编译原理(十) SLR文法分析法(算法原理和C++实现)
最后更新于：2022-04-01 14:15:32
## 前情提要
因为SLR文法分析法就是对LR(0)的一种优化，它提供了一种解决冲突的方法，所以很多之前在LR(0)提及的东西，在此只提供一个引用。
[LR(0)文法分析法](http://blog.csdn.net/qq_24451605/article/details/50152029)
## 算法描述
**SLR文法构造分析表的主要思想是：**许多冲突性的动作都可能通过考察有关非终结符的FOLLOW集而获解决。
**解决冲突的方法：**解决冲突的方法是分析所有含A和B的句型，考察集合FOLLOW(A)和FOLLOW(B)，如果这两个集合不相交，而且也不包含b，那么当状态I面临输入符号a时，我们可以使用如下策略：
- 若a=b，则移进。
- 若a∈FOLLOW(A)，则用产生式A→α进行归约；
- 若a∈FOLLOW(B)，则用产生式B→α进行归约；
- 此外，报错***
**SLR的基本算法：**
- 假定LR(0)规范族的一个项目集I中含有m个移进项目
A1→α•a1β1，A2→α•a2β2，…，Am→α•amβm；
同时含有n个归约项目
B1→α•，B2→α•，…，B3→α•，
- 如果集合{ a1,…, am}，FOLLOW(B1)，…，FOLLOW(Bn)两两不相交（包括不得有两个FOLLOW集合有#），则隐含在I中的动作冲突可以通过检查现行输入符号a属于上述n+1个集合中的哪个集合而活的解决：
- 若a是某个ai，i=1,2,…,m，则移进。
- 若a∈FOLLOW(Bi)，i=1,2,…,m，则用产生式Bi→α进行归约；
- 此外，报错
这种冲突的解决方法叫做***SLR(1)解决办法***。
**SLR语法分析表的构造方法：**
首先把G拓广为G’，对G’构造LR(0)项目集规范族C和活前缀识别自动机的状态转换函数GO。函数ACTION和GOTO可按如下方法构造：
- 若项目A→α•bβ属于Ik，GO(Ik,a)= Ij,a为终结符，置ACTION[k,a]为“把状态j和符号a移进栈”，简记为“sj”；
- 若项目A→α•属于Ik，那么，对任何非终结符a，a∈FOLLOW(A)，置ACTION[k,a]为“用产生式A→α进行归约”，简记为“rj”；其中，假定A→α为文法G’的第j个产生式
- 若项目S’→S•属于Ik，则置ACTION[k,#]为可“接受”，简记为“acc”；
- 若GO(Ik, A)= Ij，A为非终结符，则置GOTO[k, A]=j；
分析表中凡不能用规则1至4填入信息的空白格均填上“出错标志”。
语法分析器的初始状态是包含S’ →•S的项目集合的状态
***SLR解决的冲突只是移进-规约冲突和规约-规约冲突***
## 代码实现
~~~
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cctype>
#include <vector>
#include <string>
#include <queue>
#include <map>
#include <set>
#include <sstream>
#define MAX 507
#define DEBUG
/*Author : byj*/
using namespace std;
class WF
{
public:
string left,right;
int back;
int id;
WF ( char s1[] , char s2[] , int x , int y )
{
left = s1;
right = s2;
back = x;
id = y;
}
WF ( const string& s1 , const string& s2 , int x , int y )
{
left = s1;
right = s2;
back = x;
id = y;
}
bool operator < ( const WF& a ) const
{
if ( left == a.left )
return right < a.right;
return left < a.left;
}
bool operator == ( const WF& a ) const
{
return ( left == a.left )&& ( right == a.right );
}
void print ( )
{
printf ( "%s->%s\n" , left.c_str() , right.c_str() );
}
};
class Closure
{
public:
vector<WF> element;
void print ( string str )
{
printf ( "%-15s%-15s\n" , "" , str.c_str());
for ( int i = 0 ; i < element.size() ; i++ )
element[i].print();
}
bool operator == ( const Closure& a ) const
{
if ( a.element.size() != element.size() ) return false;
for ( int i = 0 ; i < a.element.size() ; i++ )
if ( element[i] == a.element[i] ) continue;
else return false;
return true;
}
};
struct Content
{
int type;
int num;
string out;
Content(){ type = -1; }
Content ( int a , int b )
:type(a),num(b){}
};
vector<WF> wf;
map<string,vector<int> > dic;
map<string,vector<int> > VN_set;
map<string,bool> vis;
string start = "S";
vector<Closure> collection;
vector<WF> items;
char CH = '$';
int go[MAX][MAX];
int to[MAX];
vector<char> V;
bool used[MAX];
Content action[MAX][MAX];
int Goto[MAX][MAX];
map<string,set<char> > first;
map<string,set<char> > follow;
void make_item ( )
{
memset ( to , -1 , sizeof ( -1 ) );
for ( int i = 0 ; i < wf.size() ; i++ )
VN_set[wf[i].left].push_back ( i );
for ( int i = 0 ; i < wf.size() ; i++ )
for ( int j = 0 ; j <= wf[i].right.length() ; j++ )
{
string temp = wf[i].right;
temp.insert ( temp.begin()+j , CH );
dic[wf[i].left].push_back ( items.size() );
if ( j )
to[items.size()-1] = items.size();
items.push_back ( WF ( wf[i].left , temp , i , items.size()) );
}
#ifdef DEBUG
puts("-------------------------项目表-------------------------");
for ( int i = 0 ; i < items.size() ; i++ )
printf ( "%s->%s back:%d id:%d\n" , items[i].left.c_str() , items[i].right.c_str() , items[i].back , items[i].id );
puts("--------------------------------------------------------");
#endif
}
void dfs ( const string& x )
{
if ( vis[x] ) return;
vis[x] = 1;
vector<int>& id = VN_set[x];
for ( int i = 0 ; i < id.size() ; i++ )
{
string& left = wf[id[i]].left;
string& right = wf[id[i]].right;
for ( int j = 0 ; j < right.length() ; j++ )
if ( isupper(right[j] ) )
{
dfs ( right.substr(j,1) );
set<char>& temp = first[right.substr(j,1)];
set<char>::iterator it = temp.begin();
bool flag = true;
for ( ; it != temp.end() ; it++ )
{
if ( *it == '~' ) flag = false;
first[left].insert (*it );
}
if ( flag ) break;
}
else
{
first[left].insert ( right[j] );
break;
}
}
}
void make_first ( )
{
vis.clear();
map<string,vector<int> >::iterator it2 = dic.begin();
for ( ; it2 != dic.end() ; it2++ )
if ( vis[it2->first] ) continue;
else dfs ( it2->first );
#ifdef DEBUG
puts ("****************FIRST集***************************");
map<string,set<char> >::iterator it = first.begin();
for ( ; it != first.end() ; it++ )
{
printf ( "FIRST(%s)={" , it->first.c_str() );
set<char> & temp = it->second;
set<char>::iterator it1 = temp.begin();
bool flag = false;
for ( ; it1 != temp.end() ; it1++ )
{
if ( flag ) printf ( "," );
printf ( "%c" , *it1 );
flag = true;
}
puts ("}" );
}
#endif
}
void append ( const string& str1 , const string& str2 )
{
set<char>& from = follow[str1];
set<char>& to = follow[str2];
set<char>::iterator it = from.begin();
for ( ; it != from.end() ; it++ )
to.insert ( *it );
}
bool _check ( const vector<int>& id, const string str )
{
for ( int i = 0 ; i < id.size() ; i++ )
{
int x = id[i];
if ( wf[x].right == str ) return true;
}
return false;
}
void make_follow ( )
{
while ( true )
{
bool goon = false;
map<string,vector<int> >::iterator it2 = VN_set.begin();
for ( ; it2 != VN_set.end() ; it2++ )
{
vector<int>& id = it2->second;
for ( int i = 0 ; i < id.size() ; i++ )
{
bool flag = true;
WF& tt = wf[id[i]];
string& left = tt.left;
const string& right = tt.right;
for ( int j = right.length()-1 ; j >= 0 ; j-- )
if ( isupper( right[j] ) )
{
if ( flag )
{
int tx = follow[right.substr(j,1)].size();
append( left , right.substr(j,1) );
int tx1 = follow[right.substr(j,1)].size();
if ( tx1 > tx ) goon = true;
if ( _check ( id , "~" ) )
flag = false;
}
for ( int k = j+1 ; k < right.length() ; k++ )
if ( isupper(right[k] ) )
{
string idd = right.substr(k,1);
set<char>& from = first[idd];
set<char>& to = follow[right.substr(j,1)];
set<char>::iterator it1 = from.begin();
int tx = follow[right.substr(j,1)].size();
for ( ; it1 != from.end() ; it1++ )
if ( *it1 != '~' )
to.insert ( *it1 );
int tx1 = follow[right.substr(j,1)].size();
if ( tx1 > tx ) goon = true;
if ( _check ( id , "~" ) )
break;
}
else
{
int tx = follow[right.substr(j,1)].size();
follow[right.substr(j,1)].insert ( right[k] );
int tx1 = follow[right.substr(j,1)].size();
if ( tx1 > tx ) goon = true;
break;
}
}
else flag = false;
}
}
if ( !goon ) break;
}
#ifdef DEBUG
puts ("***************FOLLOW集*******************");
map<string,set<char> >::iterator it = follow.begin();
for ( ; it != follow.end() ; it++ )
{
printf ( "FOLLOW(%s)={" , it->first.c_str() );
set<char> & temp = it->second;
//if ( it->first[0] == 'S' )
temp.insert ( '#' );
set<char>::iterator it1 = temp.begin();
bool flag = false;
for ( ; it1 != temp.end() ; it1++ )
{
if ( flag ) printf ( "," );
printf ( "%c" , *it1 );
flag = true;
}
puts ("}");
}
#endif
}
void make_set ( )
{
bool has[MAX];
for ( int i = 0 ; i < items.size() ; i++ )
if ( items[i].left[0] == 'S' && items[i].right[0] == CH )
{
Closure temp;
string& str = items[i].right;
vector<WF>& element = temp.element;
element.push_back ( items[i] );
int x = 0;
for ( x = 0 ; x < str.length() ; x++ )
if ( str[x] == CH )
break;
/*if ( x != str.length()-1 )
{
string tt = str.substr(x+1,1);
vector<int>& id = dic[tt];
for ( int j = 0 ; j < id.size() ; j++ )
{
int tx = id[j];
//items[tx].print();
if ( items[tx].right[0] == CH )
element.push_back ( items[tx] );
}
}*/
memset ( has , 0 , sizeof ( has ) );
has[i] = 1;
if ( x != str.length()-1 )
{
queue<string> q;
q.push( str.substr(x+1,1) );
while ( !q.empty() )
{
string u = q.front();
q.pop();
vector<int>& id = dic[u];
for( int j = 0 ; j < id.size() ; j++ )
{
int tx = id[j];
if ( items[tx].right[0] == CH )
{
if ( has[tx] ) continue;
has[tx] = 1;
if ( isupper(items[tx].right[1] ) )
q.push ( items[tx].right.substr(1,1));
element.push_back ( items[tx] );
}
}
}
}
collection.push_back ( temp );
}
for ( int i = 0 ; i < collection.size() ; i++ )
{
map<int,Closure> temp;
for ( int j = 0 ; j < collection[i].element.size() ; j++ )
{
string str = collection[i].element[j].right;
int x = 0;
for ( ; x < str.length() ; x++ )
if ( str[x] == CH ) break;
if ( x == str.length()-1 )
continue;
int y = str[x+1];
int ii;
//cout << i << "previous: " << str << endl;
str.erase ( str.begin()+x);
str.insert ( str.begin()+x+1 , CH );
//cout << i <<"after: " << str << endl;
WF cmp = WF ( collection[i].element[j].left , str , -1 , -1 );
for ( int k = 0 ; k< items.size() ; k++ )
if ( items[k] == cmp )
{
ii = k;
break;
}
//string& str1 = items[ii].right;
memset ( has , 0 , sizeof ( has ) );
vector<WF>& element = temp[y].element;
element.push_back ( items[ii] );
has[ii] = 1;
x++;
/*if ( x != str.length()-1 )
{
string tt = str.substr(x+1,1);
vector<int>& id = dic[tt];
for ( int j = 0 ; j < id.size() ; j++ )
{
int tx = id[j];
//items[tx].print();
if ( items[tx].right[0] == CH )
element.push_back ( items[tx] );
}
}*/
if ( x != str.length()-1 )
{
queue<string> q;
q.push( str.substr(x+1,1) );
while ( !q.empty() )
{
string u = q.front();
q.pop();
vector<int>& id = dic[u];
for( int j = 0 ; j < id.size() ; j++ )
{
int tx = id[j];
if ( items[tx].right[0] == CH )
{
if ( has[tx] ) continue;
has[tx] = 1;
if ( isupper(items[tx].right[1] ) )
q.push ( items[tx].right.substr(1,1));
element.push_back ( items[tx] );
}
}
}
}
}
map<int,Closure>::iterator it = temp.begin();
for ( ; it != temp.end() ; it++ )
collection.push_back ( it->second );
for ( int i = 0 ; i < collection.size() ; i++ )
sort ( collection[i].element.begin() , collection[i].element.end() );
for ( int i = 0 ; i < collection.size() ; i++ )
for ( int j = i+1 ; j < collection.size() ; j++ )
if ( collection[i] == collection[j] )
collection.erase ( collection.begin()+j );
}
#ifdef DEBUG
puts ("-------------CLOSURE---------------------");
stringstream sin;
for ( int i = 0 ; i < collection.size() ; i++ )
{
sin.clear();
string out;
sin <<"closure-I" << i;
sin >> out;
collection[i].print ( out );
}
puts("");
#endif
}
void make_V ( )
{
memset ( used , 0 , sizeof ( used ) );
for ( int i = 0 ; i < wf.size() ; i++ )
{
string& str = wf[i].left;
for ( int j = 0 ; j < str.length() ; j++ )
{
if ( used[str[j]] ) continue;
used[str[j]] = 1;
V.push_back ( str[j] );
}
string& str1 = wf[i].right;
for ( int j = 0 ; j < str1.length() ; j++ )
{
if ( used[str1[j]] ) continue;
used[str1[j]] = 1;
V.push_back ( str1[j] );
}
}
sort ( V.begin() , V.end() );
V.push_back ( '#' );
}
void make_cmp ( vector<WF>& cmp1 , int i , char ch )
{
for ( int j = 0 ; j < collection[i].element.size() ; j++ )
{
string str = collection[i].element[j].right;
int k;
for ( k = 0 ; k < str.length() ; k++ )
if ( str[k] == CH )
break;
if ( k != str.length() - 1 && str[k+1] == ch )
{
str.erase ( str.begin()+k);
str.insert ( str.begin()+k+1 , CH );
cmp1.push_back ( WF ( collection[i].element[j].left , str , -1 , -1 ) );
}
}
sort ( cmp1.begin() , cmp1.end() );
}
void make_go ( )
{
memset ( go , -1 , sizeof ( go ) );
int m = collection.size();
/*for ( int i = 0 ; i < m ; i++ )
for ( int j = 0 ; j < collection[i].element.size() ; j++ )
{
string left = collection[i].element[j].left;
string str = collection[i].element[j].right;
int x = 0;
for ( ; x < str.length() ; x++ )
if ( str[x] == CH ) break;
if ( x == str.length()-1 )
continue;
int y = str[x+1];
//cout << "before : " << str << endl;
str.erase ( str.begin()+x);
str.insert ( str.begin()+x+1 , CH );
//cout << "after : " << str << endl;
WF cmp = WF ( collection[i].element[j].left , str , -1 , -1 );
for ( int k = 0 ; k < m ; k++ )
{
bool flag = false;
for ( int t = 0 ; t < collection[k].element.size() ; t++ )
{
if ( cmp == collection[k].element[t] )
{
flag = true;
break;
}
}
if ( flag )
{
go[i][y] = k;
}
}
}*/
for ( int t = 0 ; t < V.size() ; t++ )
{
char ch = V[t];
for ( int i = 0 ; i < m ; i++ )
{
vector<WF> cmp1;
make_cmp ( cmp1 , i , ch );
cout << cmp1.size() << endl;
if ( cmp1.size() == 0 ) continue;
for ( int j = 0 ; j < m ; j++ )
{
vector<WF> cmp2;
for ( int k = 0 ; k < collection[j].element.size() ; k++ )
{
string& str = collection[j].element[k].right;
int x;
for ( x = 0 ; x < str.length() ; x++ )
if ( str[x] == CH )
break;
if ( x && str[x-1] == ch )
cmp2.push_back ( WF( collection[j].element[k].left , str , -1 , -1 ) );
}
sort ( cmp2.begin() , cmp2.end() );
cout << cmp2.size() << endl;
bool flag = true;
if ( cmp2.size() != cmp1.size() ) continue;
cout << cmp1.size() << endl;
for ( int k = 0 ; k < cmp1.size() ; k++ )
if ( cmp1[k] == cmp2[k] ) continue;
else flag = false;
cout << "out " << endl;
if ( flag )
go[i][ch] = j;
}
//cout << "YES" << endl;
}
}
#ifdef DEBUG
puts ("---------------EDGE----------------------");
stringstream sin;
string out;
for ( int i = 0 ; i < m ; i++ )
for ( int j = 0 ; j < m ; j++ )
for ( int k = 0 ; k < MAX ; k++ )
if ( go[i][k] == j )
{
sin.clear();
sin << "I" << i << "--" <<(char)(k)<<"--I"<<j;
sin >> out;
printf ( "%s\n" , out.c_str() );
}
#endif
}
void make_table ( )
{
memset ( Goto , -1 , sizeof ( Goto ) );
/*memset ( used , 0 , sizeof ( used ) );
for ( int i = 0 ; i < wf.size() ; i++ )
{
string& str = wf[i].left;
for ( int j = 0 ; j < str.length() ; j++ )
{
if ( used[str[j]] ) continue;
used[str[j]] = 1;
V.push_back ( str[j] );
}
string& str1 = wf[i].right;
for ( int j = 0 ; j < str1.length() ; j++ )
{
if ( used[str1[j]] ) continue;
used[str1[j]] = 1;
V.push_back ( str1[j] );
}
}
sort ( V.begin() , V.end() );
V.push_back ( '#' );*/
//write s to the table
for( int i = 0 ; i < collection.size() ; i++ )
for ( int j = 0 ; j < V.size() ; j++ )
{
char ch = V[j];
int x = go[i][ch];
if ( x == -1 ) continue;
if ( !isupper(ch) )
action[i][ch] = Content ( 0 , x );
else
Goto[i][ch] = x;
}
//write r and acc to the table
for ( int i = 0 ; i < collection.size() ; i++ )
for ( int j = 0 ; j < collection[i].element.size() ; j++ )
{
WF& tt = collection[i].element[j];
if ( tt.right[tt.right.length()-1] == CH )
{
if ( tt.left[0] == 'S' )
action[i]['#'] = Content ( 2 , -1 );
else
for ( int k = 0 ; k < V.size() ; k++ )
{
int y = V[k];
//cout << "YES " << endl;
//cout << tt.left << "->" << tt.right << " " << tt.back << endl;
if ( !follow[tt.left].count( V[k] ) ) continue;
//cout <<tt.left << "->" << tt.right << " " << i << " " << V[k] << " " << tt.back << endl;
action[i][y] = Content ( 1, tt.back );
}
}
}
#ifdef DEBUG
puts ( "------------------------------------------LR(0)分析表--------------------------------------------------------" );
printf ( "%10s%5c%5s" , "|" , V[0] , "|");
for ( int i = 1 ; i < V.size() ; i++ )
printf ( "%5c%5s" , V[i] , "|" );
puts ("");
for ( int i = 0 ; i < (V.size()+1)*10 ; i++ )
printf ( "-" );
puts("");
stringstream sin;
for ( int i = 0 ; i < collection.size() ; i++ )
{
printf ( "%5d%5s" , i , "|" );
for ( int j = 0 ; j < V.size() ; j++ )
{
char ch = V[j];
if ( isupper(ch) )
{
if ( Goto[i][ch] == -1 )
printf ( "%10s" , "|" );
else
printf ( "%5d%5s" , Goto[i][ch] , "|" );
}
else
{
sin.clear();
if ( action[i][ch].type == -1 )
printf ( "%10s" , "|" );
else
{
Content& temp = action[i][ch];
if ( temp.type == 0 )
sin << "S";
if ( temp.type == 1 )
sin << "R";
if ( temp.type == 2 )
sin << "acc";
if ( temp.num != -1 )
sin << temp.num;
sin >> temp.out;
printf ( "%7s%3s" , temp.out.c_str() , "|" );
}
}
}
puts ("");
}
for ( int i = 0 ; i < (V.size()+1)*10 ; i++ )
printf ( "-" );
puts("");
#endif
}
void print ( string s1 , string s2 , string s3 , string s4 , string s5 , string s6 , string s7 )
{
printf ( "%-15s|%-15s%-15s%-20s|%-15s%-15s%-15s\n" , s1.c_str() , s2.c_str() , s3.c_str() ,s4.c_str(),s5.c_str(),
s6.c_str() , s7.c_str() );
}
string get_steps ( int x )
{
stringstream sin;
sin << x;
string ret;
sin >> ret;
return ret;
}
template<class T>
string get_stk ( vector<T> stk )
{
stringstream sin;
for ( int i = 0 ; i < stk.size() ; i++ )
sin << stk[i];
string ret;
sin >> ret;
return ret;
}
string get_shift ( WF& temp )
{
stringstream sin;
sin << "reduce(" << temp.left << "->" << temp.right <<")";
string out;
sin >> out;
return out;
}
void analyse ( string src )
{
print ( "steps","op-stack" ,"input","operation","state-stack" , "ACTION" , "GOTO" );
vector<char> op_stack;
vector<int> st_stack;
src+= "#";
op_stack.push_back ( '#' );
st_stack.push_back ( 0 );
int steps= 1;
for ( int i = 0 ; i < src.length() ; i++ )
{
char u = src[i];
int top = st_stack[st_stack.size()-1];
Content& act = action[top][u];
//cout << "YES : " << i << " " << u << " " << top << " " << act.type << endl;
if ( act.type == 0 )
{
print ( get_steps ( steps++ ) , get_stk ( op_stack ) , src.substr(i), "shift", get_stk( st_stack ) , act.out , "" );
op_stack.push_back ( u );
st_stack.push_back ( act.num );
}
else if ( act.type == 1 )
{
WF& tt = wf[act.num];
int y = st_stack[st_stack.size()-tt.right.length()-1];
int x = Goto[y][tt.left[0]];
//cout << y << " " << tt.left[0] << " " << x << endl;
print ( get_steps ( steps++ ) , get_stk ( op_stack ) , src.substr(i) , get_shift(tt) ,get_stk( st_stack),act.out,get_steps(x));
for ( int j = 0 ; j < tt.right.length() ; j++ )
{
st_stack.pop_back();
op_stack.pop_back();
}
op_stack.push_back ( tt.left[0] );
st_stack.push_back ( x );
i--;
}
else if ( act.type == 2 )
{
print ( get_steps( steps++ ), get_stk( op_stack ) , src.substr(i) , "Accept" , get_stk(st_stack) , act.out , "" );
//i--;
}
else continue;
}
}
int main ( )
{
int n;
char s[MAX];
while ( ~scanf ( "%d" , &n ) )
{
for ( int i = 0 ; i < n ; i++ )
{
scanf ( "%s" , s );
int len = strlen(s),j;
for ( j = 0 ; j < len ; j++ )
if ( s[j] == '-' ) break;
s[j] = 0;
wf.push_back ( WF ( s , s+j+2 ,-1 , -1 ) );
#ifdef DEBUG
wf[wf.size()-1].print();
#endif
}
make_item();
make_first();
make_follow();
make_set();
make_V();
make_go();
make_table();
analyse ( "(i*i)+i" );
}
}
~~~
### Input
7
S->E
E->E+T
E->T
T->T*F
T->F
F->(E)
F->i
### Output
### 生成的项目表
### 非终结符的follow集合
### 项目规范族
### 构造出的DFA
### SLR文法表和一个例子的文法分析过程
