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：
/*顺序栈*/
#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!\n");
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!\n");
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!\n");
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\n",GetTop(s));
printf("出栈：\n");
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\n");
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\n");
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\n", 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\n", 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\n");
return ;
}
printf("栈中元素[");
while (pStack.top != NULL)
{
printf("%d->", pStack.top->data);
pStack.top = pStack.top->next;
}
printf("]\n");
}
/* 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\n");
flag = 0;
break;
}
}
else if (b[i] == '}')
{
if (visit(a) == '{')
{
pop(a);
}
else
{
printf("No\n");
flag = 0;
break;
}
}
else if (b[i] == ']')
{
if (visit(a) == '[')
{
pop(a);
}
else
{
printf("No\n");
flag = 0;
break;
}
}
else
{
if (visit(a) == '<')
{
pop(a);
}
else
{
printf("No\n");
flag = 0;
break;
}
}
}
}
if (flag == 1)
{
if (top != -1)
{
printf("No\n");
}
else
{
printf("Yes\n");
}
}
flag = 1;
}
}