栈及其相关操作

栈简要提点

• 栈(stack)是一个后进先出(LIFO, last in first out)的表，限制在栈顶位置对元素插入和删除。
• 栈的基本操作主要有：Push(进栈)、Pop(出栈)。
• 栈主要有两种实现方式：链表和数组。

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栈的链表实现

• 说明：利用带头指针的单链表实现：指定头指针为栈顶，入栈和出栈操作头指针及其后面的元素。

代码实现(C/C++)

#include<iostream>

using namespace std;
typedef int ElemType;

typedef struct Node {
    ElemType date;
    Node *next;
}*Stack;

void initStack(Stack St)            // 把头节点看作是栈顶
{
    St->next = nullptr;
}

int isEmpty(Stack St)              // 判断栈是否为空
{
    return St->next == nullptr;
}

void Push(Stack St, ElemType x)     // 每次从将元素插入到头节点的位置，头节点上移
{
    Node* q = new Node;
    q->date = x;
    q->next = St->next;     // q的next域指向St(头节点)的后继结点
    St->next = q;           // St(头节点/栈顶)next域指向q，实现栈往上移
}

void Pop(Stack St)      // 出栈
{
    Node* p = St->next;     // 临时结点指向头结点(栈顶)的后继结点
    St->next = p->next;     // 栈顶下移
    delete p;           // 释放空间
}

ElemType Top(Stack St)      // 取栈顶元素
{
    return St->next->date;  
}

void destroyStack(Stack St)     // 销毁栈
{
    while (St->next)
        Pop(St);
}

void print(Stack St)        // 打印栈
{
    Node *p = St->next;
    cout << "Now the Stack contents: " << endl;
    while (p)
    {
        cout << p->date << " ";
        p = p->next;
    }
    cout << endl;
}
int main()
{
    const ElemType date[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
    Stack myStack = new Node;
    initStack(myStack);     // 初始化栈
    if (isEmpty(myStack))
        cout << "Empty Stack, now Push some values... " << endl;
    for (int i = 0;i < 9;i++)
    {
        Push(myStack, date[i]);
    }
    print(myStack);
    cout << "Push a number to the Stack: \n";
    ElemType number;
    cin >> number;
    Push(myStack, number);
    print(myStack);
    cout << "Pop twice from the Stack...\n";
    Pop(myStack);
    Pop(myStack);
    cout << "The Top of the Stack now is: " << Top(myStack)<< endl;
    cout << "Destroy the Stack..." << endl;
    delete myStack;
    system("pause");
    return 0;
}

运行操作结果

Empty Stack, now Push some values...
Now the Stack contents:
9 8 7 6 5 4 3 2 1
Push a number to the Stack:
13
Now the Stack contents:
13 9 8 7 6 5 4 3 2 1
Pop twice from the Stack...
The Top of the Stack now is: 8
Destroy the Stack...

---

栈的数组实现

#include<iostream>

using namespace std;
typedef int ElemType;
const int MAXSIZE = 50;     // 设置栈的最大容量

typedef struct {
    int stacksize;
    int top;
    ElemType elemList[MAXSIZE];
}Stack;

Stack initStack()       // 初始化栈
{
    Stack St;
    St.top = 0;
    St.stacksize = 0;
    return St;
}

int isEmpty(Stack St)       // 判断栈是否为空
{
    return St.top == 0;
}

int isFull(Stack St)        // 判断栈是否满
{
    return St.top == MAXSIZE;
}

void Push(Stack &St, ElemType x)        // 入栈，St状态被改变，故要传引用
{
    St.elemList[St.top++] = x;
    St.stacksize++;
}

ElemType Pop(Stack &St)     // 出栈，St状态被改变，故要传引用
{
    St.stacksize--;
    return St.elemList[--St.top];
}

ElemType Top(Stack St)      // 取栈顶元素
{
    return St.elemList[St.top - 1];
}

void print(Stack St)        // 打印栈
{
    cout << "Now the Stack contents: " << endl;
    for (int i = St.stacksize-1;i >= 0;i--)
    {
        cout << St.elemList[i]<<" ";
    }
    cout << endl;
}

int main()
{
    const ElemType date[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
    Stack myStack = initStack();        // 初始化栈
    if (isEmpty(myStack))
        cout << "Empty Stack, now Push some values... " << endl;
    for (int i = 0;i < 9;i++)
    {
        Push(myStack, date[i]);
    }
    print(myStack);

    cout << "Push a number to the Stack: \n";
    ElemType number;
    cin >> number;
    Push(myStack, number);
    print(myStack);
    cout << "Pop twice from the Stack...\n";
    Pop(myStack);
    Pop(myStack);
    cout << "The Top of the Stack now is: " << Top(myStack) << endl;
    cout << "Destroy the Stack..." << endl;

    system("pause");
    return 0;
}

运行操作结果

Empty Stack, now Push some values...
Now the Stack contents:
9 8 7 6 5 4 3 2 1
Push a number to the Stack:
13
Now the Stack contents:
13 9 8 7 6 5 4 3 2 1
Pop twice from the Stack...
The Top of the Stack now is: 8
Destroy the Stack...