《数据结构与算法分析》学习笔记（四）——栈ADT

一、栈ADT是what？

1、定义

        栈，是限制插入和删除都只能在一个位置上进行的表。

2、图示        

                               

3、栈的基本功能

（1）是否为空

（2）进栈

（3）出栈

（4）清空

（5）取栈顶

二、栈的链表实现

#ifndef Exercise_Stack_h
#define Exercise_Stack_h

typedef struct Node *PrtToNode;
typedef PrtToNode Stack;
typedef int ElementType;


struct Node
{
    ElementType Element;
    PrtToNode Next;
};


bool IsEmpty(Stack S);

Stack CreateStack();

void MakeEmpty(Stack S);

void Push(ElementType X,Stack S);

void Pop(Stack S);

ElementType Top(Stack S);

#endif






bool IsEmpty(Stack S)
{
    return S->Next==nullptr;
}


Stack CreateStack()
{
    Stack S;
    
    S = new struct Node;
    if(S==nullptr)
    {
        std::cout<<"Create Error!"<<std::endl;
        return nullptr;
    }
    
    S->Next=nullptr;

    return S;
}

void MakeEmpty(Stack S)
{
    if(S==nullptr)
    {
        std::cout<<"not initStack Error!"<<std::endl;
        return ;
    }
    
    while (!IsEmpty(S))
    {
        Pop(S);
    }
    
}


void Push(ElementType X,Stack S)
{
    PrtToNode Temp;
    
    Temp = new struct Node;
    if(Temp==nullptr)
    {
        std::cout<<"init Node Error!"<<std::endl;
        return;
    }
    
    Temp->Element=X;
    Temp->Next=S;
    S->Next=Temp;
}


void Pop(Stack S)
{
    if(IsEmpty(S))
    {
        std::cout<<"Stack Empty!"<<std::endl;
        return;
    }
    auto temp = S->Next;
    S->Next=S->Next->Next;
    delete temp;
}


ElementType Top(Stack S)
{
    if(IsEmpty(S))
    {
        std::cout<<"Stack Empty!"<<std::endl;
        return  0;
    }
    return S->Next->Element;
}

PS：优点：不用担心栈溢出的现象

       缺点：开辟内存和释放内存的时候貌似开销比较昂贵。

三、栈的数组实现

typedef int ElementType;
const int MaxCapacity = 100;

struct StackRecord
{
    int Capacity;
    int TopOfStack;
    ElementType *Array;
};

typedef struct StackRecord *Stack;

bool IsFull(Stack S);

bool IsEmpty(Stack S);

Stack CreateStack(int MaxElements);

void DisposeStack(Stack S);

void MakeEmpty(Stack S);

void Push(ElementType X,Stack S);

void Pop(Stack S);

ElementType Top(Stack S);

ElementType TopandPop(Stack S);





Stack CreateStack(int MaxElements)
{
    Stack S;
    
    S = new struct StackRecord;
    if(S==nullptr)
    {
        std::cout<<"Out of space!"<<std::endl;
        return nullptr;
    }
    
    S->Array = new ElementType(MaxElements);
    if(S->Array==nullptr)
    {
        std::cout<<"Out of space!"<<std::endl;
        return nullptr;
    }
    
    S->Capacity=MaxElements;
    S->TopOfStack=-1;
    
    MakeEmpty(S);
    
    return S;
    
}

void DisposeStack(Stack S)
{
    if(S!=nullptr)
    {
        delete S->Array;
        delete S;
    }
}


bool IsEmpty(Stack S)
{
    return S->TopOfStack==-1;
}

void MakeEmpty(Stack S)
{
    S->TopOfStack=-1;
}

void Push(ElementType X,Stack S)
{
    if(IsFull(S))
    {
        std::cout<<"Full Stack"<<std::endl;
        return;
    }
    S->Array[++S->Array[S->TopOfStack]]=X;
             
}

ElementType Top(Stack S)
{
    if(!IsEmpty(S))
    {
        return S->Array[S->TopOfStack];
    }
    
    std::cout<<"Empty Error"<<std::endl;
    return 0;
}

void Pop(Stack S)
{
    if(IsEmpty(S))
    {
        std::cout<<"Empty Error"<<std::endl;
    }
    else{
        S->TopOfStack--;
    }
}

ElementType TopandPop(Stack S)
{
    if(!IsEmpty(S))
    {
        return S->Array[S->TopOfStack--];
    }
    std::cout<<"Empty Error"<<std::endl;
    return 0;

}

bool IsFull(Stack S)
{
    return S->Capacity==MaxCapacity;
}

优点：把不断开空间的时间省下来了；

缺点：数组商都是有限的；

四、应用

（1）括号的匹配

void test(string s)
{
    auto stack = CreateStack(100);
    
    for(auto c: s)
    {
        if(c=='['||c=='{'||c=='(')
        {
            Push(c, stack);
        }
        else
        {
           if(c==']'||c=='}'||c==')')
           {
               if(IsEmpty(stack))
               {
                   cout<<"Error!"<<endl;
               }
               else
               {
                  if(c==']')
                  {
                      auto temp = TopandPop(stack);
                      if(temp!='[')
                      {
                          cout<<"Error!"<<endl;
                      }
                  }
                   else if(c=='}')
                   {
                       auto temp = TopandPop(stack);
                       if(temp!='{')
                       {
                           cout<<"Error!"<<endl;
                       }
                   }
                   else if(c==')')
                   {
                       auto temp = TopandPop(stack);
                       if(temp!='(')
                       {
                           cout<<"Error!"<<endl;
                       }
                   }
                   else
                   {
                       cout<<"Scanf Error!"<<endl;
                   }

               }
           }
           else
           {
               cout<<"Scanf Error!"<<endl;
           }
        }
        
    }
    
    if(stack->TopOfStack==-1)
    {
        cout<<"RIGHT"<<endl;
    }
    else
    {
        cout<<"Error!"<<endl;
    }
    
}

（2）后缀表达式的计算。

后缀表达式的优点就是完全不需要考虑什么优先级之类的，直接从左边算到右边就可以了，简直方便快捷，在这里我就默默的实现下，小白勿喷

int calculate(string S)     //10以内的整数运算
{
    
    auto stack = CreateStack(100);
    
    
    for(auto c:S)
    {
        switch (c)
        {
            case '+' :
            {
                auto t1=TopandPop(stack);
                auto t2=TopandPop(stack);
                double t3=t1+t2;
                
                Push(t3, stack);
            }
                
                break;
                case '-':
            {
                auto t1=TopandPop(stack);
                auto t2=TopandPop(stack);
                double t3=t2-t1;
                
                Push(t3, stack);
            }
                break;
                case '*':
            {
                auto t1=TopandPop(stack);
                auto t2=TopandPop(stack);
                double t3=t2*t1;
                
                Push(t3, stack);
            }
                break;
                case '/':
            {
                auto t1=TopandPop(stack);
                auto t2=TopandPop(stack);
                double t3=t2/t1;
                
                Push(t3, stack);
            }
                break;
            default:
            {
                Push(c-'0', stack);
            }
                break;
        }
    }
    
    
    return Top(stack);
    
}

 3、中缀表达式转化成后缀表达式

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<vector>
#include<stack>
#include<algorithm>
using namespace std;

int pre(char a) //操作符优先级比较
{
    if(a == '=' || a == '(')
        return 0;
    else if(a == '+' || a == '-')
        return 1;
    else if(a == '*' || a == '/')
        return 2;
    else
    {
        cout<<"Error!"<<endl;
        return 0;
    }
}

int main()
{
    string str;
    stack<char> ope; //操作符
    vector<char> ans;//后缀表达式
    vector<char>::iterator start, end;
        getchar(); //清除输入垃圾
    
        while(!ope.empty()) //初始化
            ope.pop();
        ans.clear();
        ope.push('='); //结束标志
        cin>>str;
        auto len = str.length();
        for(int i = 0 ; i < len; ++i)
        {
            if(str[i] >= '0' && str[i] <= '9') //操作数直接存入ans
                ans.push_back(str[i]);
            else if(str[i] == '(') //左括号入栈
                ope.push(str[i]);
            else if(str[i] == ')') //右括号，将匹配的左括号内容存入ans,左括号出栈
            {
                while (ope.top() != '(')
                {
                    ans.push_back(ope.top());
                    ope.pop();
                }
                ope.pop(); //左括号出栈
            }
            else if(pre(str[i]) > pre(ope.top())) //优先级大于栈顶元素则入栈
                ope.push(str[i]);
            else //小于栈顶元素
            {
                while(pre(str[i]) <= pre(ope.top()))
                {
                    ans.push_back(ope.top());
                    ope.pop();
                }
                ope.push(str[i]);
            }
        }
        while(ope.top() != '=') //其余操作符存入后缀表达式中
        {
            ans.push_back(ope.top());
            ope.pop();
        }
        for(start = ans.begin(), end = ans.end(); start < end; ++start)
            printf("%c", *start);
        printf("
");
    
    return 0;
}