栈

1.栈的概念

栈（stack）又名堆栈，它是一种运算受限的线性表。限定仅在表尾进行插入和删除操作的线性表。这一端被称为栈顶，相对地，把另一端称为栈底。向一个栈插入新元素又称作进栈、入栈或压栈，它是把新元素放到栈顶元素的上面，使之成为新的栈顶元素；从一个栈删除元素又称作出栈或退栈，它是把栈顶元素删除掉，使其相邻的元素成为新的栈顶元素。

2.栈的特性："先进后出，后进先出"。

（1）顺序栈代码：

#include<bits/stdc++.h>
using namespace std;
typedef struct snode
{
    int data[105];
    int top;
}SeqStack;
void Init(SeqStack *s)    //置空栈
{
    s->top=-1;
}
int EmptyStack(SeqStack *s)  //判断栈是否为空
{
    if(s->top<0)
        return 1;   //为空返回1
    else
        return 0;
}
int Push(SeqStack *s,int x)   //将x进栈
{
    if(s->top>=105)
    {
        printf("overflow!
");
        return 0;
    }
    s->top++;
    s->data[s->top]=x;
    return 1;
}
int Pop(SeqStack *s)     //出栈
{
    int x;
    if(s->top<0)
    {
        printf("underflow!
");
        return 0;
    }
    x=s->data[s->top];
    s->top--;
    return x;
}
int GetTop(SeqStack *s)   //取栈顶元素
{
    if(s->top<0)
    {
        printf("underflow!
");
        exit(0);

    }
    return(s->data[s->top]);
}
int main()
{
  SeqStack *s;
  s=(SeqStack *)malloc(sizeof(SeqStack));
  s->top=-1;
  for(int i=1;i<=10;i++)
  {
      Push(s,i);
  }
  printf("栈顶元素%d
",GetTop(s));
  printf("出栈：
");
  for(int i=1;i<=10;i++)
  {
     printf("%d ",Pop(s));
  }
}

（2）链式栈：

#include <stdio.h>
#include <stdlib.h>
#define Empty 0        /* 栈空 */
#define Avail 1        /* 栈可用 */

typedef struct SNode
{
    int data;
    struct SNode *next;
}StackNode;
typedef struct LStack
{
    StackNode *top;        /* 栈顶指针 */
    StackNode *bottom;    /* 栈底指针 */
    int height;            /* 链式栈高度 */
}LinkStack;

LinkStack InitStack (LinkStack pStack);    /* 栈顶指针、栈底指针、栈高度初始化*/
LinkStack Push (LinkStack pStack);        /* 入栈 */
LinkStack Pop (LinkStack pStack);        /* 出栈 */
int StackEmpty (LinkStack pStack);        /* 判断栈是否为空 */
LinkStack DeletStack (LinkStack pStack);/* 清空栈 */
void DisplyStack (LinkStack pStack);    /* 遍历栈----自顶至底*/

int main()
{
    LinkStack p;
    char ch;

    p.height = 0;        /* 栈高度初始化为零 */
    p = InitStack (p); /* 栈初始化 */
    printf("Do you want to push stack(Y/N)?");
    scanf(" %c", &ch); 
    while (ch == 'Y' || ch == 'y')
    {
        p = Push(p);    /* 入栈 */
        DisplyStack(p);    /* 遍历栈 */
        printf("Do you want to push stack(Y/N)?");
        scanf(" %c", &ch); 
    }
    printf("Do you want to pop stack(Y/N)?");
    scanf(" %c", &ch);
    while (ch == 'Y' || ch == 'y')
    {
        p = Pop(p);        /* 出栈 */
        DisplyStack(p);    /* 遍历栈 */
        printf("Do you want to pop stack(Y/N)?");
        scanf(" %c", &ch);
    }

    return 0;
}
/* Function: 初始化栈顶、栈底、栈高度*/
LinkStack InitStack (LinkStack pStack)
{
    pStack.top = pStack.bottom = NULL;
    pStack.height = 0;

    return pStack;
}

/* Function: 判断栈是否为空 */
int StackEmpty (LinkStack pStack)
{
    if (pStack.top == NULL && pStack.bottom == NULL)
    {
        return Empty;
    }
    else
    {
        return Avail;
    }
}

/* Function: 入栈 */
LinkStack Push (LinkStack pStack)
{
    int data;
    StackNode *temp;

    if ((temp = (StackNode *)malloc(sizeof(StackNode))) == NULL)
    {
        printf("内存空间不足
");
        return pStack;
    }
    if (StackEmpty(pStack) == Empty)    /* 如果栈为空 */
    {
        pStack.top = pStack.bottom = temp;    /* 栈顶、栈底指针都指向新建节点 */
        temp->next = NULL;                /* 节点指针域为空 */
        printf("Please input data");
        scanf("%d", &data);
        pStack.top->data = data;
        pStack.height++;

        return pStack;
    }
    else        /* 栈不为空 */
    {
        temp->next = pStack.top;/* 新建节点指向原来的栈顶 */
        pStack.top = temp;        /* 栈顶指针指向新建节点 */
        printf("Please input data");
        scanf("%d", &data);
        pStack.top->data = data;
        pStack.height++;

        return pStack;
    }
}

/* Function: 出栈 */
LinkStack Pop (LinkStack pStack)
{
    StackNode *Second;

    
    if (StackEmpty(pStack) == Empty)    /* 判断栈是否为空 */
    {
        printf("栈为空，无法出栈
");
        return pStack;
    }
    if (pStack.top == pStack.bottom)    /* 如果出栈的元素为最后一个元素 */
    {
        printf("出栈元素为%d
", pStack.top->data);
        free(pStack.top);
        pStack.top = pStack.bottom = NULL; /* 栈顶、栈底都指针都置为空 */
        pStack.height--;

        return pStack;
    }
    printf("出栈元素为%d
", pStack.top->data);
    Second = pStack.top->next;    /* 指向栈顶的前一个元素*/

    free(pStack.top);    /* 释放栈顶节点 */
    pStack.top = Second;/* 将头指针移动到新的栈顶节点 */
    pStack.height--;

    return pStack;
}

/* Function: 遍历栈 自顶到底*/
void DisplyStack (LinkStack pStack)
{
    if (StackEmpty(pStack) == Empty)
    {
        printf("栈为空，无法遍历
");
        return ;
    }
    printf("栈中元素[");
    while (pStack.top != NULL)
    {
        printf("%d->", pStack.top->data);
        pStack.top = pStack.top->next;
    }
    printf("]
");
}

/* Function: 清空栈 */
LinkStack DeletStack (LinkStack pStack)
{
    StackNode *del;

    while (pStack.top != NULL)
    {
        del = pStack.top->next;    /* 栈顶节点的前一个节点 */
        free(pStack.top);        /* 释放节点 */
        pStack.top = del;        /* 栈顶指针移动到新栈顶 */
    }

    return pStack;
}

括号匹配：

#include <stdio.h>
#include <string.h>
int top = -1;
void push(char *a, char ch)
{
    a[++top] = ch;
}
void pop(char *a)
{
    if (top == -1)
        return;
    top--;
}
char visit(char *a)
{
    if (top != -1)
    {
        return a[top];
    }
    else
    {
        return ' ';
    }
}
int main()
{
    char a[30];
    char b[100];
    int n;
    int flag = 1;
    scanf("%d", &n);
 
    while (n--)
    {
        top = -1;
        scanf("%s", b);
        getchar();
 
        int len = (int)strlen(b);
        for (int i = 0; i < len; i++)
        {
            if (b[i] == '(' || b[i] == '{' || b[i] == '[' || b[i] == '<')
            {
                push(a, b[i]);
            }
            else
            {
                if (b[i] == ')')
                {
                    if (visit(a) == '(')
                    {
                        pop(a);
                    }
                    else
                    {
                        printf("No
");
                        flag = 0;
                        break;
                    }
                }
                else if (b[i] == '}')
                {
                    if (visit(a) == '{')
                    {
                        pop(a);
                    }
                    else
                    {
                        printf("No
");
                        flag = 0;
                        break;
                    }
                }
                else if (b[i] == ']')
                {
                    if (visit(a) == '[')
                    {
                        pop(a);
                    }
                    else
                    {
                        printf("No
");
                        flag = 0;
                        break;
                    }
                }
                else
                {
                    if (visit(a) == '<')
                    {
                        pop(a);
                    }
                    else
                    {
                        printf("No
");
                        flag = 0;
                        break;
                    }
                }
            }
        }
        if (flag == 1)
        {
            if (top != -1)
            {
                printf("No
");
            }
            else
            {
                printf("Yes
");
            }
        }
        flag = 1;
    }
}