实验三二叉树的操作及应用实验课程名：数据结构与算法专业班级：15计科1班学号：201540410109 姓名：刘江实验时间：2016.10.24-10.31 实验地点：K4-102 指导教师：冯珊成绩:一、实验目的及要求1、进一步掌握指针变量、动态变量的含义。

2、掌握二叉树的结构特性，以及各种存储结构的特点和适用范围。

3、掌握用指针类型描述、访问和处理二叉树的运算。

二、实验内容任务一：完成下列程序，该程序以二叉链表作存储结构，构建如图1所示的二叉树，并依次进行二叉树的前序、中序、后序及层次遍历。

图1解答：（1）源代码：#include<stdio.h>#include<stdlib.h>#define OK 1#define ERROR 0typedef char DataType;/* 二叉树节点的存储类型 */typedef struct Node //define stricture BiTree{ DataType data;struct Node *lchild,*rchild;}Node, *BiTree;/*按先序序列建立一棵二叉树*/BiTree CreatBiTree(BiTree &T){DataType ch;scanf("%c",&ch);if(ch==' ') {T=NULL;}else{if(!(T=(Node*)malloc(sizeof(Node)))){printf("Overflow.\n") ;exit(0);}T->data =ch;CreatBiTree(T->lchild );CreatBiTree(T->rchild );}return T;}void PrintData(DataType x){printf("%c",x);}void PreOrder(BiTree T, void (*Visit)( DataType item))/*前序遍历二叉树T，访问操作为Visit()函数*/{if(T!= NULL){Visit(T->data);PreOrder(T->lchild, Visit);PreOrder(T->rchild, Visit);}}void InOrder(BiTree T, void (*Visit)( DataType item)) /*中序t */ {if(T!= NULL){InOrder(T->lchild, Visit);Visit(T->data);InOrder(T->rchild, Visit);}}void PostOrder(BiTree T, void (*Visit)( DataType item)) /*后序 */ {if(T!= NULL){PostOrder(T->lchild, Visit);PostOrder(T->rchild, Visit);Visit(T->data);}}int main(){int choice;BiTree root;printf("下面建立一棵二叉树，结点数据输入按先序次序。

\n");printf("输入数据请注意，每一个非空结点的所有孩子数据都要给出\n"); printf("若孩子为空，请用空格符表示。

\n");printf("请输入二叉树结点的数据，这里设定为字符:\n");CreatBiTree(root);printf("================================\n");printf("1：先序序列：\n");printf("2：中序序列：\n");printf("3：后序序列：\n");printf("其它值则退出：\n");printf("================================\n");do{printf("请输入对应的操作码：");scanf("%d",&choice);switch(choice){case 1:printf("\n先序序列为：");PreOrder(root,PrintData);printf("\n");break;case 2:printf("\n中序序列为：");InOrder(root,PrintData);printf("\n");break;case 3:printf("\n后序序列为：");PostOrder(root,PrintData);printf("\n");}}while(choice>0&&choice<4);return 0;}（2）运行结果：（3）运行结果分析：运用遍历方法实现二叉树的建立任务二：完成下列程序，该程序以二叉链表作存储结构，构建如图2所示二叉树，计算二叉树深度、所有结点总数、叶子结点数、双孩子结点个数、单孩子结点个数。

图2解答：（1）源代码：#include<stdio.h>#include<stdlib.h>#define OK 1#define ERROR 0typedef char TElemType;/* 二叉树节点的存储类型 */typedef struct BiTNode //define stricture BiTree{ TElemType data;struct BiTNode *lchild,*rchild;}BiTNode, *BiTree;/*按先序序列建立一棵二叉树*/void CreatBiTree(BiTree &T){TElemType ch;scanf("%c",&ch);if(ch==' ') {T=NULL;return;}else{if(!(T=(BiTNode*)malloc(sizeof(BiTNode)))){printf("Overflo w.\n");exit(0);}(T)->data =ch;CreatBiTree(T->lchild );CreatBiTree(T->rchild );}}void PrintData(TElemType x){printf("%c",x);}void PreOrder(BiTree T, void (*Visit)( TElemType item))/*前序遍历二叉树T，访问操作为Visit()函数*/{if(T!= NULL){Visit(T->data);PreOrder(T->lchild, Visit);PreOrder(T->rchild, Visit);}}void InOrder(BiTree T, void (*Visit)( TElemType item)) /*中序t */ {if(T!= NULL){InOrder(T->lchild, Visit);Visit(T->data);InOrder(T->rchild, Visit);}}void PostOrder(BiTree T, void (*Visit)( TElemType item)) /*后序 */ {if(T!= NULL){PostOrder(T->lchild, Visit);PostOrder(T->rchild, Visit);Visit(T->data);}}//以上代码与任务一的完全相同，下面是完成任务二的代码//注意这些函数算法的相似性int BTreeDepth(BiTree BT){int leftdep,rightdep;if (BT==NULL)return(0);else{leftdep=BTreeDepth(BT->lchild);rightdep=BTreeDepth(BT->rchild);if (leftdep>rightdep)return(leftdep+1);elsereturn(rightdep+1);}}int NodeCount(BiTree BT){if (BT==NULL)return(0);elsereturn(NodeCount (BT-> lchild)+ NodeCount (BT-> rchild)+1); }int LeafCount(BiTree BT){if (BT==NULL)return(0);else if (BT-> lchild ==NULL && BT-> rchild ==NULL)return(1);elsereturn(LeafCount (BT-> lchild)+ LeafCount (BT-> rchild)); }int NotLeafCount(BiTree BT){if (BT==NULL)return(0);else if (BT-> lchild ==NULL && BT-> rchild ==NULL)return(0);elsereturn(NotLeafCount (BT-> lchild)+ NotLeafCount (BT->rchild)+1);}int OneChildCount(BiTree BT){if (BT==NULL)return(0);else if ((BT-> lchild ==NULL && BT-> rchild!=NULL) ||(BT-> lchild!=NULL && BT-> rchild ==NULL))return(OneChildCount (BT-> lchild)+ OneChildCount (BT->rchild)+1);elsereturn(OneChildCount (BT-> lchild)+ OneChildCount (BT->rchild));}int TwoChildCount(BiTree BT){if (BT==NULL)return(0);else if (BT-> lchild ==NULL || BT-> rchild ==NULL)return(TwoChildCount (BT-> lchild)+ TwoChildCount (BT->rchild));else if (BT-> lchild!=NULL && BT-> rchild!=NULL)return(TwoChildCount (BT-> lchild)+ TwoChildCount (BT->rchild)+1);}//主函数在任务一的基础上进行适当的增添int main(){int choice;BiTree root;printf("下面建立一棵二叉树，结点数据输入按先序次序。