数据结构与算法分析-第3章

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数据结构与算法分析-第3章

1 第3章-表,栈和队列

1.1 抽象数据类型

  • 抽象数据类型(abstract data type, ADT)是一些操作集合.抽象数据类型是数学的抽象

1.2 表ADT

1.2.1 链表的实现

  • linkedlist.h
#ifndef _LIST_H
#define _LIST_H
struct Node;
typedef struct Node* PtrToNode;
typedef PtrToNode List;
typedef PtrToNode Position;

List MakeEmpty();
int IsEmpty(List L);
int IsLast(Position P, List L);
Position Find(int X, List L);
void Delete(int X, List L);
Position FindPrevious(int X, List L);
void Insert(int X, List L, Position P);
void DeleteList(List L);
Position Header(List L);
Position First(List L);
Position Advance(Position P);
int Reetireve(Position P);
void printLinkedList(List L);
void fromArray(List L, int[], int);

#endif

/* Place in the implementation file  */
struct Node
{
    int Element;
    Position Next;
};
  • linkedlist.c
#include "linkedlist.h"
#include <stdio.h>
#include <stdlib.h>

/* Return true if L is empty */
int
IsEmpty(List L) {
    return L->Next == NULL;
}

List
MakeEmpty() {
    List emptylist;

    emptylist = malloc(sizeof(struct Node));

    if (emptylist == NULL) {
        perror("out of memory");
    }

    return emptylist;
}

/* Return true if P is the last position in list i */
/* Parameter L is unused in this implementation */
int
IsLast(Position P, List L) {
    return P->Next == NULL;
}

/* Return Position of X in L; NULL if not found */
Position
Find(int X, List L) {
    Position P;

    P = L->Next;

    while (P != NULL && P->Element != X) {
        P = P->Next;
    }

    return P;
}


/* Delete first occurrence of X from a list */
/* Assume use of a header Node */
void
Delete(int X, List L) {
    Position P, TmpCell;
    P = FindPrevious(X, L);

    /* Assumption of header use */
    /* X is found; delete it */
    if (!IsLast(P, L)) {
        TmpCell = P->Next;
        /* Bypass deleted cell */
        P->Next = TmpCell->Next;
        free(TmpCell);
    }
}


/* If X is not found, then Next field of returned */
/* Position is NULL */
/* Assume a header */
Position
FindPrevious(int X, List L) {
    Position P;
    P = L;
    while(P->Next != NULL && P->Next->Element != X) {
        P = P->Next;
    }
    return P;
}


/* Insert (after legal position P) */
/* Header implementation assumed */
/* Parameter L is unused in this implementation */
void
Insert(int X, List L, Position P) {
    Position TmpCell;

    TmpCell = malloc(sizeof(struct Node));
    if (TmpCell == NULL) {
        perror("Out of space!!!");
    }

    TmpCell->Element = X;
    TmpCell->Next = P->Next;
    P->Next = TmpCell;
}


/* Correct DeleteList algorithm */
void
DeleteList(List L) {
    Position P, Tmp;

    /* Header assumed */
    P = L->Next;
    L->Next = NULL;
    while(P != NULL) {
        Tmp = P->Next;
        // after free P we can‘t use P
        free(P);
        P = Tmp;
    }
}


Position
Header(List L) {
    return L;
}

Position
First(List L) {
    return L->Next;
}

Position
Advance(Position P) {
    return P->Next;
}

int Retrieve(Position P) {
    return P->Element;
}


void
printLinkedList(List L) {
    // skip header
    Position P = L->Next;
    printf("[ ");
    while (P != NULL) {
        printf("%d ", P->Element);
        P = P->Next;
    }
    printf("]
");
}


void
fromArray(List L, int args[], int size) {
    if (L == NULL) {
        L = MakeEmpty();
    }
    Position P = L;
    Position tmp;
    for (int i = 0; i < size; i++) {
        tmp = malloc(sizeof(struct Node));
        if (tmp == NULL) {
            perror("out of memory");
        }
        tmp->Element = args[i];
        P->Next = tmp;
        P = P->Next;
    }
}

1.2.2 多项式ADT

  • polynomial.h
#ifndef _POLYNOMIAL_H
#define _POLYNOMIAL_H

#define  MaxDegree 1000

/* array way */
typedef struct {
    int CoeffArray[MaxDegree + 1];
    int HighPower;
} * Polynomial;


typedef struct Node *PtrToNode;

struct Node {
    int Cofficient;
    int Exponent;
    PtrToNode Next;
};

/* Nodes sorted by exponent */
/* typedef PtrToNode Polynomial; */

void
ZeroPolynomial(Polynomial Poly);

void
AddPolynomial(const Polynomial Poly1, const Polynomial Poly2, Polynomial PolySum);


void
MultPolynomial(const Polynomial Poly1, const Polynomial Poly2, Polynomial PolyProd);

#endif
  • polynomial.c
#include "polynomial.h"
#include "utils.h"
#include <stdio.h>

void ZeroPolynomial(Polynomial poly) {
    for(int i = 0; i < MaxDegree; i++) {
        poly->CoeffArray[i] = 0;
    }
    poly->HighPower = 0;
}

void
AddPolynomial(const Polynomial Poly1,
              const Polynomial Poly2, const Polynomial PolySum) {
    int i;
    ZeroPolynomial(PolySum);
    PolySum->HighPower = Max(Poly1->HighPower, Poly2->HighPower);

    for(i = PolySum->HighPower; i >= 0; i--) {
        PolySum->CoeffArray[i] = Poly1->CoeffArray[i] + Poly2->CoeffArray[i];
    }
}

void
MultPolynomial(const Polynomial Poly1,
               const Polynomial Poly2, const Polynomial PolyProd) {
    int i, j;
    ZeroPolynomial(PolyProd);
    PolyProd->HighPower = Poly1->HighPower + Poly2->HighPower;

    if (PolyProd->HighPower > MaxDegree) {
        perror("Exceeded array size");
    } else {
        for (int i = 0; i <= Poly1->HighPower; i++) {
            for (int j = 0; j <= Poly2->HighPower; j++) {
                PolyProd->CoeffArray[i + j] +=
                    Poly1->CoeffArray[i] *
                    Poly2->CoeffArray[j];
            }
        }
    }
}

1.2.3 游标实现

  • 游标有一个全局的结构体数组, 数组下标用来代表一个地址.
  • 使用数组来模拟malloc和free.
  • 数组0索引管理着链表的空闲内存.
  • 没有可用空间,将P置为0实现.
  • cursor.h
#ifndef _CURSOR_H
#define _CURSOR_H

#define SpaceSize 13

typedef int PtrToNode;
typedef PtrToNode List;
typedef PtrToNode Position;
typedef int ElementType;

void InitializeCursorSpace(void);

List MakeEmpty(List L);
int IsEmpty(const List L);
int IsLast(const Position P, const List L);
Position Find(ElementType X, List L);
void Delete(ElementType X, List L);
Position FindPrevious(ElementType X, const List L);
void Insert(ElementType X, List L, Position P);
void DeleteList(List L);
Position Header(const List L);
Position First(const List L);
Position Advance(const Position P);
ElementType Retireve(const Position P);
List FromArray(int[], int);
void PrintCursorList(List);

struct Node {
    ElementType Element;
    Position Next;
};

#endif
  • cursor.c
#include "cursor.h"
#include <stdio.h>

/* Place in implementation file */

struct Node CursorSpace[SpaceSize];


static Position
CursorAlloc(void) {
    Position P;

    P = CursorSpace[0].Next;
    CursorSpace[0].Next = CursorSpace[P].Next;

    return P;
}

static void
CursorFree(Position P) {
    CursorSpace[P].Next = CursorSpace[0].Next;
    CursorSpace[0].Next = P;
}

void
InitializeCursorSpace(void) {
    for (int i = 0; i < SpaceSize - 1; i++) {
        CursorSpace[i].Next = i + 1;
    }
    CursorSpace[SpaceSize - 1].Next = 0;
}


List
MakeEmpty(List L) {
    if (IsEmpty(L)) {
        return L;
    }

    Position p = CursorSpace[L].Next;
    Position tmp;
    while(p) {
        tmp = p;
        p = CursorSpace[p].Next;
        CursorFree(tmp);
    }
    return L;
}


/* Return true if L is empty */
int
IsEmpty(List L) {
    return CursorSpace[L].Next == 0;
}

/* Return true if P is the last position in list l */
/* Parameter L is unused in this implementation */
int
IsLast(Position P, List L) {
    return CursorSpace[P].Next == 0;
}

/* Return Position of X in L; 0 if not found */
/* Uses a header node */
Position
Find(ElementType X, List L) {
    Position P;
    P = CursorSpace[L].Next;
    while (P && CursorSpace[P].Element != X) {
        P = CursorSpace[P].Next;
    }
    return P;
}


/* Delete first occurrence of X from a list */
/* Assume use of a header node */
void
Delete(ElementType X, List L) {
    Position P, TmpCell;

    P = FindPrevious(X, L);

    /* Assumption of header use */
    /* X is found; delete it */
    if (!IsLast(P, L)) {
        TmpCell = CursorSpace[P].Next;
        CursorSpace[P].Next = CursorSpace[TmpCell].Next;
        CursorFree(TmpCell);
    }
}


Position
FindPrevious(ElementType X, const List L) {
    Position p, tmp;
    tmp = CursorSpace[L].Next;
    while(tmp && CursorSpace[tmp].Element != X) {
        // record
        p = tmp;
        tmp = CursorSpace[tmp].Next;
    }
    return p;
}


/* Insert (after legal position P) */
/* Header implementation assumed */
/* Parameter L is unused in this implementation */
void
Insert(ElementType X, List L, Position P) {
    Position TmpCell;

    TmpCell = CursorAlloc();
    if (TmpCell == 0) {
        perror("out of memory");
    }
    CursorSpace[TmpCell].Element = X;
    CursorSpace[TmpCell].Next = CursorSpace[P].Next;
    CursorSpace[P].Next = TmpCell;
}


void DeleteList(List L) {
    List head = MakeEmpty(L);
    CursorFree(head);
}

Position
Header(const List L) {
    return L;
}

Position
First(const List L) {
    return CursorSpace[L].Next;
}

Position
Advance(const Position P) {
    return CursorSpace[P].Next;
}

ElementType
Retireve(const Position P) {
    return CursorSpace[P].Element;
}

List
FromArray(int args[], int size) {
    List list = CursorAlloc();
    Position p = list;
    for (int i = 0; i < size; i++) {
        Insert(args[i], list, p);
        p = CursorSpace[p].Next;
    }
    CursorSpace[p].Next = 0;
    return list;
}

void
PrintCursorList(List l) {
    printf("[ ");
    Position p = CursorSpace[l].Next;
    while(p) {
        printf("%d ", CursorSpace[p].Element);
        p = CursorSpace[p].Next;
    }
    printf("]
");
}

1.3 栈ADT

  • FILO(先进后出)
  • 实现方法
    • 指针实现
    • 数组实现

1.3.1 指针实现

#ifndef _STACK_H
#define _STACK_H

struct Node;
typedef struct Node *PtrNode;
typedef PtrNode Stack;
typedef int ElementType;

int IsEmpty(Stack S);
Stack CreateStack(void);
void DisposeStack(Stack S);
void MakeEmpty(Stack S);
void Push(ElementType X, Stack S);
ElementType Top(Stack S);
void Pop(Stack S);

#endif

#include "stackwithlist.h"
#include <stdio.h>
#include <stdlib.h>

struct Node {
    ElementType Element;
    PtrNode Next;
};

int
IsEmpty(Stack S) {
    return S->Next == NULL;
}

Stack CreateStack(void) {
    Stack S;

    S = malloc(sizeof(struct Node));
    if (S == NULL) {
        perror("out of memory");
    }
    S->Next = NULL;
    MakeEmpty(S);
    return S;
}

void
MakeEmpty(Stack S) {
    if (S == NULL) {
        perror("Must use CreateStack first");
    } else {
        while (!IsEmpty(S)) {
            Pop(S);
        }
    }
}

void
Push(ElementType X, Stack S) {
    PtrNode TmpCell;

    TmpCell = malloc(sizeof(struct Node));
    if (TmpCell == NULL) {
        perror("out of memory");
    } else {
        TmpCell->Element = X;
        TmpCell->Next = S->Next;
        S->Next = TmpCell;
    }
}

ElementType
Top(Stack S) {
    if (!IsEmpty(S)) {
        return S->Next->Element;
    }
    printf("empty Stack");
    /* Return value used to avoid warning */
    return 0;
}

void
Pop(Stack S) {
    PtrNode FirstCell;
    if (IsEmpty(S)) {
        perror("Empty Stack");
    } else {
        FirstCell = S->Next;
        S->Next = S->Next->Next;
        free(FirstCell);
    }
}

void
DisposeStack(Stack S) {
    MakeEmpty(S);
    free(S);
}

1.3.2 数组实现

#ifndef _STACKWITHARRAY_H
#define _STACKWITHARRAY_H

struct StackRecord;
typedef struct StackRecord* Stack;
typedef int ElementType;

int IsEmpty(Stack S);
int IsFull(Stack S);
Stack CreateStack(int MaxElements);
void DisposeStack(Stack S) ;
void MakeEmpty(Stack S);
void Push(ElementType X, Stack S);
ElementType Top(Stack S);
void Pop(Stack S);
ElementType TopAndPop(Stack S);

struct StackRecord {
    int Capacity;
    int TopOfStack;
    ElementType *Array;
};

#endif

#include "stackwitharray.h"
#include <stdio.h>
#include <stdlib.h>

#define EmptyTOS (-1)
#define MinStackSize (5)


Stack
CreateStack(int MaxElements) {
    Stack S;

    if (MaxElements < MinStackSize) {
        perror("Stack size is too small");
    }

    S = malloc(sizeof(struct StackRecord));
    if (S == NULL) {
        perror("Out of space!!!");
    }

    S->Array = malloc(sizeof(ElementType) * MaxElements);
    if (S->Array == NULL) {
        perror("Out of space!!!");
    }
    S->Capacity = MaxElements;
    MakeEmpty(S);
    return S;
}

void
DisposeStack(Stack S) {
    if (S != NULL) {
        free(S->Array);
        free(S);
    }
}


int
IsEmpty(Stack S) {
    return S->TopOfStack == EmptyTOS;
}

void
MakeEmpty(Stack S) {
    S->TopOfStack = EmptyTOS;
}


void
Push(ElementType X, Stack S) {
    if (IsFull(S)) {
        perror("Full Stack");
    } else {
        S->Array[++S->TopOfStack] = X;
    }
}

int
IsFull(Stack S) {
    return S->TopOfStack == S->Capacity;
}


ElementType
Top(Stack S) {
    if (!IsEmpty(S)) {
        return S->Array[S->TopOfStack];
    }
    perror("Empty Stack");
    /* Return value used to avoid warning */
    return 0;
}

void
Pop(Stack S) {
    if (IsEmpty(S)) {
        perror("Empty Stack");
    } else {
        S->TopOfStack--;
    }
}


ElementType
TopAndPop(Stack S) {
    if (!IsEmpty(S)) {
        return S->Array[S->TopOfStack--];
    }
    perror("Empty Stack");
    /* Return value used to avoid warning */
    return 0;
}

1.4 队列ADT

  • FIFO(先进先出)

1.4.1 数组实现方式

  • queuewitharray.h
#ifndef _QUEUEWITHARRAY_H
#define _QUEUEWITHARRAY_H

struct QueueRecord;
typedef struct QueueRecord *Queue;
typedef int ElementType;

int IsEmpty(Queue Q);
int IsFull(Queue Q);
Queue CreateQueue(int MaxElements);
void DisposeQueue(Queue Q);
void MakeEmpty(Queue Q);
void Enqueue(ElementType X, Queue Q);
ElementType Front(Queue Q);
void Dequeue(Queue Q);
ElementType FrontAndDequeue(Queue Q);

/* Queue implementation is a dynamically allocated array */
#define MinQueueSize (5)
struct QueueRecord {
    int Capacity;
    int Front;
    int Rear;
    int Size;
    ElementType *Array;
};

#endif
  • queuewitharray.c
#include <stdio.h>
#include <stdlib.h>
#include "queuewitharray.h"


int
IsEmpty(Queue Q) {
    return Q->Size == 0;
}

int
IsFull(Queue Q) {
    return Q->Size == Q->Capacity;
}

Queue
CreateQueue(int MaxElements) {
    Queue Q;
    Q = malloc(sizeof(Queue));
    if (Q == NULL) {
        perror("create Queue failed!!!");
    }
    Q->Array = malloc(sizeof(ElementType)*MaxElements);
    if (Q->Array == NULL) {
        perror("create Array failed!!!");
    }
    Q->Capacity = MaxElements;
    MakeEmpty(Q);
    return Q;
}

void
DisposeQueue(Queue Q) {
    free(Q->Array);
    free(Q);
}

void
MakeEmpty(Queue Q) {
    Q->Size = 0;
    Q->Front = 1;
    Q->Rear = 0;
}

static int
Succ(int Value, Queue Q) {
    if (++Value == Q->Capacity) {
        Value = 0;
    }
    return Value;
}

void
Enqueue(ElementType X, Queue Q) {
    if (IsFull(Q)) {
        perror("Full queue");
    } else {
        Q->Size++;
        Q->Rear = Succ(Q->Rear, Q);
        Q->Array[Q->Rear] = X;
    }
}

ElementType
Front(Queue Q) {
    return Q->Array[Q->Front];
}

void
Dequeue(Queue Q) {
    if (IsEmpty(Q)) {
        perror("Empty Queue!!!");
    }
    Q->Size--;
    Q->Front = Succ(Q->Front, Q);
}

ElementType
FrontAndDequeue(Queue Q) {
    if (IsEmpty(Q)) {
        perror("Empty Queue!!!");
    }
    Q->Size--;
    ElementType res = Q->Array[Q->Front];
    Q->Front = Succ( Q->Front, Q );
    return res;
}

1.4.2 链表实现方式

  • queuewithlist.h
#ifndef _QUEUEWITHLIST_H
#define _QUEUEWITHLIST_H

struct Queue;
struct Node;
typedef struct Node* Pnode;
typedef struct QueueRecord *Queue;
typedef int ElementType;

int IsEmpty(Queue Q);
Queue CreateQueue();
void DisposeQueue(Queue Q);
void Enqueue(ElementType X, Queue Q);
ElementType Front(Queue Q);
void Dequeue(Queue Q);
ElementType FrontAndDequeue(Queue Q);

struct QueueRecord {
    Pnode Front;
    Pnode Rear;
    int Size;
};

struct Node {
    ElementType Element;
    struct Node *Next;
};

#endif
  • queuewithlist.c
#include "queuewithlist.h"
#include <stdio.h>
#include <stdlib.h>


int
IsEmpty(Queue Q) {
    return Q->Size == 0;
}

Queue
CreateQueue() {
    Queue Q;
    Q = malloc(sizeof(struct QueueRecord));
    if (Q == NULL) {
        perror("create queue fail!!!");
    }
    Q->Size = 0;
    Q->Front = malloc(sizeof(struct Node));
    if (Q->Front == NULL) {
        printf("create front fail");
        exit(-1);
    }
    Q->Rear = Q->Front;
    Q->Front->Next = NULL;
    printf("创建队列成功
");
    return Q;
}

void
DisposeQueue(Queue Q) {
    Pnode n = Q->Front;
    Pnode tmp = n;
    while (n != NULL) {
        tmp = n->Next;
        free(n);
        n = tmp;
    }
    free(Q);
    printf("销毁队列成功
");
}


void
Enqueue(ElementType X, Queue Q) {
    Pnode P;
    P = malloc(sizeof(struct Node));
    if (P == NULL) {
        printf("create node fail");
        exit(-1);
    }
    P->Element = X;
    P->Next = Q->Rear->Next;
    Q->Rear->Next = P;
    Q->Rear = Q->Rear->Next;
    Q->Size++;
}

void
Dequeue(Queue Q) {
    if (IsEmpty(Q)) {
        printf("Empty Queue!!!");
        exit(-1);
    }
    Q->Front = Q->Front->Next;
    Q->Size--;
}

ElementType
FrontAndDequeue(Queue Q) {
    if (IsEmpty(Q)) {
        printf("Empty Queue!!!");
        exit(-1);
    }
    ElementType res = Q->Front->Element;
    Q->Front = Q->Front->Next;
    Q->Size--;
    return res;
}

Date: 2018-11-17 11:45

Author: devinkin

Created: 2018-11-17 六 11:47

Validate

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