编译原理(十) SLR文法分析法(算法原理和C++实现)

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

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