## 前情提要
[算符优先分析法(构造算法优先关系表)](http://blog.csdn.net/qq_24451605/article/details/50096487)
## 算法描述
**算符优先关系主要用于界定右句型的句柄：**
> ***<***标记句柄的左端；
***=***出现在句柄的内部；
***>***标记句柄的右端。
**发现句柄的过程：**
- 从左端开始扫描串，直到遇到第一个>为止。
- 向左扫描，跳过所有的=，直到遇到一个<为止。
- 句柄包括从上一步遇到的<右部到第一个>左部之间的所有符号，包括介于期间或者两边的非终结符
**非终结符的处理：**
因为非终结符不能影响语法分析，所以不需要区分它们，于是只用一个占位符来代替它们
**算法的主体思想：**
用栈存储已经看到的输入符号，用优先关系指导移动归约语法分析器的动作
如果栈顶的终结符和下一个输入符之间的优先关系是<或=，则语法分析器移动，表示还没有发现句柄的右端
如果是>关系，就调用归约
**算法描述：**
输入：输入字符串ω和优先关系表
输出：如果ω是语法产生的一个句子，则输出其用来归约的产生式；如果有错误，则转入错误处理
## 代码实现
~~~
#include <iostream>
#include <cstring>
#include <cstdio>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <algorithm>
#include <string>
#include <cstdlib>
#include <cctype>
#define MAX 507
using namespace std;
class WF
{
public:
string left;
vector<string> right;
WF ( const string& str )
{
left = str;
}
void insert ( char str[] )
{
right.push_back(str);
}
void print ( )
{
printf ( "%s->%s" , left.c_str() , right[0].c_str() );
for ( int i = 1 ; i < right.size() ; i++ )
printf ( "|%s" , right[i].c_str() );
puts("");
}
};
char relation[MAX][MAX];
vector<char> VT;
vector<WF> VN_set;
map<string,int> VN_dic;
set<char> first[MAX];
set<char> last[MAX];
int used[MAX];
int vis[MAX];
void dfs ( int x )
{
if ( vis[x] ) return;
vis[x] = 1;
string& left = VN_set[x].left;
for ( int i = 0 ; i < VN_set[x].right.size() ; i++ )
{
string& str = VN_set[x].right[i];
if ( isupper(str[0]) )
{
int y = VN_dic[str.substr(0,1)]-1;
if ( str.length() > 1 && !isupper(str[1] ) )
first[x].insert ( str[1] );
dfs ( y );
set<char>::iterator it = first[y].begin();
for ( ; it!= first[y].end() ; it++ )
first[x].insert ( *it );
}
else
first[x].insert ( str[0] );
}
}
void make_first ( )
{
memset ( vis , 0 , sizeof ( vis ) );
for ( int i = 0 ; i < VN_set.size() ; i++ )
if ( vis[i] ) continue;
else dfs ( i );
#define DEBUG
#ifdef DEBUG
puts("------------FIRSTVT集-------------------");
for ( int i = 0 ; i < VN_set.size() ; i++ )
{
printf ( "%s : " , VN_set[i].left.c_str() );
set<char>::iterator it = first[i].begin();
for ( ; it!= first[i].end() ; it++ )
printf ( "%c " , *it );
puts ("" );
}
#endif
}
void dfs1 ( int x )
{
if ( vis[x] ) return;
vis[x] = 1;
string& left = VN_set[x].left;
for ( int i = 0 ; i < VN_set[x].right.size() ; i++ )
{
string& str = VN_set[x].right[i];
int n = str.length() -1;
if ( isupper(str[n] ) )
{
int y = VN_dic[str.substr(n,1)]-1;
if ( str.length() > 1 && !isupper(str[n-1]) )
last[x].insert ( str[1] );
dfs1 ( y );
set<char>::iterator it = last[y].begin();
for ( ; it != last[y].end() ; it++ )
last[x].insert ( *it );
}
else
last[x].insert ( str[n] );
}
}
void make_last ( )
{
memset ( vis , 0 , sizeof ( vis ) );
for ( int i = 0 ; i < VN_set.size() ; i++ )
if ( vis[i] ) continue;
else dfs1 ( i );
#define DEBUG
#ifdef DEBUG
puts("--------------LASTVT集---------------------");
for ( int i = 0 ; i < VN_set.size() ; i++ )
{
printf ( "%s : " , VN_set[i].left.c_str() );
set<char>::iterator it = last[i].begin();
for ( ; it!= last[i].end() ; it++ )
printf ( "%c " , *it );
puts ("" );
}
#endif
}
void make_table ( )
{
for ( int i = 0 ; i < MAX ; i++ )
for ( int j = 0 ; j < MAX ; j++ )
relation[i][j] = ' ';
for ( int i = 0 ; i < VN_set.size() ; i++ )
for ( int j = 0 ; j < VN_set[i].right.size() ; j++ )
{
string& str = VN_set[i].right[j];
for ( int k = 0 ; k < str.length()-1 ; k++ )
{
if ( !isupper(str[k]) && !isupper(str[k+1]) )
relation[str[k]][str[k+1]] = '=';
if ( !isupper(str[k]) && isupper(str[k+1]) )
{
int x = VN_dic[str.substr(k+1,1)]-1;
set<char>::iterator it = first[x].begin();
for ( ; it != first[x].end() ; it++ )
relation[str[k]][*it] = '<';
}
if ( isupper(str[k]) && !isupper(str[k+1]) )
{
int x = VN_dic[str.substr(k,1)]-1;
set<char>::iterator it = last[x].begin();
for ( ; it != last[x].end() ; it++ )
relation[*it][str[k+1]] = '>';
}
if ( k > str.length()-2 ) continue;
if ( !isupper(str[k]) && !isupper(str[k+2]) && isupper(str[k+1]) )
relation[str[k]][str[k+2]] = '=';
}
}
#define DEBUG
#ifdef DEBUG
for ( int i = 0 ; i < VT.size()*5 ; i++ )
printf ("-");
printf ( "算符优先关系表" );
for ( int i = 0 ; i < VT.size()*5 ; i++ )
printf ( "-" );
puts("");
printf ( "|%8s|" , "" );
for ( int i = 0 ; i < VT.size() ; i++ )
printf ( "%5c%5s" , VT[i] , "|" );
puts ("");
for ( int i = 0 ; i < (VT.size()+1)*10 ; i++ )
printf ("-");
puts("");
for ( int i = 0 ; i < VT.size() ; i++ )
{
printf ( "|%4c%5s" , VT[i] , "|");
for ( int j = 0 ; j < VT.size() ; j++ )
printf ( "%5c%5s" , relation[VT[i]][VT[j]] , "|" );
puts ("");
for ( int i = 0 ; i < (VT.size()+1)*10 ; i++ )
printf ("-");
puts("");
}
#endif
}
int fa[MAX];
int _find ( int x )
{
return x==fa[x]?x:fa[x] = _find ( fa[x] );
}
bool judge ( char x , char y )
{
if ( _find ( x ) == _find ( y ) )
return true;
return false;
}
void _union ( char x , char y )
{
x = _find(x);
y = _find(y);
fa[x] = y;
}
void print ( string s1 , string s2 , string s3 , string s4 , string s5 , string s6 )
{
printf ( "%-14s|%-15s%-15s%-15s%-15s%-15s\n" , s1.c_str(), s2.c_str(), s3.c_str() ,s4.c_str(),s5.c_str() , s6.c_str() );
}
void init ( )
{
for ( int i = 0 ; i < MAX ; i++ )
fa[i] = i;
for ( int i = 0 ; i < VN_set.size() ; i++ )
{
string& left = VN_set[i].left;
for ( int j = 0 ; j < VN_set[i].right.size() ; j++ )
{
string& str = VN_set[i].right[j];
if ( left.length() == 1 && str.length() == 1 )
{
// cout << left[0] << " " << str[0] << endl;
_union ( left[0] , str[0] );
// cout << _find(left[0]) << " " << _find ( str[0] ) << endl;
}
}
}
print("步骤","栈","优先关系","当前符号","剩余符号","动作");
}
string get_stk ( vector<char>& stk )
{
string ret = "";
for ( int i = 0 ; i < stk.size() ; i++ )
ret += stk[i];
return ret;
}
bool check ( const string& str1 , const string& str2 )
{
if ( str1.length() != str2.length() )
return false;
for ( int i = 0 ; i < str1.length() ; i++ )
if ( isupper(str1[i]) )
{
if ( !judge(str1[i],str2[i])) return false;
}
else
{
if ( str1[i] != str2[i] ) return false;
}
return true;
}
string reduction ( string src )
{
for ( int i = 0 ; i < VN_set.size() ; i++ )
for ( int j = 0 ; j < VN_set[i].right.size() ; j++ )
if ( check ( VN_set[i].right[j] , src ) )
return VN_set[i].left;
return "";
}
void move_reduction ( string src )
{
init ();
//cout <<"flag : " << check ( "P+P" , "E+T" ) << endl;;
vector<char> stk;
int steps= 1;
src += "#";
stk.push_back ( '#' );
for ( int i = 0 ; i < src.length() ; i++ )
{
char top = stk[stk.size()-1];
for ( int j = stk.size()-1 ; j >= 0 ; j-- )
if ( isupper(stk[j]) ) continue;
else
{
top = stk[j];
break;
}
char ch = relation[top][src[i]];
if ( ch == '<' || ch == '=' )
{
string temp = "";
if ( i == src.length() - 1 )
print ( temp+(char)(steps+48) , get_stk( stk ) , temp+ch , temp+src[i] , "" , "移进" );
else
print ( temp+(char)(steps+48) , get_stk( stk ) , temp+ch , temp+src[i] , src.substr(i+1,src.length()-i-1) , "移进" );
stk.push_back ( src[i] );
}
else
{
string temp ="";
string str ="";
int x = stk.size()-2;
if ( i == src.length() )
print ( temp+(char)(steps+48) , get_stk(stk) , temp+ch , temp + src[i] , "" , "归约" );
else
print ( temp+(char)(steps+48) , get_stk(stk) , temp+ch , temp + src[i] , src.substr(i+1,src.length()-i-1) , "归约" );
while ( true )
{
if ( stk.size() == 0 ) break;
if ( !isupper(stk[x] ) &&relation[stk[x]][top] == '<' )
break;
x--;
}
for ( int j = stk.size()-1 ; j > x; j-- )
{
str += stk[j];
stk.pop_back();
}
//cout << "YES : " << i <<" " << str << endl;
str = reduction(str);
//cout << "finish: " << i << " " << str << endl;
for ( int j = 0 ; j < str.length() ; j++ )
stk.push_back ( str[j] );
/*if ( i == src.length() )
print ( temp+(char)(steps+48) , get_stk(stk) , temp+ch , temp + src[i] , "" , "移进" );
else
print ( temp+(char)(steps+48) , get_stk(stk) , temp+ch , temp + src[i] , src.substr(i+1,src.length()-i-1) , "移进" );
stk.push_back ( src[i] );*/
i--;
}
steps++;
}
//string temp ="";
//cout << "result" << endl;
//print ( temp+(char)(steps+48) , get_stk(stk) , "","","","");
}
int main ( )
{
int n;
char s[MAX];
while ( ~scanf ( "%d" , &n ) )
{
memset ( used , 0 , sizeof ( used ) );
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;
if ( !VN_dic[s] )
{
VN_set.push_back ( WF(s) );
VN_dic[s] = VN_set.size();
}
int x = VN_dic[s]-1;
VN_set[x].insert ( s+j+2 );
for ( int k = 0 ; k < j; k++ )
if ( !isupper(s[k] ) )
{
if ( used[s[k]] ) continue;
used[s[k]] = 1;
VT.push_back ( s[k] );
}
for ( int k = j+2 ; k < len; k++ )
if ( !isupper(s[k] ) )
{
if ( used[s[k]] ) continue;
VT.push_back ( s[k] );
used[s[k]] = VT.size();
}
}
#define DEBUG
#ifdef DEBUG
puts ("************VT集*******************");
for ( int i = 0 ; i < VT.size() ; i++ )
printf ( "%c " , VT[i] );
puts ("");
puts("*************产生式*****************");
for ( int i = 0 ; i < VN_set.size() ; i++ )
VN_set[i].print();
puts("************************************");
#endif
make_first();
make_last();
make_table();
move_reduction("i+i");
}
}
~~~
### Input:
6
S->#E#
P->i
F->P
T->F
E->T
E->E+T
### Output:
