LR（0）分析表的构造假若一个文法G的拓广文法G的活前缀识别自动机中的每个状态（项目集）不存在下述情况：1) 既含移进项目又含归约项目，或者2) 含有多个归约项目，则称G是一个LR（0）文法。换言之，LR（0）文法规范族的每个项目集不包含任何冲突项目。 对于LR（0）文法，我们可直接从它的项目集规范族C和活前缀识别自动机的状态转换函数GO构造出LR分析表。下面是构造LR（0）分析表的算法。 假定C＝I0,I1,…,InC＝I0,I1,…,In。前面，我们已习惯用数码表示状态，因此，令每个项目集IkIk的下标kk作为分析器的状态。特别是，令那个包含项目S→SS→·S的集合IkIk的下标k为分析器的初态。分析表的ACTIONACTION子表和GOTOGOTO子表可按如下方法构造： - 若项目A→aabA→a·ab属于IkIk且GO（Ik,a）＝Ij，aGO（Ik,a）＝Ij，a为终结符，则置ACTION[k,a]ACTION[k,a]为“把（j,aj,a）移进栈”，简记为“sjsj”。
- 若项目A→aA→a·属于IkIk，那么，对任何终结符aa（或结束符#），置ACTION[k,a]ACTION[k,a]为“用产生式A→aA→a进行归约”，简记为“rjrj”（假定产生式A→aA→a是文法GG的第jj个产生式）。
- 若项目S→SS→S·属于IkIk，则置ACTION[kACTION[k,#]]为“接受”，简记为“accacc”。
- 若GO（Ik,A）＝Ij，AGO（Ik,A）＝Ij，A为非终结符，则置GOTO[k,A]=jGOTO[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置上“报错标志”。
由于假定LR（0）LR（0）文法规范族的每个项目集不含冲突项目，因此，按上法构造的分析表的每个入口都是唯一的（即，不含多重定义）。我们称如此构造的分析表是一张LR（0）LR（0）表。使用LR（0）LR（0）表的分析器叫做一个LR（0） LR（0）分析器。 代码：#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cctype>
#include <vector>
#include <string>
#include <queue>
#include <map>
#include <sstream>
#define MAX 507
#define DEBUG
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;
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];
void make_item ( )
{
memset ( to, -1, sizeof ( -1 ) );
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\n", items[i].left.c_str(), items[i].right.c_str() );
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;
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 )
{
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 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 ) );
//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;
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_set();
make_V();
make_go();
make_table();
analyse( "(a+i)*b" );
}
}
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