数据结构之完全二叉树

完全二叉树性质:如果二叉树结点个数为N对于编号为i左孩子存在的条件: 2 * i <= N右孩子存在的条件: 2 * i + 1 <= N数据类型//让完全二叉树的结点保存其编号typedef int DataType;typedef struct bitree{    DataType data;    struct bitree *lchild;    struct bitree *rchild;}BiTree;create(1)    |    root <1>    if(1 * 2 <= N)        root->lchild = create(2)                            |                            root <2>                            if(2 * 2 <= N)                                root->lchild = create(4)                                                    |                                                    root <4>                                                    if(4 * 2 <= N)                                                        root->lchild = create(8)                                                                            |                                                                            root <8>                                                                            if(8 * 2 <= N)                                                                            if(8 * 2 + 1 <= N)                                                                            return root                                                    if(4 * 2 + 1 <= N)                                                        root->rchild = create(9)                                                                            |                                                                            root <9>                                                                            if(9 * 2 <= N)                                                                            if(9 * 2 + 1 <= N)                                                                            return root                                                    return root                            if(2 * 2 + 1 <= N)                                root->rchild = create(5)                                                    |                                                    root <5>                                                    if(5 * 2 <= N)                                                    if(5 * 2 + 1 <= N)                                                    return root                            return root    if(1 * 2 + 1 <= N)        root->rchild = create(3)                            |                            root <3>                            if(3 * 2 <= N)                                root->lchild = create(6)                                                    |                                                    root <6>                                                    if(6 * 2 <= N)                                                    if(6 * 2 + 1 <= N)                                                    return root                            if(3 * 2 + 1 <= N)                                root->rchild = create(7)                                                    |                                                    root <7>                                                    if(7 * 2 <= N)                                                    if(7 * 2 + 1 <= N)                                                    return root                            return root    return root

#ifndef __BTREE__H#define __BTREE__H#include <stdio.h>#include <stdlib.h> #include <string.h>#define N 9//新定义一个数据类型typedef struct {    char c;    int num;}BType;//定义一个结构体typedef struct bitree{    BType data;    struct bitree *lchild;    struct bitree *rchild;}Btree;extern Btree *alloc_node(int i);extern Btree *create_binary_tree(int i);extern int pre_order(Btree *root);extern int in_order(Btree *root);extern int post_order(Btree *root);extern void level_order(Btree *root);#endif

#ifndef __LINKQUEUE__H#define __LINKQUEUE__H#include <stdio.h>#include <stdlib.h>#include <string.h>typedef int DataType;//结点类型struct node{    DataType data;    struct node *next;};//队列头typedef struct{    //front指向链表头    struct node *front;    //rear指向链表尾    struct node *rear;}LinkQueue;extern LinkQueue *creat_linkqueue();extern int is_empty_linkqueue(LinkQueue *q);extern int enter_linkqueue(LinkQueue *q,DataType data);extern DataType delete_linkqueue(LinkQueue *q);#endif

#include "linkqueue.h"//新建一个队列头LinkQueue *creat_linkqueue(){    //先分配一个头结点，head保存其地址    //在为队列头在堆区分配空间，q保存其首地址    struct node *head = NULL;    LinkQueue *q = NULL;    //创建空链表，链表队列头结点    head = (struct node *)malloc(sizeof(struct node));    memset(head,0,sizeof(struct node));//清空后指针域为NULL。表示空链表    //队列头，指向链表头跟链表尾    q = (LinkQueue *)malloc(sizeof(LinkQueue));     q->front = head;    q->rear = head;    return q; }///链表判空int is_empty_linkqueue(LinkQueue *q){    return q->front == q->rear;}//尾插法插入数据int enter_linkqueue(LinkQueue *q,DataType data){    struct node *temp = NULL;    temp = (struct node *)malloc(sizeof(struct node));    temp->data = data;        temp->next = q->rear->next;    q->rear->next = temp;    //更新rear    q->rear = temp;    return 0;}//删头法对头数据出队DataType delete_linkqueue(LinkQueue *q){    struct node *temp = NULL;    //保存原头结点首地址    temp = q->front;    //更新front    q->front = q->front->next;    free(temp);    temp = NULL;    return  q->front->data;}

#include "btree.h"#include "linkqueue.h"//新建一个数据结点，Btree *alloc_node(int i){    Btree *root = NULL;    root = (Btree *)malloc(sizeof(Btree));    root->data.num = i;    root->lchild = root->rchild = NULL;    printf("Input %d node char:",i);    scanf("%c",&root->data.c);    while(getchar() != '\n');    return root;}//新建一个二叉树Btree *create_binary_tree(int i){    Btree *root = NULL;    root = alloc_node(i);    //结点有左孩子的条件：2i<=N    if(i * 2 <= N)    {        //条件满足递归条用本函数创建左结点        root->lchild = create_binary_tree(2 * i);    }    //本结点有右孩子的条件为：2i+1<=N    if(i * 2 + 1 <= N)    {        //条件满足递归条用本函数创建右结点        root->rchild = create_binary_tree(i * 2 + 1);    }    //返回新建的结点    return root;}//先序遍历二叉树,规则：头->左->右//先访问跟结点，再访问左子树最后访问右子树int pre_order(Btree *root){    if(root == NULL)        return ;    printf("%d :%c \n",root->data.num,root->data.c);    pre_order(root->lchild);    pre_order(root->rchild);}//中序遍历二叉树，规则：左->头->右int in_order(Btree *root){    if(root == NULL)        return ;        in_order(root->lchild);    printf("%d :%c \n",root->data.num,root->data.c);    //printf("%d ",root->data);    in_order(root->rchild);        return ;}//后序遍历二叉树，规则：左->右->头int post_order(Btree *root){    if(root == NULL)        return ;        post_order(root->lchild);    post_order(root->rchild);    printf("%d :%c \n",root->data.num,root->data.c);    //printf("%d ",root->data);        return ;}//分层遍历每一个结点void level_order(Btree *root){    LinkQueue *q = NULL;    Btree *t = NULL;    q = creat_linkqueue();    enter_linkqueue(q,root);    while(!is_empty_linkqueue(q))    {        t = delete_linkqueue(q);        printf("(%-3d : %c) ",t->data.num,t->data.c);        if(t->lchild != NULL)        {            enter_linkqueue(q,t->lchild);        }        if(t->rchild != NULL)        {            enter_linkqueue(q,t->rchild);        }    }    putchar('\n');        return ;}

#include "btree.h"#include "linkqueue.h"int main(){    Btree *root = NULL;    root = create_binary_tree(1);   pre_order(root);/*{{{*/   putchar('\n');      in_order(root);   putchar('\n');   post_order(root);   putchar('\n');/*}}}*/   level_order(root);   return 0;}