##前情了解
[快速通道](http://blog.csdn.net/qq_24451605/article/details/50086689)
##算法分析
預測分析程序的總控程序在任何時候都是按STACK棧頂符號X和當前的輸入符號a行事的。如下圖所示，對于任何(X,a)，總控程序每次都執行下述三種可能的動作之一：
- 若X = a = ‘#’，則宣布分析成功，停止分析過程。
- 若X = a ≠‘#’，則把X從STACK棧頂彈出，讓a指向下一個輸入符號。
- 若X是一個非終結符，則查看分析表M。
- 若M[X,a]中存放著關于X的一個產生式，那么，先把X彈出STACK棧頂，然后把產生式的右部符號串按反序一一推進STACK棧（若右部符號為ε，則意味著不推什么東西進棧）。
- 在把產生式的右部符號退進棧的同時應該做這個產生式對應的語義動作（目前暫且不管）。
- 若M[X,a]中存放著“出錯標志”，則調用出錯診斷程序ERROR。
##代碼實現
~~~
#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;
//大寫字母為非終止符(可以多一個'的標號做區分)，小寫字母為終止符,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;
//檢查一個字符是否屬于一個字符串的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;
}
//檢查一個字符是否屬于一個字符串的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" , "步驟","符號棧","輸入串","所用產生式" );
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 );
}
}
~~~
### 輸入
### 輸出
