数据结构与算法（5）- 栈

1.栈的定义

栈是限定仅在表尾进行插入和删除的线性表，对表尾端称作栈顶，表头端称作栈底，不含元素的空表成为空栈，栈的修改原则是后进先出。

2.顺序存储实现栈

操作相对简单，由于在初始化时限定了存储空间，所以空间局限性大。

2.1 结构

#define OK 1
#define ERROR 0
#define TRUE 1
#define FALSE 0
#define MAXSIZE 20 /* 存储空间初始分配量 */
typedef int Status;
typedef int SElemType; /* SElemType类型根据实际情况而定，这里假设为int */
/* 顺序栈结构 */
typedef struct
{
    SElemType data[MAXSIZE];
    int top; /* 用于栈顶指针 */
}SqStack;

2.2基本操作

//1构建一个空栈
Status InitStack(SqStack *S){
    S->top = -1;
    return OK;
}
//2 将栈置空
Status ClearStack(SqStack *S){
    S->top = -1;
    return OK;
}
//3 判断顺序栈是否为空;
Status StackEmpty(SqStack S){
    if (S.top == -1){
        return TRUE;
    }else{
        return FALSE;
    }
}
//4 返回栈的长度
int StackLength(SqStack S){
    return S.top + 1;
}
//5 获取栈顶
Status GetTop(SqStack S,SElemType *e){
    if (S.top == -1){
        return ERROR;
    }else{
        *e = S.data[S.top];
    }
    return OK;
}
//6 插入元素e为新栈顶元素
Status PushData(SqStack *S, SElemType e){
    if (S->top == MAXSIZE -1) {
        return ERROR;
    }
    S->top ++;
    S->data[S->top] = e;
    return OK;
}
//7 删除S栈顶元素,并且用e带回
Status Pop(SqStack *S,SElemType *e){
    if (S->top == -1) {
        return ERROR;
    }
    *e = S->data[S->top];
    S->top--;
    return OK;
}
int main(int argc, const char * argv[]) {
    SqStack S;
    int e;
    if (InitStack(&S) == OK) {
        for (int j = 1 ; j < 10; j++) {
            PushData(&S, j);
        }
    }
    printf("顺序栈中元素为:\n");
    StackTraverse(S);
    Pop(&S, &e);
    printf("弹出栈顶元素为: %d\n",e);
    StackTraverse(S);
    printf("是否为空栈:%d\n",StackEmpty(S));
    GetTop(S, &e);
    printf("栈顶元素:%d \n栈长度:%d\n",e,StackLength(S));
    ClearStack(&S);
    printf("是否已经清空栈 %d, 栈长度为:%d\n",StackEmpty(S),StackLength(S));
    return 0;
}

3.链式结构实现栈

空间大小不固定，可扩展性强

3.1结构定义

#define OK 1
#define ERROR 0
#define TRUE 1
#define FALSE 0
#define MAXSIZE 20 /* 存储空间初始分配量 */
typedef int Status;
typedef int SElemType; /* SElemType类型根据实际情况而定，这里假设为int */
/* 链栈结构 */
typedef struct StackNode
{
    SElemType data;
    struct StackNode *next;
}StackNode,*LinkStackPtr;
typedef struct
{
    LinkStackPtr top;
    int count;
}LinkStack;

3.2常规操作

/*1 构造一个空栈S */
Status InitStack(LinkStack *S)
{
    S->top=NULL;
    S->count=0;
    return OK;
}
/*2 把链栈S置为空栈*/
Status ClearStack(LinkStack *S){
    LinkStackPtr p,q;
    p = S->top;
    while (p) {
        q = p;
        p = p->next;
        free(q);
    }
    S->count = 0;
    return OK;
}
/*3 判断是否为空栈*/
Status StackEmpty(LinkStack S){
    if (S.count == 0)
        return TRUE;
    else
        return FALSE;
}
/*4 返回S的元素个数,即栈的长度*/
int StackLength(LinkStack S){
    return S.count;
}
/*5 若链栈S不为空,则用e返回栈顶元素,并返回OK ,否则返回ERROR*/
Status GetTop(LinkStack S,SElemType *e){
    if(S.top == NULL)
        return ERROR;
    else
        *e = S.top->data;
    return OK;
}
/*6 插入元素e到链栈S (成为栈顶新元素)*/
Status Push(LinkStack *S, SElemType e){
    LinkStackPtr temp = (LinkStackPtr)malloc(sizeof(StackNode));
    temp->data = e;
    temp->next = S->top;
    S->top = temp;
    S->count++;
    return OK;
}
/*7 若栈不为空,则删除S的栈顶元素,用e返回其值.并返回OK,否则返回ERROR*/
Status Pop(LinkStack *S,SElemType *e){
    LinkStackPtr p;
    if (StackEmpty(*S)) {
        return ERROR;
    }
    *e = S->top->data;
    p = S->top;
    S->top= S->top->next;
    free(p);
    S->count--;
    return OK;
}
int main(int argc, const char * argv[]) {
    int j;
    LinkStack s;
    int e;
    if(InitStack(&s)==OK)
        for(j=1;j<=10;j++)
            Push(&s,j);
    printf("栈中元素依次为：");
    StackTraverse(s);
    Pop(&s,&e);
    printf("弹出的栈顶元素 e=%d\n",e);
    StackTraverse(s);
    printf("栈空否：%d(1:空 0:否)\n",StackEmpty(s));
    GetTop(s,&e);
    printf("栈顶元素 e=%d 栈的长度为%d\n",e,StackLength(s));
    ClearStack(&s);
    printf("清空栈后，栈空否：%d(1:空 0:否)\n",StackEmpty(s));
    return 0;
}