##前情了解
[快速通道](http://blog.csdn.net/qq_24451605/article/details/50086689)
##算法分析
预测分析程序的总控程序在任何时候都是按STACK栈顶符号X和当前的输入符号a行事的。如下图所示，对于任何(X,a)，总控程序每次都执行下述三种可能的动作之一：
- 若X = a = ‘#’，则宣布分析成功，停止分析过程。
- 若X = a ≠‘#’，则把X从STACK栈顶弹出，让a指向下一个输入符号。
- 若X是一个非终结符，则查看分析表M。
- 若M[X,a]中存放着关于X的一个产生式，那么，先把X弹出STACK栈顶，然后把产生式的右部符号串按反序一一推进STACK栈（若右部符号为ε，则意味着不推什么东西进栈）。
- 在把产生式的右部符号退进栈的同时应该做这个产生式对应的语义动作（目前暂且不管）。
- 若M[X,a]中存放着“出错标志”，则调用出错诊断程序ERROR。
##代码实现
~~~
#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <cstdlib>
#include <vector>
#include <string>
#include <cctype>
#include <stack>
#include <map>
#include <set>
#define MAX 507
using namespace std;
//大写字母为非终止符(可以多一个'的标号做区分)，小写字母为终止符,用~代替epsilon
class WF
{
public:
string left;
set<string> right;
WF ( char s[] )
{
left = s;
}
void print ( )
{
printf ( "%s->" , left.c_str() );
set<string>::iterator it = right.begin();
if ( right.begin()!= right.end() )
{
printf ( "%s" , it->c_str() );
it++;
}
for(; it != right.end() ; it++ )
printf ( "|%s" , it->c_str() );
puts("");
}
void insert ( char s[] )
{
right.insert ( s );
}
};
map<string,set<char> > first;
map<string,set<char> > follow;
map<string,int> VN_dic;
vector<WF> VN_set;
bool used[MAX];
void dfs ( int x )
{
if ( used[x] ) return;
used[x] = 1;
string& left = VN_set[x].left;
set<string>& right = VN_set[x].right;
set<string>::iterator it = right.begin();
for ( ; it!= right.end() ; it++ )
for ( int i = 0 ; i < it->length() ; i++ )
{
if ( !isupper( it->at(i) ) && it->at(i) != '\'' )
{
first[left].insert ( it->at(i) );
break;
}
if ( isupper( it->at(i) ) )
{
int y;
if ( i != it->length()-1 && it->at(i+1) == '\'' )
y = VN_dic[it->substr(i,2)]-1;
else y = VN_dic[it->substr(i,1)]-1;
string& tleft = VN_set[y].left;
dfs ( y );
set<char>& temp = first[tleft];
set<char>::iterator it1 = temp.begin();
bool flag = true;
for ( ; it1 != temp.end() ; it1++ )
{
if ( *it1 == '~' ) flag = false;
first[left].insert( *it1 );
}
if ( flag ) break;
}
else continue;
}
}
void make_first ( )
{
memset ( used , 0 , sizeof ( used ) );
for ( int i = 0 ; i < VN_set.size() ; i++ )
dfs ( i );
#define DEBUG
#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 );
}
void make_follow ( )
{
while ( true )
{
bool goon = false;
for ( int i = 0 ; i < VN_set.size() ; i++ )
{
string& left = VN_set[i].left;
set<string>& right = VN_set[i].right;
set<string>::iterator it = right.begin();
for ( ; it!= right.end() ; it++ )
{
bool flag = true;
const string& str = *it;
for ( int j = it->length()-1 ; j >= 0 ; j-- )
{
if ( str[j] == '\'' )
{
int x = VN_dic[it->substr(j-1,2)]-1;
if ( flag )
{
int tt = follow[it->substr(j-1,2)].size();
append ( left , it->substr(j-1,2) );
int tt1 = follow[it->substr(j-1,2)].size();
if ( tt1 > tt ) goon = true;
if ( !VN_set[x].right.count("~" ) )
flag = false;
}
for ( int k = j+1 ; k < it->length() ; k++ )
{
if ( isupper(str[k]) )
{
string id;
if ( k != it->length()-1 && str[k+1] == '\'' )
id = it->substr(k,2);
else id = it->substr(k,1);
set<char>& from = first[id];
set<char>& to = follow[it->substr(j-1,2)];
int tt = to.size();
set<char>::iterator it1 = from.begin();
for ( ; it1 != from.end() ; it1++ )
if ( *it1 != '~' )
to.insert ( *it1 );
int tt1 = follow[it->substr(j-1,2)].size();
if ( tt1 > tt ) goon = true;
if ( !VN_set[VN_dic[id]-1].right.count("~") )
break;
}
else if ( str[k] != '\'' )
{
int tt = follow[it->substr(j-1,2)].size();
follow[it->substr(j-1,2)].insert ( str[k] );
int tt1 = follow[it->substr(j-1,2)].size();
if ( tt1 > tt )
goon = true;
break;
}
else continue;
}
j--;
}
else if ( isupper(str[j] ) )
{
int x = VN_dic[it->substr(j,1)]-1;
if ( flag )
{
int tt = follow[it->substr(j,1)].size();
append ( left , it->substr(j,1) );
if ( !VN_set[x].right.count("~") )
flag = false;
int tt1 = follow[it->substr(j,1)].size();
if ( tt1 > tt ) goon = true;
}
for ( int k = j+1 ; k < it->length() ; k++ )
{
if ( isupper( str[k] ) )
{
string id;
if ( k != it->length()-1 && str[k+1] == '\'' )
id = it->substr(k,2);
else id = it->substr(k,1);
set<char>& from = first[id];
set<char>& to = follow[it->substr(j,1)];
set<char>::iterator it1 = from.begin();
int tt = follow[it->substr(j,1)].size();
for ( ; it1 != from.end() ; it1++ )
if ( *it1 != '~' )
to.insert( *it1 );
int tt1 = follow[it->substr(j,1)].size();
if ( tt1 > tt ) goon = true;
if ( !VN_set[VN_dic[id]-1].right.count("~") )
break;
}
else if ( str[k] != '\'' )
{
int tt = follow[it->substr(j,1)].size();
follow[it->substr(j,1)].insert ( str[k] );
int tt1 = follow[it->substr(j,1)].size();
if ( tt1 > tt ) goon = true;
break;
}
else continue;
}
}
else flag = false;
}
}
}
if ( !goon ) break;
}
#define DEBUG
#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;
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
}
vector<map<char,string> > predict_table;
//检查一个字符是否属于一个字符串的FIRST集合
bool check_first ( const string& text , char ch )
{
for ( int i = 0 ; i < text.length() ; i++ )
{
bool hasEmpty = false;
if ( !isupper(text[i]) && text[i] != '\'' )
{
if ( text[i] != ch ) return false;
else return true;
}
else if ( isupper(text[i] ) )
{
string temp;
if ( i != text.length()-1 && text[i+1] == '\'' )
temp = text.substr(i,2);
else
temp = text.substr(i,1);
set<char>& dic = first[temp];
set<char>::iterator it = dic.begin();
for ( ; it != dic.end() ; it++ )
{
if ( *it == '~' ) hasEmpty = true;
if ( *it == ch ) return true;
}
if ( !hasEmpty) break;
}
else continue;
}
return false;
}
//检查一个字符是否属于一个字符串的FOLLOW集合
bool check_follow ( const string& text , char ch )
{
set<char>& dic = follow[text];
set<char>::iterator it = dic.begin();
for ( ; it != dic.end() ; it++ )
if ( *it == ch ) return true;
return false;
}
void make_table ()
{
map<char,string> temp;
vector<char> letter;
bool vis[500];
memset ( vis , 0 , sizeof ( vis ) );
for ( int i = 0 ; i < VN_set.size() ; i++ )
{
set<string>& right = VN_set[i].right;
set<string>::iterator it = right.begin();
for ( ; it != right.end() ; it++ )
for ( int j = 0 ; j < it->length() ; j++ )
if ( !isupper(it->at(j)) && it->at(j) != '\'' )
{
if ( vis[it->at(j)] ) continue;
vis[it->at(j)] = true;
letter.push_back ( it->at(j) );
}
}
for ( int i = 0 ; i < VN_set.size() ; i++ )
{
temp.clear();
string& left = VN_set[i].left;
set<string>& right = VN_set[i].right;
set<string>::iterator it = right.begin();
for ( ; it != right.end() ; it++ )
for ( int j = 0 ; j < letter.size() ; j++ )
{
//cout << *it << " " << letter[j] << endl;
if ( check_first ( *it , letter[j] ) )
{
//cout << "YES" << endl;
temp[letter[j]] = *it;
}
if ( it->at(0) == '~' && check_follow ( left, letter[j] ))
temp[letter[j]] = *it;
}
predict_table.push_back ( temp );
}
#define DEBUG
#ifdef DEBUG
for ( int i = 0 ; i <= (letter.size()+1)*10 ; i++ )
printf ( "-" );
puts ("");
printf ( "|%9s" , "|" );
for ( int i = 0 ; i < letter.size() ; i++ )
printf ( "%5c%5s" , letter[i] , "|" );
puts("");
for ( int i = 0 ; i <= (letter.size()+1)*10 ; i++ )
printf ( "-" );
puts("");
for ( int i = 0 ; i < VN_set.size() ; i++ )
{
printf ( "|%5s%4s" , VN_set[i].left.c_str() , "|" );
for ( int j = 0 ; j < letter.size() ; j ++ )
if ( predict_table[i].count(letter[j] ) )
printf ( "%7s%3s" , predict_table[i][letter[j]].c_str() , "|" );
else printf ( "%10s" , "|" );
puts("");
for ( int i = 0 ; i <= (letter.size()+1)*10 ; i++ )
printf ( "-" );
puts ("");
}
#endif
}
void print ( int steps , stack<string> stk , string src , string wf , int x )
{
printf ( "%-10d" , steps );
string out = "";
while ( !stk.empty() )
{
out = stk.top()+out;
stk.pop();
}
printf ( "#%-9s" , out.c_str() );
out ="";
for ( int i = x ; i < src.length() ; i++ )
out += src[i];
printf ( "%-10s" , (out+"#").c_str() );
printf ( "%-10s\n" , wf.c_str() );
}
void analyse ( const string& src )
{
stack<string> stk;
stk.push ( "E" );
int steps = 0;
int idx = 0;
printf ( "%-10s%-10s%-10s%-10s\n" , "步骤","符号栈","输入串","所用产生式" );
while ( !stk.empty() )
{
string u = stk.top();
string tmp="";
stk.pop();
if ( !isupper(u[0]) )
{
if ( idx == src.length() && u[0] == '~' );
else if ( src[idx] == u[0] )
idx++;
}
else
{
int x = VN_dic[u]-1;
tmp = predict_table[x][src[idx]];
for ( int i = tmp.length()-1 ; i >= 0 ; i-- )
{
if ( tmp[i] == '\'' )
{
string v = tmp.substr(i-1,2);
stk.push ( v );
i--;
}
else
{
string v = tmp.substr(i,1);
stk.push( v );
}
}
tmp = u+"->"+tmp;
}
print ( steps++ , stk , src , tmp , idx );
}
}
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;
if ( !VN_dic[s] )
{
VN_set.push_back ( s );
VN_dic[s] = VN_set.size();
}
int x = VN_dic[s]-1;
VN_set[x].insert ( s+j+2 );
}
make_first();
make_follow();
make_table();
string in = "i*i+i";
analyse( in );
}
}
~~~
### 输入
### 输出
