堆栈

一、堆栈的链式存储

#include<stdio.h>
#include<stdlib.h>
#include<string.h>

struct Node{
    int data;
    struct Node* next;
}; 
typedef struct Node* Stack;

int IsEmpty(Stack S);
Stack CreateStack();
void MakeEmpty(Stack S);
void Push(Stack S);
int Top(Stack S);
void Pop(Stack S);
int TopAndPop(Stack S); 

int IsEmpty(Stack S)
{
    return S->next==NULL; 
}

void MakeEmpty(Stack S)
{
    if(S==NULL) printf("Must use create first!!!
");
    while(S!=NULL)
    {
        Pop(S);
    }
}

Stack CreateStack()
{
    Stack S=(Stack)malloc(sizeof(struct Node));
    if(S==NULL) printf("Out of Space!!!
");
    S->next=NULL;
    if(!IsEmpty(S)) Pop(S);
    return S;
}

void Push(int x,Stack S)
{
    Stack tp=(Stack)malloc(sizeof(struct Node));
    if(tp==NULL) printf("Out of Space!!!
");
    tp->data=x;
    tp->next=S->next;
    S->next=tp;
}

void Pop(Stack S)
{
    Stack tp=S->next;
    S->next=tp->next;
    free(tp);
}

int Top(Stack S)
{
    return S->next->data;
}

int main(void)
{
    int n,i,x;
    Stack S=CreateStack(),p;
    scanf("%d",&n);
    for(i=0;i<n;i++)
    {
        scanf("%d",&x);
        Push(x,S);
    }
    while(!IsEmpty(S))
    {
        printf("%d ",Top(S));
        Pop(S);
    }
    return 0;
}

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复杂度：O(n)，线性，所以效率很高，但要对内存是否合法进行判断。

二、堆栈的顺序存储

#include<stdio.h>
#include<string.h>
#include<stdlib.h>

const int maxn = 1200;
const int EmptyTOS = -1;

struct Node{
    int TopOfStack,Capcity;
    int *array;
};
typedef struct Node* Stack;

int IsEmpty(Stack S);
int IsFull(Stack S);
Stack CreateStack(int size);
void MakeEmpty(Stack S);
int Top(Stack S);
void Push(int x,Stack S);
void Pop(Stack S);

void MakeEmpty(Stack S)
{
    S->TopOfStack=EmptyTOS;
}

int IsEmpty(Stack S)
{
    return S->TopOfStack==EmptyTOS;
}

int IsFull(Stack S)
{
    return S->TopOfStack==S->Capcity-1;
}

Stack CreateStack(int size)
{
    Stack S;
    if(size>maxn)
    {
        printf("Stack is too small");
        return NULL;
    }
    S=(Stack)malloc(sizeof(struct Node));
    if(S==NULL) printf("Out of Space!!!");
    S->array=(int*)malloc(sizeof(int)*size);
    if(S->array==NULL)
    printf("Out of Space!!!
");
    S->Capcity=size;
    MakeEmpty(S); 
    return S;
}

void Push(int x,Stack S)
{
    if(IsFull(S)) printf("the stack is full");
    S->array[++S->TopOfStack]=x;
}

int Top(Stack S)
{
    if(!IsEmpty(S))
    return S->array[S->TopOfStack];
}

void Pop(Stack S)
{
    if(IsEmpty(S)) printf("the stack if empty");
    else S->TopOfStack--;
}

int main(void)
{
    int n,i,x;
    
    scanf("%d",&n);
    Stack S=CreateStack(n);
    while(n--)
    {
        scanf("%d",&x);
        Push(x,S);
    }
    while(!IsEmpty(S))
    {
        printf("%d ",Top(S));
        Pop(S);
    }
    return 0;
}

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要注意堆栈空和满的时候并且分配内存给数组。

三、堆栈的应用

1、平衡符号

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;

struct Node{
    char data;
    struct Node* next;
};
typedef struct Node* Stack;

int IsEmpty(Stack S)
{
    return S->next==NULL;
}

void Push(char x,Stack S)
{
    Stack tp=(Stack)malloc(sizeof(struct Node));
    tp->data=x;
    tp->next=S->next;
    S->next=tp;
}

void Pop(Stack S)
{
    if(IsEmpty(S)) printf("stack is empty");
    Stack tp=S->next;
    S->next=tp->next;
    free(tp);
}

char Top(Stack S)
{
    return S->next->data;
}

void MakeEmpty(Stack S)
{
    if(!IsEmpty(S))
    {
        Pop(S);
    }
}

Stack CreateStack()
{
    Stack S;
    S=(Stack)malloc(sizeof(struct Node));
    if(S==NULL) printf("Out of Space!!!");
    S->next=NULL;
    MakeEmpty(S);
    return S;
}

int main(void)
{
    int n,i,fg=0,len;
    char str[120],ch;
    Stack S=CreateStack();
    gets(str);
    len=strlen(str);
    for(i=0;i<len;i++)
    {
        if(!IsEmpty(S)) ch=Top(S);
        if(str[i]=='(') Push(str[i],S);
        else if(str[i]==')')
        {
            if(ch==')') Pop(S);
        }
        else if(str[i]=='{') Push(str[i],S);
        else if(str[i]=='}')
        {
            if(ch=='{') Pop(S);
        }
        else if(str[i]=='[') Push(str[i],S);
        else if(str[i]==']')
        {
            if(ch=='[') Pop(S);
        }
        
        if(fg) break;
    }
    if(fg) printf("No
");
    else printf("Yes
");
    return 0;
}

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2、中缀表达式转后缀表达式

要求：如果表达式中带有'+' , '-' , '*' ,' /' , '(' , ')'，这六种符号和0--9的实数，将他们的中缀表达式转换为后缀表达式。

（1）如果是数字0--9，就直接输出

（2）如果是符号‘(’，就让它直接入栈

（3）如果是符号‘)’，就让找到‘(’，并且在找到之前输出栈中的符号（因为括号内的元素要先进行运算，并且不用考虑优先级的先后，因为之前入栈前已经考虑过了）

（4）如果是加减乘除四种运算符号，就在栈中找到比即将进栈元素优先级小的元素（因为优先级大的元素要先进行运算）

（5）最后如果栈不空，就将栈中的元素输出。

代码实现：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
using namespace std;

struct Node{
    char x;
    struct Node* next;
};
typedef struct Node* Stack;

int IsEmpty(Stack S)
{
    return S->next==NULL; 
}

void Pop(Stack S)
{
    if(!IsEmpty(S))
    {
        Stack tp=S->next;
        S->next=tp->next;
        free(tp);
    }
}

void Push(char ch,Stack S)
{
    Stack tp=(Stack)malloc(sizeof(struct Node));
    tp->x=ch;
    tp->next=S->next;
    S->next=tp;
}

char Top(Stack S)
{
    if(S->next==NULL)
    {
        printf("Stack Empty");
    }
    else return S->next->x;
}

Stack CreateStack()
{
    Stack S;
    S=(Stack)malloc(sizeof(struct Node));
    if(S==NULL)
    {
        printf("Out of Space!!!
");
    }
    S->next=NULL;
    return S;
}

int main(void)
{
    Stack S=CreateStack();
    double x,sum=0;
    char ch;
    while(cin>>ch&&ch!='#')
    {
        if(ch>='0'&&ch<='9') cout<<ch;
        else if(ch=='(') Push(ch,S);
        else if(ch==')')
        {
            while(!IsEmpty(S)&&Top(S)!='(')
            {
                cout<<Top(S);
                Pop(S);
            }
            Pop(S);
        }
        else if(ch=='-'||ch=='+')
        {
            while(!IsEmpty(S)&&Top(S)!='(')
            {
                cout<<Top(S);
                Pop(S);
            }
            Push(ch,S);
        }
        else if(ch=='*'||ch=='/')
        {
            while(!IsEmpty(S)&&Top(S)!='+'&&Top(S)!='-'&&Top(S)!='(')
            {
                cout<<Top(S);
                Pop(S);
            }
            Push(ch,S);
        }
    }
    while(!IsEmpty(S)) 
    {
        cout<<Top(S);
        Pop(S);
    }
    return 0;
}

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