编译原理之表达式语法分析(一)——自顶向下

文法变换

G(E):

E→Eω0T|T E为算术表达式，T为项

T→Tω1F|F F为因式项，ω0为 +或 -， ω1为 * 或 /

F→i|(E) i 为变量或常量

G(E)不是LL(1)文法，所以需要进行文法变换

G’(E):

E→T{ω0T}

T→F{ω1F}

F→i|(E)

或者G”(E):

E→TA

A→{ω0T}A

T→FB

B→{ω1F}B

F→i|(E)

递归下降法

Preset.h

#ifndef PRESET_H_INCLUDED
#define PRESET_H_INCLUDED

std::string Str;
int top;

void HandleE();
void HandleA();
void HandleT();
void HandleB();
void HandleF();

#endif // PRESET_H_INCLUDED

main.c

#include <iostream>
#include <cstdio>
#include <cstring>
#include "Preset.h"

using namespace std;

int main()
{
while(cin >> Str)
{
top=0;
if(Str[top]=='#')
cout << "Yes" << endl;
else cout << "No" << endl;
}
return 0;
}

void HandleE()
{
HandleT();
HandleA();
}

void HandleA()
{
if(Str[top]=='+' || Str[top]=='-')
{
top++;
HandleT();
HandleA();
}
}

void HandleT()
{
HandleF();
HandleB();
}

void HandleB()
{
if(Str[top]=='*' || Str[top]=='/')
{
top++;
HandleF();
HandleB();
}
}

void HandleF()
{
if(isalpha(Str[top]))
top++;
else if(Str[top]=='(')
{
top++;
HandleE();
if(Str[top]==')')
top++;
}
}

LL(1)

LL(1)分析表如下:

栈顶符/当前符	i	+	*	(	)	#
E	1			1
A		2			3	3
T	4			4
B		3	5		3	3
F	6			7
)					6
#						OK

其中

(AT,P)

(AT,N)

(空,P)

(BF,P)

(BF,N)

(空,N)

( )E,N)

P表示不变，N表示读取下一个

故

AT ——1、2

BF——4、5

空——3、6

）E——7

P——1、3、4

N——2、5、6、7

Preset.h

#ifndef PRESET_H_INCLUDED
#define PRESET_H_INCLUDED

std::string Str;

int top;//栈顶符指针
int stop;//当前符指针

int tell();

std::string Stack_ch;

#endif // PRESET_H_INCLUDED

main.c

#include <iostream>
#include <cstring>
#include <string>
#include <cstdio>
#include "Preset.h"

using namespace std;

int main()
{
while(cin >> Str)
{
top=0;
stop=0;
Stack_ch[top]='#';
Stack_ch[++top]='E';
int ans=0;
ans=tell();
while(ans!=-1 && ans!=0)
{
ans=tell();
}
if(ans==-1)cout << "Yes" << endl;
else cout << "No" << endl;
}
return 0;
}

int tell()
{
int op=-1;
if(Stack_ch[top]=='#' && Str[stop]=='#')
{
return op;
}
op=0;
switch(Stack_ch[top])
{
case 'E':
if(Str[stop]=='(' || isalpha(Str[stop]))op=1;
break;
case 'A':
if(Str[stop]=='+' || Str[stop]=='-')op=2;
else if(Str[stop]==')' || Str[stop]=='#')op=3;
break;
case 'T':
if(Str[stop]=='(' || isalpha(Str[stop]))op=4;
break;
case 'B':
if(Str[stop]=='+' || Str[stop]=='-' || Str[stop]==')' || Str[stop]=='#')op=3;
else if(Str[stop]=='*' || Str[stop]=='/')op=5;
break;
case 'F':
if(Str[stop]=='(')op=7;
else if(isalpha(Str[stop]))op=6;
break;
case ')':
if(Str[stop]==')')op=6;
break;
default:
break;
}
if(op==0)return op;
top--;
if(op==2 || op==5 || op==6 || op==7)stop++;
switch(op)
{
case 1:
case 2:
Stack_ch[++top]='A';
Stack_ch[++top]='T';
break;
break;
case 4:
case 5:
Stack_ch[++top]='B';
Stack_ch[++top]='F';
break;
case 7:
Stack_ch[++top]=')';
Stack_ch[++top]='E';
break;
default:
break;
}
return op;
}