王道数据结构之中缀转后缀并计算（栈）——考研复习笔记

所实现的算法：

• 括号匹配检查
• 中缀表达式转后缀表达式
• 计算转乘后缀后的表达式

 数据类型

//用来转后缀表达式 
typedef struct{
	char data[MaxSize];
	int top;
}SqStack,SNode;

　　

//用来计算后缀表达式 
typedef struct{
	float Num[MaxSize];
	int top;
}NuStack,NNode;

　　

 

完整代码：

/*    中缀转后缀并计算 
*/
#include <iostream>
#include <stdlib.h>
#include <string.h>

using namespace std;
#define MaxSize 100

typedef struct{
    char data[MaxSize];
    int top;
}SqStack,SNode;


typedef struct{
    float Num[MaxSize];
    int top;
}NuStack,NNode;


//运算符优先级 
int Priority(char op){
    switch(op){
        case '+':
            return 1;
        case '-':
            return 1;
        case '*':
            return 2;
        case '/':
            return 2;
        default:
            return 0;
    }
}

void Init(SqStack &P){
    P.top=-1;
} 

void Init_Nu(NuStack &S)
{
    S.top=-1;
}

bool Empty(SqStack P){
    if (P.top==-1) return true;
    return false;
}

bool Empty_Num(NuStack S){
    if (S.top==-1) return true;
    return false;
}

bool Push(SqStack &P, char ch){
    P.data[++P.top]=ch;
    return true;
} 

bool Push_Nu(NuStack &S, float ch){
    //cout<<ch<<endl;
    S.Num[++S.top]=ch;
    return true;
} 

bool Pop_1(SqStack &P){
    P.top--;
    return true;
}

bool Pop_2(NuStack &S,float &x){
    x=S.Num[S.top--];
    return true;
}

char GetTop(SqStack S){
    return S.data[S.top];
}

float GetNum(NuStack S){
    return S.Num[S.top];
}

//转后缀并计算 
void Convert(NuStack &S,SqStack &P,char ch[],int len){
    char Cov_ch[MaxSize];
    int cnt =0;
    for(int i=0;i<len;i++){
        if(ch[i]<='9'&&ch[i]>='0'){
            Cov_ch[cnt++]=ch[i];
        }else{
            if(Empty(P)) Push(P,ch[i]);
            else if(ch[i]=='(') Push(P,ch[i]);
            else if(ch[i]==')'){
                while(GetTop(P)!='('){
                    Cov_ch[cnt++]=GetTop(P);
                    Pop_1(P);
                }
            Pop_1(P);
            }
            else{
                while(Priority(ch[i])<=Priority(GetTop(P))){
                    Cov_ch[cnt++]=GetTop(P);
                    Pop_1(P);
                    if(Empty(P)) break;
                }
                Push(P,ch[i]);
            }            
        }
    }
    while(!Empty(P)){
        Cov_ch[cnt++]=GetTop(P);
        Pop_1(P);
    }
    
    for(int i=0;i<cnt;i++){
        cout<<Cov_ch[i]; 
    }
    puts("");
    float a,b;
    for(int i=0;i<cnt;i++){
        if(Cov_ch[i]>='0'&&Cov_ch[i]<='9'){
            Push_Nu(S,Cov_ch[i]-'0');
        }else{
            switch(Cov_ch[i]){
                case '+':
                    Pop_2(S,a);
                    Pop_2(S,b);
                    Push_Nu(S,b+a);
                    break;
                case '-':
                    Pop_2(S,a);
                    Pop_2(S,b);
                    Push_Nu(S,b-a);
                    break;
                case '*':
                    Pop_2(S,a);
                    Pop_2(S,b);
                    Push_Nu(S,a*b);
                    break;
                case '/':
                    Pop_2(S,a);
                    Pop_2(S,b);
                    Push_Nu(S,b/a);
                    break;
                default:
                    break; 
            }    
        }
    }
    cout<<GetNum(S);
}
//括号检查 
bool bracketCheck(char str[],int ll){  
    SqStack Q;
    Q.top=-1;
    char x;
    char bracket[MaxSize];
    int cnt=0;
    for(int i=0;i<ll;i++){
        if(str[i]=='('||str[i]==')') bracket[cnt++]=str[i];
    }
    for(int i=0;i<cnt;i++){
        if(bracket[i]=='('){
            Push(Q,bracket[i]);
        }
        else{
            if(Empty(Q)) return false;
            x=GetTop(Q);
            Pop_1(Q);
            if((bracket[i]==')'&&x!='('))
                 return false;
        }
    }
    return Empty(Q);
}

int main(){
    SqStack P;
    NuStack S;
    Init(P);
    Init_Nu(S);
    char ch[MaxSize];
    cin>>ch;
    int len = strlen(ch);
    if(!bracketCheck(ch,len)){
        cout<<"It's a wrong expression"<<endl;
    }else{
        Convert(S,P,ch,len);
    }
    return 0;
}