[編譯器][C/C++] simple regex to NFA＠Morris' Blog

2014-03-14 22:17:48| 人氣7,122| 回應0 | 上一篇 | 下一篇

[編譯器][C/C++] simple regex to NFA

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請參考 http://mypaper.pchome.com.tw/zerojudge/post/1324174148

Input format:

輸入只會有一筆 NFA 描述，輸入以 EOF(end-of-file) 為結尾。

輸入第一行為字母集(set of input symbols Σ)，表示方法為 "(c₁, c₂, … c_n, size)"。其中 c_i 為 ASCII [32, 127] 的可視字符，其中特別以 'l' 字符表示 lambda。size(size = n-1)則為字母集的大小。

接下來會有數行表示每一個狀態的轉移，每一行上會有 n 個集合以 ‘(’ 和 ‘)’ 做為區隔，每個集合中會用逗號(‘,’)區隔每一個狀態編號。對於第 i 行的第 j 個集合 s(i, j)，表示 state_i 可以藉由 c_j 轉移到 s(i, j) 中任意狀態。

若第 i 行上的集合出現 ‘*’，表示 state_i 是一個 accepting state F_i。特別以 state₁ 作為 start state。

(1 <= i <= m, 1 <= j <= n < size)

Output format:

輸出一組 DFA，格式如下。
輸出第一行為字母集 C_DFA (按照字典順序輸出)。

接下來會有輸出 m 行，每行上表示每一個狀態的轉移，第一個集合為對應原本 NFA 的元素集合，接下來會有 C_DFA.size() 個狀態，每個狀態皆以集合的方式呈現。對於第 i 行的第 j+1 個狀態 state_j，表示 state_i 可以藉由 C_DFA[j] 轉移到 state_j。

並且對應 NFA 的元素集合，採用最小字典順序的方式輸出(即排序後輸出)，若該狀態可以被 accepted，則使用一個 ‘*’ 放到狀態最前面輸出。

請參考範例輸入輸出。

為了方便起見，這個程式用來讀入一個簡單的正規表達式並且轉成指定的 NFA Table (格式如上)。

simple regex 是只由 a-z 構成主要字符，能當作 operator 的只有 '(', ')', '|', '*'

寫的方式還正在想辦法改進，對於每一個狀態都是一個指標來儲存，用來方便串接 NFA 的狀態複製，但這樣的情況會造成，想要複製 NFA 的時候，對於每一個狀態並不是真的複製，整個程式在運行時，每個狀態皆會一直保留，忘了著手 free() 和 clone() ...

Sample Input

(a|b)*a
(a|b)*bb
(b)*(ab(b)*)*b
(aaaa|b)*
a*((ba)*baa)*b*

Sample Output

(l,a,b)
(2,3)(0)(0)
(4,5)(0)(0)
(6)(0)(0)
(0)(7)(0)
(0)(0)(8)
(0)(9)(0)
(10)(0)(0)
(10)(0)(0)
(*)(*)(*)
(2,3)(0)(0)

(l,a,b)
(2,3)(0)(0)
(4,5)(0)(0)
(6)(0)(0)
(0)(7)(0)
(0)(0)(8)
(0)(0)(9)
(10)(0)(0)
(10)(0)(0)
(0)(0)(11)
(2,3)(0)(0)
(*)(*)(*)

(l,a,b)
(2,3)(0)(0)
(0)(0)(4)
(5)(0)(0)
(2,3)(0)(0)
(6,7)(0)(0)
(0)(8)(0)
(9)(0)(0)
(0)(0)(10)
(0)(0)(11)
(12)(0)(0)
(*)(*)(*)
(13,14)(0)(0)
(0)(0)(15)
(6,7)(0)(0)
(13,14)(0)(0)

(l,a,b)
(2,3)(0)(0)
(4,5)(0)(0)
(*)(*)(*)
(0)(6)(0)
(0)(0)(7)
(0)(8)(0)
(9)(0)(0)
(0)(10)(0)
(2,3)(0)(0)
(0)(11)(0)
(9)(0)(0)

(l,a,b)
(2,3)(0)(0)
(0)(4)(0)
(5)(0)(0)
(2,3)(0)(0)
(6,7)(0)(0)
(8,9)(0)(0)
(10)(0)(0)
(0)(0)(11)
(12)(0)(0)
(13,14)(0)(0)
(0)(15)(0)
(0)(0)(16)
(0)(0)(17)
(*)(*)(*)
(8,9)(0)(0)
(0)(18)(0)
(13,14)(0)(0)
(0)(19)(0)
(6,7)(0)(0)

#include <stdio.h>
#include <stdlib.h>
#include <vector>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <sstream>
#include <iostream>
#include <algorithm>
using namespace std;
class State {
   public:
       State(int ac=0) {
           accepted = ac;
       }
       bool accepted;
       int nameLabel;
       map<char, vector<State*> > trans;
};
class DFA {
   public:
       State* Q0;
       vector<State*> Q, F;
};
class NFA {
   public:
       static char lambda;
       State* Q0;
       vector<State*> Q;
       vector<State*> F;
       vector< vector<State*> > make_deterministic(DFA &M, vector<char> alpha);
       static NFA getNFAbyString(const char str[]);
       static NFA getNFA_Star(NFA nfa);
       static NFA getNFA_OR(NFA n1, NFA n2);
       static NFA getNFA_AND(NFA n1, NFA n2);
       void print();
       void printTable();
       void buildLabel();
   private:
       vector<State*> getSetOf(vector<State*> set_of_states, char c);
       vector<State*> getClose(vector<State*> set_of_states);
};
char NFA::lambda = 0;
vector<State*> NFA::getSetOf(vector<State*> set_of_states, char c) {
   set<State*> h;
   vector<State*> ret;
   queue<State*> q;
   State* index;
   for(int i = 0; i < set_of_states.size(); i++) {
       index = set_of_states[i];
       q.push(index);
   }
   while(!q.empty()) {
       index = q.front(), q.pop();
       vector<State*> state_trans = index->trans[c];
       for(int i = 0; i < state_trans.size(); i++) {
           if(h.find(state_trans[i]) == h.end()) {
               h.insert(state_trans[i]);
               ret.push_back(state_trans[i]);
           }
       }
   }
   return ret;
}
/*
* Add to S all states reachable from it
* using only lembda transitions of N
*/
vector<State*> NFA::getClose(vector<State*> set_of_states) {
   set<State*> h;
   vector<State*> ret;
   queue<State*> q;
   State* index;
   for(int i = 0; i < set_of_states.size(); i++) {
       index = set_of_states[i];
       q.push(index), h.insert(index);
   }
   while(!q.empty()) {
       index = q.front(), q.pop();
       ret.push_back(index);
       vector<State*> state_trans = index->trans[NFA::lambda];
       for(int i = 0; i < state_trans.size(); i++) {
           if(h.find(state_trans[i]) == h.end()) {
               h.insert(state_trans[i]);
               q.push(state_trans[i]);
           }
       }
   }
   sort(ret.begin(), ret.end());
   return ret;
}
vector< vector<State*> > NFA::make_deterministic(DFA &M, vector<char> alpha) {
   vector< vector<State*> > T;
   vector<State*> stateSet;
   stateSet.push_back(Q0);
   vector<State*> init_state = getClose(stateSet);
   T.push_back(init_state);
   M.Q.push_back(new State());
   for(int i = 0; i < T.size(); i++) {
       State* state = M.Q[i];
       for(int j = 0; j < T[i].size(); j++)
           if(T[i][j]->accepted)
               state->accepted = 1;
       state->nameLabel = i;
       if(state->accepted)   M.F.push_back(state);
       for(int j = 0; j < alpha.size(); j++) {
           if(alpha[j] == NFA::lambda)
               continue;
           vector<State*> next_state = getSetOf(T[i], alpha[j]);
           next_state = getClose(next_state);
           int existIdx = -1;
           for(int k = 0; k < T.size(); k++) {
               if(T[k] == next_state) {
                   existIdx = k;
                   break;
               }
           }
           if(existIdx < 0) {
               T.push_back(next_state);
               M.Q.push_back(new State());
               existIdx = T.size()-1;
           }
           M.Q[i]->trans[alpha[j]].push_back(M.Q[existIdx]);
       }
   }
   M.Q0 = M.Q[0];
   return T;
}

NFA NFA::getNFAbyString(const char str[]) {
   NFA ret;
   ret.Q.push_back(new State());
   ret.Q0 = ret.Q[0];
   for(int i = 0; str[i]; i++) {
       ret.Q.push_back(new State());
       ret.Q[i]->trans[str[i]].push_back(ret.Q[i+1]);
   }
   ret.Q[ret.Q.size()-1]->accepted = 1;
   ret.F.push_back(ret.Q[ret.Q.size()-1]);
   return ret;
}

NFA NFA::getNFA_Star(NFA nfa) {
   State *s1, *s2;
   s1 = new State();
   s2 = new State(true);
   for(int i = 0; i < nfa.F.size(); i++) {
       nfa.F[i]->accepted = 0;
       nfa.F[i]->trans[NFA::lambda].push_back(s2);
       nfa.F[i]->trans[NFA::lambda].push_back(nfa.Q0);
   }
   s1->trans[NFA::lambda].push_back(nfa.Q0);
   s1->trans[NFA::lambda].push_back(s2);
   nfa.F.clear();
   nfa.F.push_back(s2);
   nfa.Q.push_back(s1);
   nfa.Q.push_back(s2);
   nfa.Q0 = s1;
   return nfa;
}

NFA NFA::getNFA_OR(NFA n1, NFA n2) {
   State *s1, *s2;
   s1 = new State();
   s2 = new State(true);
   s1->trans[NFA::lambda].push_back(n1.Q0);
   s1->trans[NFA::lambda].push_back(n2.Q0);
   for(int i = 0; i < n1.F.size(); i++) {
       n1.F[i]->accepted = 0;
       n1.F[i]->trans[NFA::lambda].push_back(s2);
   }
   n1.F.clear();
   for(int i = 0; i < n2.F.size(); i++) {
       n2.F[i]->accepted = 0;
       n2.F[i]->trans[NFA::lambda].push_back(s2);
   }
   for(int i = 0; i < n2.Q.size(); i++)
       n1.Q.push_back(n2.Q[i]);
   n1.F.push_back(s2);
   n1.Q.push_back(s1);
   n1.Q.push_back(s2);
   n1.Q0 = s1;
   return n1;
}
NFA NFA::getNFA_AND(NFA n1, NFA n2) {
   for(int i = 0; i < n1.F.size(); i++) {
       n1.F[i]->accepted = 0;
       n1.F[i]->trans[NFA::lambda].push_back(n2.Q0);
   }
   n1.F.clear();
   for(int i = 0; i < n2.F.size(); i++)
       n1.F.push_back(n2.F[i]);
   for(int i = 0; i < n2.Q.size(); i++)
       n1.Q.push_back(n2.Q[i]);
   return n1;
}
bool cmp(const State* a, const State* b) {
   return a->nameLabel < b->nameLabel;
}
void NFA::print() {
   printf("start[%d]\n", Q0->nameLabel);
   for(int i = 0; i < F.size(); i++) {
       printf("F[%d]", F[i]->nameLabel);
   }
   puts("");
   sort(Q.begin(), Q.end(), cmp);
   for(int i = 0; i < Q.size(); i++) {
       printf("Q[%d] : ", Q[i]->nameLabel);
       for(map<char, vector<State*> >::iterator it = Q[i]->trans.begin();
           it != Q[i]->trans.end(); it++) {
           printf("[%c,", it->first == 0 ? '~' : it->first);
           for(vector<State*>::iterator jt = it->second.begin();
               jt != it->second.end(); jt++) {
               printf(" %d", (*jt)->nameLabel);
           }
           printf("]");
       }
       puts("");
   }
}
void NFA::printTable() {
   set<char> alpha;
   sort(Q.begin(), Q.end(), cmp);
   for(int i = 0; i < Q.size(); i++) {
       for(map<char, vector<State*> >::iterator it = Q[i]->trans.begin();
           it != Q[i]->trans.end(); it++) {
           alpha.insert(it->first);
       }
   }
   for(set<char>::iterator it = alpha.begin(); it != alpha.end(); it++) {
       putchar(it == alpha.begin() ? '(' : ',');
       if(*it == NFA::lambda)   printf("l");
       else                   printf("%c", *it);
   }
   puts(")");
   for(int i = 0; i < Q.size(); i++) {
       for(set<char>::iterator it = alpha.begin();
           it != alpha.end(); it++) {
           vector<State*> &v = Q[i]->trans[*it];
           if(v.size() == 0)
               printf(Q[i]->accepted ? "(*)" : "(0)");
           else {
               printf("(%s", Q[i]->accepted ? "*" : "");
               sort(v.begin(), v.end(), cmp);
               for(int j = 0; j < v.size(); j++) {
                   printf("%d%c", v[j]->nameLabel+1, j == v.size()-1 ? ')' : ',');
               }
           }
       }
       puts("");
   }
}

void NFA::buildLabel() {
   set<State*> R;
   queue<State*> Q;
   int labelIdx = 0;
   Q.push(Q0), R.insert(Q0);
   while(!Q.empty()) {
       State* node = Q.front();
       Q.pop();
       node->nameLabel = labelIdx++;
       for(map<char, vector<State*> >::iterator it = node->trans.begin();
           it != node->trans.end(); it++) {
           for(vector<State*>::iterator jt = it->second.begin();
               jt != it->second.end(); jt++) {
               if(R.find(*jt) == R.end()) {
                   R.insert(*jt);
                   Q.push(*jt);
               }
           }
       }
   }
}
int priority_op(char c) {
    switch(c) {
        case '(':return 0;
        case '*':return 1;
        case '|':case '+':return 2;
    }
    return -1;
}
void trans(char infix[], char buffer[]) {
    int len = strlen(infix);
    char *ptr = buffer;
    stack<char> op;
    stack<int> elem;
    elem.push(0);
    *ptr = '\0';
    for(int i = 0; i < len; i++) {
        if(infix[i] >= 'a' && infix[i] <= 'z') {
           while(!op.empty() && op.top() == '*') {
               sprintf(ptr, "* ", op.top()), op.pop();
               while(*ptr)   ptr++;
           }
           while(infix[i] >= 'a' && infix[i] <= 'z' && i < len) {
               sprintf(ptr, "%c", infix[i]);
               while(*ptr)    ptr++;
               i++;
            }
            i--;
            sprintf(ptr, " ");
            while(*ptr)    ptr++;
            elem.top()++;
        }else {
            if(infix[i] == ')') {
                while(!op.empty() && op.top() != '(') {
                   if(op.top() == '|')   elem.top()--;
                    sprintf(ptr, "%c ", op.top()), op.pop();
                    while(*ptr) ptr++;
                }
                while(elem.top() > 1) {
                    sprintf(ptr, "+ ");
                    while(*ptr) ptr++;
                    elem.top()--;
                }
                elem.pop();
                elem.top()++;
                op.pop();
            } else {
                if(infix[i] != '(') {
                   while(!op.empty() && priority_op(op.top()) >= priority_op(infix[i])) {
                       sprintf(ptr, "%c ", op.top()), op.pop();
                       while(*ptr) ptr++;
                   }
                } else {
                   while(!op.empty() && op.top() == '*') {
                       sprintf(ptr, "* ", op.top()), op.pop();
                       while(*ptr)   ptr++;
                   }
                   elem.push(0);
                }
                op.push(infix[i]);
            }
        }
    }
    while(!op.empty()) {
        sprintf(ptr, "%c ", op.top()), op.pop();
        while(*ptr) ptr++;
    }
    while(elem.top() > 1) {
        sprintf(ptr, "+ ");
        while(*ptr) ptr++;
        elem.top()--;
    }
    elem.pop();
}
NFA calcPostfix(char postfix[]) {
    int len = strlen(postfix);
    stack<NFA> stk;
    stringstream sin(postfix);
    string token;
    while(sin >> token) {
       if(token[0] == '*') {
           NFA a;
            a = stk.top(), stk.pop();
            stk.push(NFA::getNFA_Star(a));
       } else if(token[0] == '|' || token[0] == '+') {
           NFA a, b;
            b = stk.top(), stk.pop();
            a = stk.top(), stk.pop();
            switch(token[0]) {
               case '|':stk.push(NFA::getNFA_OR(a, b));break;
               case '+':stk.push(NFA::getNFA_AND(a, b));break;
           }
       } else {
           stk.push(NFA::getNFAbyString(token.c_str()));
       }
    }
    return stk.top();
}
int main() {
   char s[1024], postfix[1024];
   while(scanf("%s", s) == 1) {
       trans(s, postfix);
       // puts(postfix);
       NFA ret = calcPostfix(postfix);
       ret.buildLabel();
       ret.printTable();
   }
   return 0;
}
/*
// strings ending with a
(a|b)*a
// strings ending with bb
(a|b)*bb
// strings ending with b and not containing aa
(b)*(ab(b)*)*b

(aaaa|b)*

a*((ba)*baa)*b*

an(ba)*bn

*/

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