode(b);    printf("\n");    printf("层次遍历序列:\n");    LevelOrder(b);    DestroyBTNode(b);    return 0;}

 

 

 

（2）二叉树构造算法的验证

一：由先序序列和中序序列遍历二叉树

#include <stdio.h>#include <malloc.h>#include "btree.h"BTNode *CreateBT1(char *pre,char *in,int n)/*pre存放先序序列,in存放中序序列,n为二叉树结点个数,本算法执行后返回构造的二叉链的根结点指针*/{    BTNode *s;    char *p;    int k;    if (n<=0) return NULL;    s=(BTNode *)malloc(sizeof(BTNode));     //创建二叉树结点*s    s->data=*pre;    for (p=in; p<in+n; p++)                 //在中序序列中找等于*ppos的位置k        if (*p==*pre)                       //pre指向根结点            break;                          //在in中找到后退出循环    k=p-in;                                 //确定根结点在in中的位置    s->lchild=CreateBT1(pre+1,in,k);        //递归构造左子树    s->rchild=CreateBT1(pre+k+1,p+1,n-k-1); //递归构造右子树    return s;}int main(){    ElemType pre[]="ABDGCEF",in[]="DGBAECF";    BTNode *b1;    b1=CreateBT1(pre,in,7);    printf("b1:");    DispBTNode(b1);    printf("\n");    return 0;}

二：由中序序列和后序序列遍历二叉树

#include <stdio.h>#include <malloc.h>#include "btree.h"BTNode *CreateBT2(char *post,char *in,int n)/*post存放后序序列,in存放中序序列,n为二叉树结点个数,本算法执行后返回构造的二叉链的根结点指针*/{    BTNode *s;    char r,*p;    int k;    if (n<=0) return NULL;    r=*(post+n-1);                          //根结点值    s=(BTNode *)malloc(sizeof(BTNode));     //创建二叉树结点*s    s->data=r;    for (p=in; p<in+n; p++)                 //在in中查找根结点        if (*p==r)            break;    k=p-in;                                 //k为根结点在in中的下标    s->lchild=CreateBT2(post,in,k);         //递归构造左子树    s->rchild=CreateBT2(post+k,p+1,n-k-1);  //递归构造右子树    return s;}int main(){    ElemType in[]="DGBAECF",post[]="GDBEFCA";    BTNode *b2;    b2=CreateBT2(post,in,7);    printf("b2:");    DispBTNode(b2);    printf("\n");    return 0;}

三：由顺序存储结构转化为二叉链存储结构

#include <stdio.h>#include <malloc.h>#include "btree.h"#define N 30typedef ElemType SqBTree[N];BTNode *trans(SqBTree a,int i){    BTNode *b;    if (i>N)        return(NULL);    if (a[i]=='#')        return(NULL);           //当节点不存在时返回NULL    b=(BTNode *)malloc(sizeof(BTNode)); //创建根节点    b->data=a[i];    b->lchild=trans(a,2*i);                 //递归创建左子树    b->rchild=trans(a,2*i+1);               //递归创建右子树    return(b);                              //返回根节点}int main(){    BTNode *b;    ElemType s[]="0ABCD#EF#G####################";    b=trans(s,1);    printf("b:");    DispBTNode(b);    printf("\n");    return 0;}

 

（3）中序线索化二叉树的算法验证

#include <stdio.h>#include <malloc.h>#define MaxSize 100typedef char ElemType;typedef struct node{    ElemType data;    int ltag,rtag;      //增加的线索标记    struct node *lchild;    struct node *rchild;} TBTNode;void CreateTBTNode(TBTNode * &b,char *str){    TBTNode *St[MaxSize],*p=NULL;    int top=-1,k,j=0;    char ch;    b=NULL;             //建立的二叉树初始时为空    ch=str[j];    while (ch!='\0')    //str未扫描完时循环    {        switch(ch)        {        case '(':            top++;            St[top]=p;            k=1;            break;      //为左结点        case ')':            top--;            break;        case ',':            k=2;            break;                          //为右结点        default:            p=(TBTNode *)malloc(sizeof(TBTNode));            p->data=ch;            p->lchild=p->rchild=NULL;            if (b==NULL)                    //*p为二叉树的根结点                b=p;            else                            //已建立二叉树根结点            {                switch(k)                {                case 1:                    St[top]->lchild=p;                    break;                case 2:                    St[top]->rchild=p;                    break;                }            }        }        j++;        ch=str[j];    }}void DispTBTNode(TBTNode *b){    if (b!=NULL)    {        printf("%c",b->data);        if (b->lchild!=NULL || b->rchild!=NULL)        {            printf("(");            DispTBTNode(b->lchild);            if (b->rchild!=NULL) printf(",");            DispTBTNode(b->rchild);            printf(")");        }    }}TBTNode *pre;                       //全局变量void Thread(TBTNode *&p){    if (p!=NULL)    {        Thread(p->lchild);          //左子树线索化        if (p->lchild==NULL)        //前驱线索        {            p->lchild=pre;          //建立当前结点的前驱线索            p->ltag=1;        }        else p->ltag=0;        if (pre->rchild==NULL)      //后继线索        {            pre->rchild=p;          //建立前驱结点的后继线索            pre->rtag=1;        }        else pre->rtag=0;        pre=p;        Thread(p->rchild);          //右子树线索化    }}TBTNode *CreaThread(TBTNode *b)     //中序线索化二叉树{    TBTNode *root;    root=(TBTNode *)malloc(sizeof(TBTNode));  //创建根结点    root->ltag=0;    root->rtag=1;    root->rchild=b;    if (b==NULL)                //空二叉树        root->lchild=root;    else    {        root->lchild=b;        pre=root;               //pre是*p的前驱结点,供加线索用        Thread(b);              //中序遍历线索化二叉树        pre->rchild=root;       //最后处理,加入指向根结点的线索        pre->rtag=1;        root->rchild=pre;       //根结点右线索化    }    return root;}void ThInOrder(TBTNode *tb){    TBTNode *p=tb->lchild;      //指向根结点    while (p!=tb)    {        while (p->ltag==0) p=p->lchild;        printf("%c ",p->data);        while (p->rtag==1 && p->rchild!=tb)        {            p=p->rchild;            printf("%c ",p->data);        }        p=p->rchild;    }}int main(){    TBTNode *b,*tb;    CreateTBTNode(b,"A(B(D(,G)),C(E,F))");    printf(" 二叉树:");    DispTBTNode(b);    printf("\n");    tb=CreaThread(b);    printf(" 线索中序序列:");    ThInOrder(tb);    printf("\n");    return 0;}

（4）哈弗曼编码的算法验证

#include <stdio.h>#include <string.h>#define N 50        //叶子结点数#define M 2*N-1     //树中结点总数//哈夫曼树的节点结构类型typedef struct{    char data;  //结点值    double weight;  //权重    int parent;     //双亲结点    int lchild;     //左孩子结点    int rchild;     //右孩子结点} HTNode;//每个节点哈夫曼编码的结构类型typedef struct{    char cd[N]; //存放哈夫曼码    int start;} HCode;//构造哈夫曼树void CreateHT(HTNode ht[],int n){    int i,k,lnode,rnode;    double min1,min2;    for (i=0; i<2*n-1; i++)         //所有结点的相关域置初值-1        ht[i].parent=ht[i].lchild=ht[i].rchild=-1;    for (i=n; i<2*n-1; i++)         //构造哈夫曼树    {        min1=min2=32767;            //lnode和rnode为最小权重的两个结点位置        lnode=rnode=-1;        for (k=0; k<=i-1; k++)            if (ht[k].parent==-1)   //只在尚未构造二叉树的结点中查找            {                if (ht[k].weight<min1)                {                    min2=min1;                    rnode=lnode;                    min1=ht[k].weight;                    lnode=k;                }                else if (ht[k].weight<min2)                {                    min2=ht[k].weight;                    rnode=k;                }            }        ht[i].weight=ht[lnode].weight+ht[rnode].weight;        ht[i].lchild=lnode;        ht[i].rchild=rnode;        ht[lnode].parent=i;        ht[rnode].parent=i;    }}//实现哈夫曼编码void CreateHCode(HTNode ht[],HCode hcd[],int n){    int i,f,c;    HCode hc;    for (i=0; i<n; i++) //根据哈夫曼树求哈夫曼编码    {        hc.start=n;        c=i;        f=ht[i].parent;        while (f!=-1)   //循序直到树根结点        {            if (ht[f].lchild==c)    //处理左孩子结点                hc.cd[hc.start--]='0';            else                    //处理右孩子结点                hc.cd[hc.start--]='1';            c=f;            f=ht[f].parent;        }        hc.start++;     //start指向哈夫曼编码最开始字符        hcd[i]=hc;    }}//输出哈夫曼编码void DispHCode(HTNode ht[],HCode hcd[],int n){    int i,k;    double sum=0,m=0;    int j;    printf("  输出哈夫曼编码:\n"); //输出哈夫曼编码    for (i=0; i<n; i++)    {        j=0;        printf("      %c:\t",ht[i].data);        for (k=hcd[i].start; k<=n; k++)        {            printf("%c",hcd[i].cd[k]);            j++;        }        m+=ht[i].weight;        sum+=ht[i].weight*j;        printf("\n");    }    printf("\n  平均长度=%g\n",1.0*sum/m);}int main(){    int n=8,i;      //n表示初始字符串的个数    char str[]= {'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h'};    double fnum[]= {0.07,0.19,0.02,0.06,0.32,0.03,0.21,0.1};    HTNode ht[M];    HCode hcd[N];    for (i=0; i<n; i++)    {        ht[i].data=str[i];        ht[i].weight=fnum[i];    }    printf("\n");    CreateHT(ht,n);    CreateHCode(ht,hcd,n);    DispHCode(ht,hcd,n);    printf("\n");    return 0;}