數據結構與算法（5）- 棧

1.棧的定義

棧是限定僅在表尾進行插入和刪除的線性表，對錶尾端稱做棧頂，表頭端稱做棧底，不含元素的空表成爲空棧，棧的修改原則是後進先出。

2.順序存儲實現棧

操做相對簡單，因爲在初始化時限定了存儲空間，因此空間侷限性大。

2.1 結構

#define OK 1
#define ERROR 0
#define TRUE 1
#define FALSE 0
#define MAXSIZE 20 /* 存儲空間初始分配量 */
typedef int Status;
typedef int SElemType; /* SElemType類型根據實際狀況而定，這裏假設爲int */
/* 順序棧結構 */
typedef struct
{
    SElemType data[MAXSIZE];
    int top; /* 用於棧頂指針 */
}SqStack;
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2.2基本操做

//1構建一個空棧
Status InitStack(SqStack *S){
    S->top = -1;
    return OK;
}
//2 將棧置空
Status ClearStack(SqStack *S){
    S->top = -1;
    return OK;
}
//3 判斷順序棧是否爲空;
Status StackEmpty(SqStack S){
    if (S.top == -1){
        return TRUE;
    }else{
        return FALSE;
    }
}
//4 返回棧的長度
int StackLength(SqStack S){
    return S.top + 1;
}
//5 獲取棧頂
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爲新棧頂元素
Status PushData(SqStack *S, SElemType e){
    if (S->top == MAXSIZE -1) {
        return ERROR;
    }
    S->top ++;
    S->data[S->top] = e;
    return OK;
}
//7 刪除S棧頂元素,而且用e帶回
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("順序棧中元素爲:\n");
    StackTraverse(S);
    Pop(&S, &e);
    printf("彈出棧頂元素爲: %d\n",e);
    StackTraverse(S);
    printf("是否爲空棧:%d\n",StackEmpty(S));
    GetTop(S, &e);
    printf("棧頂元素:%d \n棧長度:%d\n",e,StackLength(S));
    ClearStack(&S);
    printf("是否已經清空棧 %d, 棧長度爲:%d\n",StackEmpty(S),StackLength(S));
    return 0;
}
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3.鏈式結構實現棧

空間大小不固定，可擴展性強

3.1結構定義

#define OK 1
#define ERROR 0
#define TRUE 1
#define FALSE 0
#define MAXSIZE 20 /* 存儲空間初始分配量 */
typedef int Status;
typedef int SElemType; /* SElemType類型根據實際狀況而定，這裏假設爲int */
/* 鏈棧結構 */
typedef struct StackNode
{
    SElemType data;
    struct StackNode *next;
}StackNode,*LinkStackPtr;
typedef struct
{
    LinkStackPtr top;
    int count;
}LinkStack;
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3.2常規操做

/*1 構造一個空棧S */
Status InitStack(LinkStack *S)
{
    S->top=NULL;
    S->count=0;
    return OK;
}
/*2 把鏈棧S置爲空棧*/
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 判斷是否爲空棧*/
Status StackEmpty(LinkStack S){
    if (S.count == 0)
        return TRUE;
    else
        return FALSE;
}
/*4 返回S的元素個數,即棧的長度*/
int StackLength(LinkStack S){
    return S.count;
}
/*5 若鏈棧S不爲空,則用e返回棧頂元素,並返回OK ,不然返回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到鏈棧S (成爲棧頂新元素)*/
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 若棧不爲空,則刪除S的棧頂元素,用e返回其值.並返回OK,不然返回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("棧中元素依次爲：");
    StackTraverse(s);
    Pop(&s,&e);
    printf("彈出的棧頂元素 e=%d\n",e);
    StackTraverse(s);
    printf("棧空否：%d(1:空 0:否)\n",StackEmpty(s));
    GetTop(s,&e);
    printf("棧頂元素 e=%d 棧的長度爲%d\n",e,StackLength(s));
    ClearStack(&s);
    printf("清空棧後，棧空否：%d(1:空 0:否)\n",StackEmpty(s));
    return 0;
}
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