1. 需求分析

1. 设计和实现一个简易的图书管理系统，通过AVL树的插入、查找和删除等，完成各功能；
2. 每种书的登记内容至少包括书号、书名、著者、现存量和总库存量等五项；
3. 书的数据用二叉排序树存储，借阅登记信息采用顺序表—链表存储；
4. 采编入库：新购入一种书，经分类和确定书号之后登记到图书帐目中去。如果这种书在帐中已有，则只将该书的总库存量增加。图书按登记的先后顺序入库（利用平衡二叉树实现动态查找表的插入），书号为图书的关键字。初始时，平衡二叉树为空树；
5. 借阅：如果一种书的现存量大于零，则借出一本，登记借阅者的图书证号和归还期限。借阅者借阅图书时，先检查借阅者有无超期未归还图书，如有，则不能借阅，如无，利用平衡二叉树实现动态查找表的查找，登记借阅信息。同一种书不能重复借阅；
6. 归还：注销对借阅者的登记，改变该书的现存量（如果借阅者归还所有的书，则注销该借阅者的信息）；
7. 清除库存：将该图书从平衡二叉树中删除，同时确保二叉树平衡；
8. 凹入表打印平衡二叉树，同时展示结点平衡因子bf，确保插入和删除操作的正确性。

2. 项目核心设计

本程序使用C语言编写与AVL树相关的内容，故函数形参中未使用引用变量，需修改的实参均以指针形式呈现。后因图书管理系统封装函数的需求，更改.c文件为.cpp文件，从而引入class。

项目核心部分为AVL树的生成和结点删除的同时如何保证树的平衡性，下面对其实现原理进行解释。基于此，构建图书管理系统，系统逻辑和具体功能见MindMap。

2.1 结点插入

对结点插入的解释以向其根结点左侧插入为例，右插类似，不做赘述。
若插入结点的关键词小于根结点的关键词，则插入根结点的左孩子。插入后，向根结点回溯时，返回一个taller，告知根结点因插入新结点而高度是否发生改变。此时分三种情况进行讨论：

1. 若根结点原本右高（RH），则因新结点的插入而使根结点等高（EH），taller=FALSE告知根结点未因插入新结点而高度发生改变；
2. 若根结点原本等高（EH），则因新结点的插入而使根结点左高（LH），taller=TRUE告知根结点因插入新结点高度增高；
3. 若根结点原本左高（LH），向左插入新结点后，根结点失衡，故因左调平根结点。

    else if(LT(elem.number,(*T)->data.number)) {//insert its left child treeif(!InsertAVLTree(&((*T)->lchild),taller,elem)) return ERROR;if(!*taller) return OK;switch((*T)->bf) { //update the BF of the nodecase LH://adjust to make it balancedL_Balance(T);*taller=FALSE; break;case EH: (*T)->bf=LH; *taller=TRUE; break;case RH: (*T)->bf=EH; *taller=FALSE; break;}//switch((*T)->bf)}

左调平根结点时，根据根结点左孩子的平衡因子，判断是LL型还是LR型，采用不同的调平方法。无论何种调平方法，都应遵循以下两原则：

1. 确保二叉树性质不变，即中序遍历结果不变；
2. 使最小失衡子树的高度降低。

若左孩子的平衡因子为左高（LH），说明为LL型，修改根结点和其左孩子的平衡因子EH，向左旋转根结点。若左孩子的平衡因子为右高（RH），说明为LR型，此时，根据其左孩子的右孩子的平衡因子，修改结点平衡因子再分三种情况进行讨论：

1. 若其左的右孩子为左高（LH），则左和左的右孩子BF=EH，根结点BF=RH；
2. 若其左的右孩子为等高（EH），则左孩子和根结点BF=EH。（左的右孩子已为EH）；
3. 若其左的右孩子为右高（RH），则根结点和左的右孩子BF=EH，左孩子BF=LH。

void LibManage::L_Balance(AVLTree *t){//adjust the root to make left tree balancedTNode *lc=(*t)->lchild,*rd;switch(lc->bf){ //check condition: LL or LR, through BF of root's lchildcase EH: //a case when deleting the node(*t)->bf=LH; lc->bf=RH;R_Rotate(t);break;case LH: //LL(*t)->bf=lc->bf=EH; //modify BFR_Rotate(t); //R rotate root nodebreak;case RH: //LRrd=lc->rchild;switch(rd->bf){ //modify BF according to different BF conditionscase LH: lc->bf=rd->bf=EH;  (*t)->bf=RH; break;case EH: lc->bf=(*t)->bf=EH; break;case RH: rd->bf=(*t)->bf=EH; lc->bf=LH; break;}//switch(rd->bf)L_Rotate(&((*t)->lchild)); //part Left rotation, firstlyR_Rotate(t); //root Right rotation, thenbreak;}//switch(lc->bf)
}

修正平衡因子后，对失衡子树进行旋转。先对失衡子树根结点的左孩子进行（局部）左旋转，再对根结点进行（整体）右旋。至此，结点左插调平完成。以下为左调平操作示意图解。

2.2 结点删除

AVL树结点的删除操作同二叉搜索树结点删除相同，但删除结点后需要调整使AVL树重新平衡。根据所删结点的双亲和孩子情况，分三种情况进行讨论：

1. 若所删结点为叶子结点（无孩子），直接删除之。若其无双亲（即为AVL树的根结点），置AVL树根（root）为空（NULL）；
2. 若所删结点只有一孩子，令其双亲结点连接其孩子（至于是双亲的左还是右连接之，只需判断双亲和孩子的关键词大小，若双亲>孩子，则双亲左连之，反之，则双亲右连之）。若无双亲，可置树根（root）为所删结点的孩子；
3. 若所删结点两孩子均存在，则可通过寻找其（在中序遍历下的）前驱或后继，来实现删除操作。为同程序一致，这里以寻找前驱为例。进入所删结点的左孩子，向其右方（通过遍历）寻至其最右方的结点（姑且称作待删结点的相邻点），将待删结点的值替换为相邻点的值。再进入待删结点的左子树中（递归），删除相邻点。

else if(EQ(bknum,(*curT)->data.number)) {//find the node, and delete itif(!((*curT)->lchild)) {//if(the node has no left child or has neither left nor right one)if(!preT) *curT=(*curT)->rchild;//if(the node has no parent)else if(LT(bknum,preT->data.number)) preT->lchild=(*curT)->rchild;//check the current node is its parent's left child or its right oneelse preT->rchild=(*curT)->rchild;*shorter=TRUE;}//if(!((*curT)->lchild))else if(!((*curT)->rchild)) {//if(the node has no right child but has left one)if(!preT) *curT=(*curT)->lchild;//if(the node has no parent)else if(LT(bknum,preT->data.number)) preT->lchild=(*curT)->lchild;//check the current node is its parent's left child or its right oneelse preT->rchild=(*curT)->lchild;*shorter=TRUE;}//else if(!((*curT)->rchild))else {//if(the node has both right and left child)TNode *tempT=(*curT)->lchild; //enter curT's left childwhile(tempT->rchild) //find curNode's precursor in inorder traversetempT=tempT->rchild;BookCpy(&((*curT)->data),tempT->data); //assign the precursor's data to the node that needs to be deletedDeleteAVLTree(&((*curT)->lchild),NULL,shorter, tempT->data.number); //delete the precursor of the deleted elem in curT's left child

接下来，对删除结点后的调平工作进行解释，同样，以删除根结点左子树中的结点为例，右子树中删除操作类似，不做赘述。

若所删结点的关键词<根结点的关键词，则进入根结点左子树中进行删除操作。删除后，向根结点回溯时，返回一个shorter，告知根结点因删除结点而高度是否发生改变。此时分三种情况进行讨论：

1. 根结点原本左高（LH），删除后，根结点等高（EH），shorter=TRUE；
2. 根结点原本等高（EH），删除后，根结点右高（RH），shorter=FALSE；
3. 根结点原本右高（RH），删除后，根结点失衡，应当对其进行右调平R_Balance()操作。

调平前，需根据根结点的右孩子的平衡因子，判断调平后，失衡子树shorter情况如何，此时分三种情况进行讨论：

1. 根的右孩子BF=LH，调平后，shorter=TRUE；
2. 根的右孩子BF=EH，调平后，shorter=FALSE；
3. 根的右孩子BF=RH，调平后，shorter=TRUE。（也可与情况1归并）

else if(LT(bknum,(*curT)->data.number)) {//if the keynum is less than the curT's numberif(!DeleteAVLTree(&((*curT)->lchild),*curT,shorter,bknum)) return ERROR;if(!*shorter) return OK;switch((*curT)->bf) {case LH: (*curT)->bf=EH; *shorter=TRUE; break;case EH: (*curT)->bf=RH; *shorter=FALSE; break;case RH://another 3 conditions need to be considered, according to curT's right child BFswitch((*curT)->rchild->bf) {case LH: *shorter=TRUE; break;case EH: *shorter=FALSE; break;case RH: *shorter=TRUE; break;}//switch((*curT)->rchild->bf)R_Balance(curT);}//switch((*curT)->bf)}//else if(LT(bknum,(*curT)->data.number))

判断回溯的shorter的结果后，开始右调平。右调平操作与结点插入时的右调平基本无异，但需在“通过根结点右孩子BF值判断是RR型还是RL型失衡”时，增加一种EH的情况。因为在插入时，只考虑了因插入才会产生的LH和RH情况，未将删除时所会遇到的EH纳入其中。当BF=EH时，先更新各结点的平衡因子，根结点的BF=RH，根结点右孩子的BF=LH，再根结点左旋。（同理，左平衡操作时，也需补充“EH条件”）。

void LibManage::R_Balance(AVLTree *t){//adjust the root to make right tree balancedTNode *rc=(*t)->rchild,*ld;switch(rc->bf){ //check condition: RL or RR, through BF of root's rchildcase EH: //a case when deleting the node(*t)->bf=RH; rc->bf=LH;L_Rotate(t);break;//......

以下为右调平操作图解。

3 测试结果

//为模拟方便起见，添加初始图书、阅读者和阅读者的借阅数据
//book={number,name,author,stock,total}
Book book1={“01”,“PromisedLand”,“Obama”,6,8};
Book book2={“02”,“Humans”,“Stanton”,4,5};
Book book3={“03”,“Becoming”,“Michelle”,0,3};
Book book4={“04”,“DeepEnd”,“Kinney”,0,6};
InsertAVLTree(&tree,&taller,book1);
InsertAVLTree(&tree,&taller,book2);
InsertAVLTree(&tree,&taller,book3);
InsertAVLTree(&tree,&taller,book4);
//reader={code,name,telephone,firstarc}
Reader reader1={1,“Sylvan”,“95566”,NULL};
Reader reader2={2,“JIXIANG”,“10086”,NULL};
AddReader(reader_list,reader1);
AddReader(reader_list,reader2);
//reader={booknumber,bookname,return date,*next}
ArcBox arcbox1={“01”,“PromisedLand”,20251211,NULL};
ArcBox arcbox2={“02”,“Humans”,20300201,NULL};
AddReaderBook(reader_list.readers[0],arcbox1);
AddReaderBook(reader_list.readers[0],arcbox2);
AddReaderBook(reader_list.readers[1],arcbox1);

(以下内容均来自终端)
//启动图书管理系统，设置系统时间
Launch Library Management System Successfully!
Set current time:20201120 successfully!

//菜单界面，待用户输入指令
* * * MENU * * *
(1). Add books
(2). Lend books
(3). Return books
(4). Erase books
(5). Print All Books
(6). Print All Readers
(7). *(Testing MODE)
(0). [ E X I T ]
* * * * * * * * *
Menu->Option:

//功能一、采编入库
Menu->Option: 1
- - - - Add Book - - - -
Book Number: ISBN 01
Increment: 2
Find the BOOK...
Would you like to increase it? (y/n)...
y
Original stock: 6 
Original total amount: 8 
- - - - Book Info - - - -
Name: PromisedLand
Author: Obama
Number: ISBN 01
Total: 10
Stock: 8
- - - - - - - - - - - - -
Increase successfully! 
Menu->Option: 1
- - - - Add Book - - - -
Book Number: ISBN 05
Increment: 3
ERROR: Can't find BOOK: ISBN 05 Would you like to create a new item? (y/n)...
y
Number: ISBN 05
Stock/Total: 3
Name: Sherlock
Author: Arthur
- - - - Book Info - - - -
Name: Sherlock
Author: Arthur
Number: ISBN 05
Total: 3
Stock: 3
- - - - - - - - - - - - -
Add new book successfully!  

//功能二、借阅
Menu->Option: 2
- - - - Lend Book - - - -
Reader Code: 01
- - - - Reader Info - - - -
Name: Sylvan
Code: 00001
Tele: 95566
Borrowed books: 
<Humans> | ISBN 02 |  Deadline:20300201([Normal])
<PromisedLand> | ISBN 01 |  Deadline:20251211([Normal])
- - - - - - - - - - - - -
Book Number to lend: ISBN 02
No borrow permission: The reader has borrowed a same book <Humans>.
//……相同操作省略
Book Number to lend: ISBN 03
ERROR: Book Stock of <Becoming> is not enough...
Menu->Option: 2
- - - - Lend Book - - - -
Reader Code: 02
- - - - Reader Info - - - -
Name: JIXIANG
Code: 00002
Tele: 10086
Borrowed books: 
<PromisedLand> | ISBN 01 |  Deadline:20251211([Normal])
- - - - - - - - - - - - -
Book Number to lend: ISBN 02
Return Date(e.g.20201230): 20191230
Lend Book Successfully!
Menu->Option: 2
- - - - Lend Book - - - -
Reader Code: 02
- - - - Reader Info - - - -
Name: JIXIANG
Code: 00002
Tele: 10086
Borrowed books: 
<Humans> | ISBN 02 |  Deadline:20191230(![Overdue]!)
<PromisedLand> | ISBN 01 |  Deadline:20251211([Normal])
- - - - - - - - - - - - -
No borrow permission: The reader has a book <Humans> needs to be returned before 20191230
Menu->Option: 2
- - - - Lend Book - - - -
Reader Code: 05
ERROR: Can't find reader 00005...
Would you like to create one? (y/n)...
y
Code: 00005 
Name: Benedict
Tele: 197362
- - - - Reader Info - - - -
Name: Benedict
Code: 00005
Tele: 197362
Borrowed books: (Empty) 
- - - - - - - - - - - - -
Add reader successfully! 
Book Number to lend: ISBN 01
Return Date(e.g.20201230): 20201231
Lend Book Successfully!

//功能三、还书
Menu->Option: 3
- - - - Return Book - - - -
Reader Code: 01
- - - - Reader Info - - - -
Name: Sylvan
Code: 00001
Tele: 95566
Borrowed books: 
<Humans> | ISBN 02 |  Deadline:20300201([Normal])
<PromisedLand> | ISBN 01 |  Deadline:20251211([Normal])
- - - - - - - - - - - - -
Book Number to return: ISBN 02
Return Successfully!
Menu->Option: 3
- - - - Return Book - - - -
Reader Code: 01
- - - - Reader Info - - - -
Name: Sylvan
Code: 00001
Tele: 95566
Borrowed books: 
<PromisedLand> | ISBN 01 |  Deadline:20251211([Normal])
- - - - - - - - - - - - -
Book Number to return: ISBN 01
Warning: Reader Sylvan has returned all books, now erase his or her info from the memory... 
Erased successfully! 
Return Successfully! 
Menu->Option: 6
- - - - Reader Info - - - -
Name: JIXIANG
Code: 00002
Tele: 10086
Borrowed books: 
<PromisedLand> | ISBN 01 |  Deadline:20251211([Normal])
- - - - - - - - - - - - -

//功能四、清除库存
Menu->Option: 4
- - - - Erase Book - - - -
Book Number to erase: ISBN 01
Delete book successfully! 
Menu->Option: 5
- - - - Book Info - - - -
Name: Becoming
Author: Michelle
Number: ISBN 03
Total: 3
Stock: 0
- - - - Book Info - - - -
Name: Humans
Author: Stanton
Number: ISBN 02
Total: 5
Stock: 4
- - - - Book Info - - - -
Name: DeepEnd
Author: Kinney
Number: ISBN 04
Total: 6
Stock: 0
- - - - - - - - - - - - -

//功能五、展示所有图书
//功能六、展示所有借阅者
//功能七、测试模式：便捷地测试AVL树的插入与删除。

4 总结分析

4.1 调试过程中的问题是如何解决的，以及对设计与实现的回顾讨论和分析

平衡二叉排序树(Balanced Binary Sort Tree)，又称AVL树，是一种时间复杂度较低的理想的动态查找表。通过在树结点TNode中，增设整型变量bf（即平衡因子balance factor），来判定结点是否平衡。Bf为该结点左子树高与右子树高的差值，当其绝对值超过1以后，结点失衡，需要对其进行调平操作。

写程序过程中，遇到逻辑问题后，通过一步步debug，发现问题，解决问题。

4.2 算法的时间和空间复杂度的分析，以及进一步改进的设想

经分析，平衡二叉树的查找、插入和删除其时间复杂度均为¹：

$$◯\left(\log n\right).$$

是一种理想的动态查找表。

4.3 本次实验的经验和体会

通过使用C语言编写平衡二叉树插入和删除部分，大量使用指针变量，深入理解了指针的含义和用法。函数中，重复使用回溯的方法进行二叉树平衡，加强了对算法逻辑对掌握。

使用C++编写图书管理部分，学习和培养了考虑项目要全面的能力。

语法错误越来越少，而真正困难的逻辑部分问题增多。

在编写平衡二叉树插入和删除时，调试过程中遇到许多问题，如旋转错误、结点平衡因子错误等等。Edsger W. Dijkstra曾说过，

“有效的程序员不应该浪费很多时间用于程序调试，他们应该一开始就不要把故障引入。” ²

表明，在写程序前就应当理清逻辑和考虑所有情况，因此，后续还需继续培养编程的逻辑性和严谨性。

5 完整代码(C++)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<time.h>/* status macro definition */
#define OK 1
#define ERROR 0
#define OVER_FLOW -2/* memory length macro definition */
#define MAXNAMELEN 15
#define MAXBOOKNUMBERLEN 20
#define MAXREADERNUM 20 //the max amount of all readers
#define MAXREADERCODEDIGIT 5 //max reader code digits
#define INDENTATION 0 //for printing the BiTree/* some macros related to AVLTree */
#define EQ(a,b) (!strcmp((a),(b)))
#define LT(a,b) (strcmp((a),(b))<0)
#define LH +1
#define EH 0
#define RH -1typedef int Status;
typedef enum {FALSE,TRUE} boolean;
typedef char *KeyType;
typedef char NameType[MAXNAMELEN];
typedef char *BookNum,BookNumType[MAXBOOKNUMBERLEN];
typedef char TeleType[11+1]; //telephone: 11digits
typedef unsigned int DateType; //return date
//typedef Book DataType; //data type in TNodetypedef struct{BookNumType number; //no prefix 'ISBN'NameType name;NameType author;int stock; //current amount of the bookint total; //total amount of the book
}Book,DataType;typedef struct TNode{DataType data;int bf; //balance factorstruct TNode *lchild,*rchild;
}TNode,*AVLTree;typedef struct ArcBox{BookNumType bknum;NameType bknam;DateType return_date; //e.g. 20010205struct ArcBox *next;
}ArcBox;typedef struct{int code;NameType name;TeleType tele; //telephoneArcBox *first_arc;
}Reader;typedef struct{Reader *readers;int length,size;
}AdjList;class LibManage{
public:AVLTree tree;AdjList reader_list;DateType current_date;LibManage();~LibManage() {DestoryTree(tree);}void Menu();void AddBook();void LendBook();void ReturnBook();void EraseBook();void OutputBooks();void OutputReaders();void TestMode();
private:void gettime();void PrintBook(Book b);void PrintBiTree_Simple(AVLTree T,int indent);void PrintBiTree_Detail(AVLTree T);void BookCpy(Book *a,Book b);void L_Rotate(AVLTree *t);void R_Rotate(AVLTree *t);void L_Balance(AVLTree *t);void R_Balance(AVLTree *t);TNode* SearchAVLTree(AVLTree T,BookNum bn);Status InsertAVLTree(AVLTree *T,boolean *taller,DataType elem);Status DeleteAVLTree(AVLTree *curT,AVLTree preT,boolean *shorter,KeyType bknum);Status InitAdjList(AdjList &list);Status AddReader(AdjList &list,const Reader &r);Status AddReaderBook(Reader &r,const ArcBox &ab);Status SearchReader(AdjList list,int code);Status DeleteReader(AdjList &list,int code);Status CheckBorrowPermission(Reader r,BookNum bknum=NULL);ArcBox* SearchBorrowedBook(Reader r,KeyType bknum,ArcBox* &prep);void ReaderCpy(Reader &r1,const Reader &r2);void PrintReader(const Reader &r);void PrintBorrowedBooks(Reader r);void DestoryTree(AVLTree &T);
};void LibManage::gettime(){//get system time and convert it to unsigned inttime_t rawtime;struct tm *ptminfo;time(&rawtime); //get time raw infoptminfo=localtime(&rawtime); //convert raw time info to processed and readable time infocurrent_date=((ptminfo->tm_year)+1900)*10000+(ptminfo->tm_mon)*100+(ptminfo->tm_mday);printf("Set current time:%u successfully! \n",current_date);
}LibManage::LibManage() {tree=NULL; //initialize treeInitAdjList(reader_list); //initialize AdjListprintf("Launch Library Management System Successfully! \n");gettime();/* Simulate a library, so add some items first *///book={number,name,author,stock,total}boolean taller=FALSE;Book book1={"01","PromisedLand","Obama",6,8};Book book2={"02","Humans","Stanton",4,5};Book book3={"03","Becoming","Michelle",0,3};Book book4={"04","DeepEnd","Kinney",0,6};InsertAVLTree(&tree,&taller,book1);InsertAVLTree(&tree,&taller,book2);InsertAVLTree(&tree,&taller,book3);InsertAVLTree(&tree,&taller,book4);//reader={code,name,telephone,firstarc}Reader reader1={1,"Sylvan","95566",NULL};Reader reader2={2,"JIXIANG","10086",NULL};AddReader(reader_list,reader1);AddReader(reader_list,reader2);//reader={booknumber,bookname,return date,*next}ArcBox arcbox1={"01","PromisedLand",20251211,NULL};ArcBox arcbox2={"02","Humans",20300201,NULL};AddReaderBook(reader_list.readers[0],arcbox1);AddReaderBook(reader_list.readers[0],arcbox2);AddReaderBook(reader_list.readers[1],arcbox1);
}void LibManage::DestoryTree(AVLTree &T){//free the memory of the tree, using post-order traverse to guarantee that the node's parent won't get lostif(!T) return;DestoryTree(T->lchild);DestoryTree(T->rchild);free(T); T=NULL;
}//the following function is related to AVLTreevoid LibManage::L_Rotate(AVLTree *t){//left rotate root node, and update the rootTNode *rc=(*t)->rchild;(*t)->rchild=rc->lchild;rc->lchild=*t;(*t)=rc;
}
void LibManage::R_Rotate(AVLTree *t){//right rotate root node, and update the rootTNode *lc=(*t)->lchild;(*t)->lchild=lc->rchild;lc->rchild=*t;(*t)=lc;
}
void LibManage::L_Balance(AVLTree *t){//adjust the root to make left tree balancedTNode *lc=(*t)->lchild,*rd;switch(lc->bf){ //check condition: LL or LR, through BF of root's lchildcase EH: //a case when deleting the node(*t)->bf=LH; lc->bf=RH;R_Rotate(t);break;case LH: //LL(*t)->bf=lc->bf=EH; //modify BFR_Rotate(t); //R rotate root nodebreak;case RH: //LRrd=lc->rchild;switch(rd->bf){ //modify BF according to different BF conditionscase LH: lc->bf=rd->bf=EH;  (*t)->bf=RH; break;case EH: lc->bf=(*t)->bf=EH; break;case RH: rd->bf=(*t)->bf=EH; lc->bf=LH; break;}//switch(rd->bf)L_Rotate(&((*t)->lchild)); //part Left rotation, firstlyR_Rotate(t); //root Right rotation, thenbreak;}//switch(lc->bf)
}
void LibManage::R_Balance(AVLTree *t){//adjust the root to make right tree balancedTNode *rc=(*t)->rchild,*ld;switch(rc->bf){ //check condition: RL or RR, through BF of root's rchildcase EH: //a case when deleting the node(*t)->bf=RH; rc->bf=LH;L_Rotate(t);break;case RH: //RR(*t)->bf=rc->bf=EH; //modify BFL_Rotate(t); //L rotate root nodebreak;case LH: //RLld=rc->lchild;switch(ld->bf){ //modify BF according to different BF conditionscase LH: (*t)->bf=rc->bf=EH; ld->bf=RH; break;case EH: rc->bf=(*t)->bf=EH; break;case RH: ld->bf=rc->bf=EH; (*t)->bf=LH; break;}//switch(rd->bf)R_Rotate(&((*t)->rchild)); //part Right rotation, firstlyL_Rotate(t); //root Left rotation, thenbreak;}//switch(lc->bf)
}TNode* LibManage::SearchAVLTree(AVLTree T,BookNum bn){/* if the booknum can be found in AVLTree, then return its address, else return NULL */if(!T) return NULL;if(EQ(bn,T->data.number)) return T;if(LT(bn,T->data.number)) return SearchAVLTree(T->lchild,bn);return SearchAVLTree(T->rchild,bn);
}Status LibManage::InsertAVLTree(AVLTree *T,boolean *taller,DataType elem){/* insert an elem to AVLTree, and adjust the tree to keep its balance. If elem has existed, then return ERROR, else return OK *//* parameter 'taller' means that after inserting the elem, the tree is taller or not. */if(!*T) { //create a new node*T=(TNode*)malloc(sizeof(TNode));if(!*T) exit(OVER_FLOW);BookCpy(&((*T)->data),elem);(*T)->bf=EH;(*T)->lchild=(*T)->rchild=NULL;*taller=TRUE;}else if(EQ(elem.number,(*T)->data.number)) {//if the node has already existedPrintBook((*T)->data);printf("ERROR: book <%s> has already been in the AVL Tree. \n",elem.name);*taller=FALSE;return ERROR;}else if(LT(elem.number,(*T)->data.number)) {//insert its left child treeif(!InsertAVLTree(&((*T)->lchild),taller,elem)) return ERROR;if(!*taller) return OK;switch((*T)->bf) { //update the BF of the nodecase LH://adjust to make it balancedL_Balance(T);*taller=FALSE; break;case EH: (*T)->bf=LH; *taller=TRUE; break;case RH: (*T)->bf=EH; *taller=FALSE; break;}//switch((*T)->bf)}else {//insert its right child treeif(!InsertAVLTree(&((*T)->rchild),taller,elem)) return ERROR;if(!*taller) return OK;switch((*T)->bf) { //update the BF of the nodecase LH: (*T)->bf=EH; *taller=FALSE; break;case EH: (*T)->bf=RH; *taller=TRUE; break;case RH://adjust to make it balancedR_Balance(T);*taller=FALSE; break;}//switch((*T)->bf)}return OK;
}Status LibManage::DeleteAVLTree(AVLTree *curT,AVLTree preT,boolean *shorter,KeyType bknum){/* delete a node in AVLTree according to its book number, and adjust the tree to keep its balance. If elem has existed, then return OK, else return ERROR *///©SylvanDing/* parameter 'shorter' means that after deleting the node, the tree is shorter or not. */if(!*curT) {//if the node doesn't existprintf("ERROR: Can't find BOOK: ISBN %s \n",bknum);*shorter=FALSE;return ERROR;}//if(!*curT)else if(EQ(bknum,(*curT)->data.number)) {//find the node, and delete itif(!((*curT)->lchild)) {//if(the node has no left child or has neither left nor right one)if(!preT) *curT=(*curT)->rchild;//if(the node has no parent)else if(LT(bknum,preT->data.number)) preT->lchild=(*curT)->rchild;//check the current node is its parent's left child or its right oneelse preT->rchild=(*curT)->rchild;*shorter=TRUE;}//if(!((*curT)->lchild))else if(!((*curT)->rchild)) {//if(the node has no right child but has left one)if(!preT) *curT=(*curT)->lchild;//if(the node has no parent)else if(LT(bknum,preT->data.number)) preT->lchild=(*curT)->lchild;//check the current node is its parent's left child or its right oneelse preT->rchild=(*curT)->lchild;*shorter=TRUE;}//else if(!((*curT)->rchild))else {//if(the node has both right and left child)TNode *tempT=(*curT)->lchild; //enter curT's left childwhile(tempT->rchild) //find curNode's precursor in inorder traversetempT=tempT->rchild;BookCpy(&((*curT)->data),tempT->data); //assign the precursor's data to the node that needs to be deletedDeleteAVLTree(&((*curT)->lchild),NULL,shorter, tempT->data.number); //delete the precursor of the deleted elem in curT's left childif(!*shorter) return OK;switch((*curT)->bf) {case LH: (*curT)->bf=EH; *shorter=TRUE; break;case EH: (*curT)->bf=RH; *shorter=FALSE; break;case RH://another 3 conditions need to be considered, according to curT's right child BFswitch((*curT)->rchild->bf) {case LH: *shorter=TRUE; break;case EH: *shorter=FALSE; break;case RH: *shorter=TRUE; break;}//switch((*curT)->rchild->bf)R_Balance(curT);}//switch((*curT)->bf)}}//else if(EQ(bknum,(*curT)->data.number))else if(LT(bknum,(*curT)->data.number)) {//if the keynum is less than the curT's numberif(!DeleteAVLTree(&((*curT)->lchild),*curT,shorter,bknum)) return ERROR;if(!*shorter) return OK;switch((*curT)->bf) {case LH: (*curT)->bf=EH; *shorter=TRUE; break;case EH: (*curT)->bf=RH; *shorter=FALSE; break;case RH://another 3 conditions need to be considered, according to curT's right child BFswitch((*curT)->rchild->bf) {case LH: *shorter=TRUE; break;case EH: *shorter=FALSE; break;case RH: *shorter=TRUE; break;}//switch((*curT)->rchild->bf)R_Balance(curT);}//switch((*curT)->bf)}//else if(LT(bknum,(*curT)->data.number))else {//if the keynum is larger than the curT's number, enter its right childif(!DeleteAVLTree(&((*curT)->rchild),*curT,shorter,bknum)) return ERROR;if(!*shorter) return OK;switch((*curT)->bf) {case LH://another 3 conditions need to be considered, according to curT's left child BFswitch((*curT)->lchild->bf) {case LH: *shorter=TRUE; break;case EH: *shorter=FALSE; break;case RH: *shorter=TRUE; break;}//switch((*curT)->rchild->bf)L_Balance(curT);case EH: (*curT)->bf=LH; *shorter=FALSE; break;case RH: (*curT)->bf=EH; *shorter=TRUE; break;}//switch((*curT)->bf)}//elsereturn OK;
}void LibManage::TestMode(){//this mode is for testing AVLTree's insertion and deletion quickly and easilyBook bk={"","","",0,0};AVLTree testT=NULL; boolean flag;printf("- - - Testing Mode - - -\n");printf("//This mode allows you to test AVLTree's insertion and deletion quickly and easily. Whenever you insert or delete an item, it will print the AVLTree: KeyValue(BalanceFactor) \n//Have created a new Empty AVLTree for testing... \n//Input numbers(like 01,21,36...) to insert it, input 'end' to stop inserting. \n");//©SylvanDingdo{flag=FALSE;scanf("%s",bk.number);getchar();if(EQ(bk.number,"end")) break;InsertAVLTree(&testT,&flag,bk);printf("* Tree Print * \n");PrintBiTree_Simple(testT,INDENTATION);}while(1);printf("//End inserting, and then you can input the item you wanna delete, input 'quit' to exit testing mode... \n");do{flag=FALSE;scanf("%s",bk.number);getchar();if(EQ(bk.number,"quit")) break;DeleteAVLTree(&testT,NULL,&flag,bk.number);printf("* Tree Print * \n");PrintBiTree_Simple(testT,INDENTATION);}while(1);printf("//Exit TESTING MODE... \n");
}//the following function is about Library Managementvoid LibManage::Menu(){printf("* * * MENU * * *\n");printf("(1). Add books\n");printf("(2). Lend books\n");printf("(3). Return books\n");printf("(4). Erase books\n");printf("(5). Print All Books\n");printf("(6). Print All Readers\n");printf("(7). *(Testing MODE)\n");printf("(0). [ E X I T ]\n");printf("* * * * * * * * *\n");
}void LibManage::BookCpy(Book *a,Book b){//copy b's info and assign it to astrcpy(a->number,b.number);strcpy(a->name,b.name);strcpy(a->author,b.author);a->stock=b.stock;a->total=b.total;
}void LibManage::PrintBook(Book b){printf("- - - - Book Info - - - -\n");printf("Name: %s\n",b.name);printf("Author: %s\n",b.author);printf("Number: ISBN %s\n",b.number);printf("Total: %d\n",b.total);printf("Stock: %d\n",b.stock);printf("- - - - - - - - - - - - -\n");
}void LibManage::PrintBiTree_Simple(AVLTree T,int indent){if(!T) return;printf("%*s%s(%d)\n",indent,"",T->data.number,T->bf);PrintBiTree_Simple(T->lchild,indent+1);PrintBiTree_Simple(T->rchild,indent+1);
}void LibManage::PrintBiTree_Detail(AVLTree T){if(!T) return;PrintBook(T->data);PrintBiTree_Detail(T->lchild);PrintBiTree_Detail(T->rchild);
}void LibManage::AddBook(){//to add a new book when bknum-related book doesn't exist in AVLTree, or increase its original amountAVLTree *T=&tree;TNode *node=NULL; char flag;BookNumType bknum; int amount;printf("- - - - Add Book - - - -\n");printf("Book Number: ISBN ");scanf("%s",bknum);printf("Increment: ");scanf("%d",&amount);getchar();if(!(node=SearchAVLTree(*T,bknum))) {boolean taller=FALSE;Book new_book; NameType bk_name,aut_name;printf("ERROR: Can't find BOOK: ISBN %s \n Would you like to create a new item? (y/n)...\n",bknum);scanf("%c",&flag);switch(flag){case 'n':case 'N': return; break;case 'y':case 'Y':printf("Number: ISBN %s\n",bknum);printf("Stock/Total: %d\n",amount);printf("Name: ");scanf("%s",bk_name);printf("Author: ");scanf("%s",aut_name);strcpy(new_book.number,bknum);strcpy(new_book.name,bk_name);strcpy(new_book.author,aut_name);new_book.stock=new_book.total=amount;if(!InsertAVLTree(T,&taller,new_book)) return;PrintBook(new_book);printf("Add new book successfully!  \n");break;default: printf("Error: Wrong command, try again...\n");}//switch(flag)}//if(!(node=SearchAVLTree(*T,bknum)))else {printf("Find the BOOK...\nWould you like to increase it? (y/n)...\n");scanf("%c",&flag);switch(flag){case 'n':case 'N': return; break;case 'y':case 'Y':printf("Original stock: %d \nOriginal total amount: %d \n",node->data.stock,node->data.total);node->data.stock+=amount;node->data.total+=amount;PrintBook(node->data);printf("Increase successfully! \n");break;default: printf("Error: Wrong command, try again...\n");}//switch(flag)}//else
}void LibManage::
LendBook(){//to lend booksint code,index; char flag;printf("- - - - Lend Book - - - -\n");printf("Reader Code: ");scanf("%d",&code);getchar();if((index=SearchReader(reader_list,code))<0) {index=reader_list.length;Reader newreader; newreader.first_arc=NULL;printf("ERROR: Can't find reader %0*d...\nWould you like to create one? (y/n)...\n",MAXREADERCODEDIGIT,code);scanf("%c",&flag);switch(flag){case 'n':case 'N': return; break;case 'y':case 'Y':printf("Code: %0*d \n",MAXREADERCODEDIGIT,code);newreader.code=code;printf("Name: ");scanf("%s",newreader.name);printf("Tele: ");scanf("%s",newreader.tele);if(!AddReader(reader_list,newreader)) return;PrintReader(reader_list.readers[reader_list.length-1]);printf("Add reader successfully! \n");break;default: printf("Error: Wrong command, try again...\n"); return;}//switch(flag)}//if(index<0)else {PrintReader(reader_list.readers[index]);if(!CheckBorrowPermission(reader_list.readers[index])) return;}//if(index>=0)BookNumType bknum; TNode *tptr;printf("Book Number to lend: ISBN ");scanf("%s",bknum);if(!CheckBorrowPermission(reader_list.readers[index],bknum)) return;if(!(tptr=SearchAVLTree(tree,bknum)))printf("ERROR: Can't find book: %s in Library System... \n",bknum);else if(tptr->data.stock<=0)printf("ERROR: Book Stock of <%s> is not enough... \n",tptr->data.name);else {ArcBox *new_arcbox=(ArcBox*)malloc(sizeof(ArcBox));if(!new_arcbox) exit(OVER_FLOW);--tptr->data.stock;printf("Return Date(e.g.20201230): ");scanf("%u",&(new_arcbox->return_date));strcpy(new_arcbox->bknum,bknum);strcpy(new_arcbox->bknam,tptr->data.name);new_arcbox->next=reader_list.readers[index].first_arc;reader_list.readers[index].first_arc=new_arcbox;printf("Lend Book Successfully! \n");}
}void LibManage::ReturnBook(){//to return booksint code,index; TNode *tptr;BookNumType bknum; ArcBox *abptr,*pre_abptr;printf("- - - - Return Book - - - -\n");printf("Reader Code: ");scanf("%d",&code);getchar();if((index=SearchReader(reader_list,code))<0) {printf("ERROR: Can't find reader %0*d...\n",MAXREADERCODEDIGIT,code);return;}PrintReader(reader_list.readers[index]);printf("Book Number to return: ISBN ");scanf("%s",bknum);if(!(abptr=SearchBorrowedBook(reader_list.readers[index],bknum,pre_abptr))) {printf("ERROR: No lended book: %s...\n",bknum);return;}if(!pre_abptr)reader_list.readers[index].first_arc=abptr->next;elsepre_abptr->next=abptr->next;free(abptr);if(!reader_list.readers[index].first_arc) {printf("Warning: Reader %s has returned all books, now erase his or her info from the memory... \n",reader_list.readers[index].name);DeleteReader(reader_list,index);printf("Erased successfully! \n");}if((tptr=SearchAVLTree(tree,bknum)))++tptr->data.stock;printf("Return Successfully! \n");
}void LibManage::EraseBook(){//to erase bookBookNumType bknum; boolean shorter;printf("- - - - Erase Book - - - -\n");printf("Book Number to erase: ISBN ");scanf("%s",bknum);getchar();if(DeleteAVLTree(&tree,NULL,&shorter,bknum))printf("Delete book successfully! \n");
}void LibManage::OutputBooks(){//in-order traverse the AVLTreeif(!tree){printf("No book... \n");return;}PrintBiTree_Detail(tree);
}void LibManage::OutputReaders(){if(reader_list.length<=0) {printf("No reader... \n");return;}for(int i=0;i<reader_list.length;++i)PrintReader(reader_list.readers[i]);
}//the following function is about Readers ManagementStatus LibManage::InitAdjList(AdjList &list){//initialize reader adjacency listif(!(list.readers=(Reader*)malloc(MAXREADERNUM*sizeof(Reader)))) exit(OVER_FLOW);list.length=0; list.size=MAXREADERNUM;return OK;
}Status LibManage::AddReader(AdjList &list, const Reader &newr){//add a new reader to reader listif(list.length>=list.size) {printf("ERROR: System unable to hold more readers... \n");return ERROR;}ReaderCpy(list.readers[list.length++],newr);return OK;
}Status LibManage::AddReaderBook(Reader &r,const ArcBox &ab){//for stimulating a whole library management//no real functionArcBox *abptr=(ArcBox*)malloc(sizeof(ArcBox));if(!abptr) exit(OVER_FLOW);strcpy(abptr->bknum,ab.bknum);strcpy(abptr->bknam,ab.bknam);abptr->return_date=ab.return_date;abptr->next=r.first_arc;r.first_arc=abptr;return OK;
}Status LibManage::SearchReader(AdjList list,int code){//if 'code' exists, then return its index, else return -1int index=0;while(index<list.length&&code!=list.readers[index].code) ++index;if(index<list.length) return index;else return -1;
}Status LibManage::DeleteReader(AdjList &list,int index){while(index<list.length) {ReaderCpy(list.readers[index],list.readers[index+1]);++index;}--list.length;return OK;
}Status LibManage::CheckBorrowPermission(Reader r,BookNum bknum){//if the second parameter 'bknum'=NULL, only check whether the borrower has overdue unreturned book, if he does, return 0, else return 1//if the 'bknum'!=NULL, then check if there has any same book that he has already borrowed. if he does, return 0, else return 1ArcBox *p=r.first_arc;if(!bknum) {while(p&&p->return_date>=current_date)p=p->next;if(p) {printf("No borrow permission: The reader has a book <%s> needs to be returned before %u \n",p->bknam,p->return_date);return 0;}else return 1;}//if(!bknum)else {while(p&&!EQ(bknum,p->bknum))p=p->next;if(p) {printf("No borrow permission: The reader has borrowed a same book <%s>. \n",p->bknam);return 0;}else return 1;}//else
}ArcBox* LibManage::SearchBorrowedBook(Reader r,KeyType bknum,ArcBox* &prep){//if bknum can be found in reader's borrowed list, then return its arcbox's address, else return NULL.//prep return temp's precursor, when it has no precursor, return NULLArcBox *temp=r.first_arc; prep=NULL;while(temp&&!EQ(bknum,temp->bknum)){prep=temp;temp=temp->next;}return temp;
}void LibManage::ReaderCpy(Reader &r1,const Reader &r2){//copy reader's info from r2 to r1strcpy(r1.name,r2.name);strcpy(r1.tele,r2.tele);r1.code=r2.code;r1.first_arc=r2.first_arc;
}void LibManage::PrintReader(const Reader &r){printf("- - - - Reader Info - - - -\n");printf("Name: %s\n",r.name);printf("Code: %0*d\n",MAXREADERCODEDIGIT,r.code);printf("Tele: %s\n",r.tele);PrintBorrowedBooks(r);printf("- - - - - - - - - - - - -\n");
}void LibManage::PrintBorrowedBooks(Reader r){printf("Borrowed books: \n");if(!r.first_arc) printf("\t(Empty) \n");while(r.first_arc) {printf("<%s> | ISBN %s |  Deadline:%u(%s)\n",r.first_arc->bknam,r.first_arc->bknum,r.first_arc->return_date,current_date>r.first_arc->return_date? "![Overdue]!":"[Normal]");r.first_arc=r.first_arc->next;}
}int main(int argc, char *argv[]){LibManage LMSystem;int opt;LMSystem.Menu();do{printf("Menu->Option: ");scanf("%d",&opt);getchar();switch(opt){case 0: break;case 1: LMSystem.AddBook(); break;case 2: LMSystem.LendBook(); break;case 3: LMSystem.ReturnBook(); break;case 4: LMSystem.EraseBook(); break;case 5: LMSystem.OutputBooks(); break;case 6: LMSystem.OutputReaders(); break;case 7: LMSystem.TestMode(); break;default: printf("ERROR: Wrong command, try again... \n"); break;}//switch(opt)}while(opt);return 0;
}

头一次写文章难免有些纰漏，还望各位指正。

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1. 二叉搜索树，平衡二叉树，红黑树的算法效率 ↩︎

2. 艾兹格·W·迪科斯彻 (Edsger Wybe Dijkstra，1930年5月11日~2002年8月6日) ↩︎