《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("\n"); return 0; }
