数据结构——栈

定义

限定仅在表尾进行插入和删除操作的线性表。（先入后出）

顺序结构

C定义
[cpp]
#define MAXSIZE 20

#pragma mark 顺序栈

typedef int SElemType;
typedef struct {
    SElemType data[MAXSIZE];
    int top;
}SqStack;

#define MAXSIZE 20

#pragma mark 顺序栈

typedef int SElemType;
typedef struct {
SElemType data[MAXSIZE];
int top;
}SqStack;

压栈操作
[cpp]
int Push(SqStack *S, SElemType e)
{
    if (S->top == MAXSIZE -1)
        return 0;
    S->data[++S->top] = e;
    return 1;
}

int Push(SqStack *S, SElemType e)
{
    if (S->top == MAXSIZE -1)
        return 0;
    S->data[++S->top] = e;
    return 1;
}

弹栈操作
[cpp]
int Pop(SqStack *S, SElemType *e)
{
    if (S->top == -1)
        return 0;
    *e = S->data[S->top--];
    return 1;
}

int Pop(SqStack *S, SElemType *e)
{
    if (S->top == -1)
        return 0;
    *e = S->data[S->top--];
    return 1;
}

共享栈

共享栈可以看做是两个顺序栈倒下，栈尾相对的数据结构。通常在两个栈空间需求有相反关系时使用，例如买入就要卖出等等。

C定义
[cpp]
typedef struct {
    SElemType data[MAXSIZE];
    int top1;
    int top2;
}SqDoubleStack;

typedef struct {
    SElemType data[MAXSIZE];
    int top1;
    int top2;
}SqDoubleStack;

压栈
[cpp]
int PushDouble(SqDoubleStack *S, SElemType e, int stackNumber)
{
    //栈满
    if (S->top1 + 1 == S->top2)
        return 0;
    if (stackNumber == 1)
        S->data[++S->top1] = e;
    else if (stackNumber == 2)
        S->data[--S->top2] = e;
    return 1;
}

int PushDouble(SqDoubleStack *S, SElemType e, int stackNumber)
{
    //栈满
    if (S->top1 + 1 == S->top2)
        return 0;
    if (stackNumber == 1)
        S->data[++S->top1] = e;
    else if (stackNumber == 2)
        S->data[--S->top2] = e;
    return 1;
}

弹栈
[cpp]
int PopDouble(SqDoubleStack *S, SElemType *e, int stackNumber)
{
    if (stackNumber == 1)
        if (S->top1 == -1)
            return 0;
        *e = S->data[S->top1--];
    if (stackNumber == 2)
        if (S->top2 == MAXSIZE)
            return 0;
        *e = S->data[S->top2++];
    return 1;
}

int PopDouble(SqDoubleStack *S, SElemType *e, int stackNumber)
{
    if (stackNumber == 1)
        if (S->top1 == -1)
            return 0;
        *e = S->data[S->top1--];
    if (stackNumber == 2)
        if (S->top2 == MAXSIZE)
            return 0;
        *e = S->data[S->top2++];
    return 1;
}

链栈

栈的链式存储结构类似于线性表中的链式存储结构。

C定义
[cpp]
typedef struct StackNode{
    SElemType data;
    struct StackNode *next;
}StackNode, *LinkStackPtr;

typedef struct LinkStack{
    LinkStackPtr top;
    int count;
}LinkStack;

typedef struct StackNode{
SElemType data;
struct StackNode *next;
}StackNode, *LinkStackPtr;

typedef struct LinkStack{
LinkStackPtr top;
int count;
}LinkStack;

压栈
[cpp]
int PushLink(LinkStack *S,SElemType e)
{
    LinkStackPtr p = (LinkStackPtr)malloc(sizeof(StackNode));
    p->data = e;
    p->next = S->top;
    S->top = p;
    S->count++;
    return 1;
}

int PushLink(LinkStack *S,SElemType e)
{
    LinkStackPtr p = (LinkStackPtr)malloc(sizeof(StackNode));
    p->data = e;
    p->next = S->top;
    S->top = p;
    S->count++;
    return 1;
}

弹栈
[cpp]
int PopLink(LinkStack *S,SElemType *e)
{
    LinkStackPtr p;
    *e = S->top->data;
    p = S->top;
    S->top = S->top->next;
    free(p);
    S->count--;
    return 1;
}

int PopLink(LinkStack *S,SElemType *e)
{
    LinkStackPtr p;
    *e = S->top->data;
    p = S->top;
    S->top = S->top->next;
    free(p);
    S->count--;
    return 1;
}

对比顺序栈和链栈

两个数据结构操作都不复杂，时间复杂度相同为O(1)。
顺序栈需要固定的长度，但是存取时定位方便。
链栈要求有指针域，因此需要增加一些内存开销，但不同于顺序栈限制长度。

栈的应用 —— 递归
例如比较有名的斐波那契数列：
[cpp]
int Fbi(int i)
{
    if (i < 2)
        return i == 0? 0: 1;
    return Fbi(i - 1) + Fbi(i - 2);
}

int Fbi(int i)
{
    if (i < 2)
        return i == 0? 0: 1;
    return Fbi(i - 1)

补充：软件开发 , C++ ,