编译原理：求非终结符的FOLLOW集合

还是先把代码给贴出来，回头再找时间写篇文章总结一下，分析一下数据结构和算法

#pragma once
#include <iostream>
#include <algorithm>
#include <fstream>
#include <map>
#include <set>
#include <string>
#include <stack>

using namespace std;

/*----------------------------------------全局变量存放终结符和非终结符---------------------------------------------------*/
set<string> non_terminal;                                                       //存放非终结符
set<string> productions;                                                        //存放产生式
std::map<string, string> match_map;                                             //存放非终结符和其对应的产生式的文法的键值对
std::map<string, set<string>> first;                                            //string:非终结符;set<string>:非终结符所对应的first集合
std::map<string, set<string>> follow;                                           //string:非终结符;set<string>:非终结符所对应的follow集合
bool is_not_changing = false;


void divide_words(string grammar, map<string, string>& match_map) {
    for (int i = 0; i < (int)grammar.length(); ++i) {
        if (grammar[i] == '-' && grammar[i + 1] == '>') {
            /* code */
            string left = grammar.substr(0, i);                                 //一句文法的左边即非终结符
            string right = grammar.substr(i + 2, grammar.length() - 1);         //一句文法的右边即非终结符对应的产生式
            non_terminal.insert(left);                                          //插入非终结符集合里
            productions.insert(right);                                          //插入产生式集合里
            match_map.insert(make_pair(left, right));                           //将一句文法里的非终结符和其对应的产生式作为键值对插入到匹配map里
            break;
        }
    }
}
/*将被'|'隔开的产生式拆分成对应多个的单词*/
void divide_right(string grammar_right, set<string>& small_right) {
    /*或许可以用grammar.find_first_of一个一个找|，然后用substr分开子串，最后再insert到small_right中去*/
    size_t found = grammar_right.find('|');
    if (found != string::npos) {
        int i = 0;
        string temp = "\0";
        while ((size_t)i < grammar_right.length()) {
            if (grammar_right[i] != '|') {
                temp += grammar_right[i];
                i = i + 1;
            }
            else {
                i = i + 1;
                small_right.insert(temp);
                temp = "\0";
            }
            if (i == grammar_right.length()) {
                small_right.insert(temp);
                temp = "\0";
            }
        }
    }
    else {
        small_right.insert(grammar_right);
    }
}
/*对每个非终结符non_term寻找它的非终结符集合first*/
void find_first(string non_term, set<string>& first) {
    set<string> or_words;                                               //存放产生式中被'|'隔开的单词
    auto search = match_map.find(non_term);
    if (search != match_map.end()) {
        divide_right(search->second, or_words);
        //匹配非终结符是否在or_words的开头
        for (set<string>::iterator i = or_words.begin(); i != or_words.end(); i++) {
            for (set<string>::iterator j = non_terminal.begin(); j != non_terminal.end(); j++) {
                if ((*i).find(*j) == 0) {                               //在or_words[i]的开头找到了一个非终结符
                                                                        //递归寻找非终结符j的first集合
                    find_first((*j), first);
                }
                else {                                                  //在or_words[i]的开头如果没有找到非终结符，即终结符
                    if ((*i)[0] >= 'a' && (*i)[0] <= 'z') {
                        first.insert(*i);
                    }
                    switch ((*i)[0]) {
                    case '(':
                        first.insert(string("("));
                        break;
                    case ')':
                        first.insert(string(")"));
                        break;
                    case '+':
                        first.insert(string("+"));
                        break;
                    case '*':
                        first.insert(string("*"));
                        break;
                    case '#':
                        first.insert(string("#"));
                        break;
                    default:                                            //如果没有匹配到符号的话就把这个单词插入到first集合中
                                                                        //first.insert(*i);
                        break;
                    }
                    continue;                                           //找到之后跳出循环，避免进行多余的遍历浪费时间
                }
            }
        }
    }
}

//对非终结符的follow集进行初始化，开始符号的follow集初始化成{$}，其余的初始化成空集
void initial_follow() {
    for (set<string>::iterator i = non_terminal.begin(); i != non_terminal.end(); i++) {
        if (i == non_terminal.begin()) {
            set<string> startFollow;
            startFollow.insert("$");
            auto pair = make_pair(*i, startFollow);
            follow.insert(pair);
        }
        set<string> temp_follow;
        auto pair = make_pair(*i, temp_follow);
        follow.insert(pair);
    }
}
//判断一个非终结符的first集合中是不是含有空串#
bool first_contains_null(set<string> &first) {
    auto find = first.find("#");
    if (find != first.end()) {
        return true;
    }
    return false;
}
//判断一个字符串str是否是非终结符，如果是返回true,否则返回false
bool is_non_terminal(string str) {
    auto find = non_terminal.find(str);
    if (find != non_terminal.end()) {
        return true;
    }
    return false;
}

bool is_letter(char a) {                                                        //是否是小写字母
    if (a >= 'a' && a <= 'z') {
        return true;
    }
    return false;
}

bool is_cap_letter(char a) {
    return (a >= 'A' && a <= 'Z') ? true : false;
}

//返回一个产生式的右部str的最后一个终结符或者非终结符
string find_last(string &str) {

    if ("\0" == str) {
        return "\0";
    }
    if ('\'' == str.at(str.size() - 1)) {
        string s = str.substr(str.size() - 2, 2);
        str = str.substr(0, str.size() - 2);
        return s;
    }
    else if (is_letter( str.at(str.size() - 1) ) && is_letter( str.at( str.size() - 2) ) ) {
        string s = str.substr(str.size() - 2, 2);
        str = str.substr(0, str.size() - 2);
        return s;
    }
    else {
        string s = str.substr(str.size() - 1, 1);
        str = str.substr(0, str.size() - 1);
        return s;
    }
}



int cal_follow_total_size() {                                                   //计算所有follow集合的总size
    int total_size = 0;
    for (map<string, set<string>>::iterator i = follow.begin(); i != follow.end(); i++) {
        total_size += i->second.size();
    }
    return total_size;
}

void find_follow(std::map<string, set<string>>& Follow) {
    while (!is_not_changing) {
        int fomer_size = cal_follow_total_size();
        for (std::map<string, string>::iterator i = match_map.begin(); i != match_map.end(); i++) {//对每一个产生式进行遍历
            set<string> or_words;
            string left = (*i).first;                                       //左边的非终结符A
            string right = (*i).second;                                     //右边的产生式A->b1b2b3B...
            divide_right(right, or_words);
            for (set<string>::iterator j = or_words.begin(); j != or_words.end(); j++) {
                set<string> temp = Follow.find(left)->second;
                string str;
                string word = *j;
                for (; word != "\0"; ) {
                    str = find_last(word);
                    if (!is_non_terminal(str)) {                        //是终结符
                        temp.clear();
                        temp.insert(str);
                    }
                    else {
                        for (set<string>::iterator k = temp.begin(); k != temp.end(); k++) {
                            if ("#" != (*k)) {
                                (Follow.find(str)->second).insert(*k);
                            }
                        }
                        if (!first_contains_null(first.find(str)->second)) {
                            temp = first.find(str)->second;
                        }
                        else {
                            for (set<string>::iterator m = first.find(str)->second.begin(); m != first.find(str)->second.end(); m++) {
                                temp.insert(*m);
                            }
                        }
                    }
                }
            }
        }
        //判断是否发生变化
        int latter_size = cal_follow_total_size();
        is_not_changing = fomer_size == latter_size ? true : false;
    }
}
int main() {
    /*读取文法文件*/
    const char* filename = "wenfa.txt";
    ifstream inFile(filename);
    if (!inFile) {
        cout << "\nFiled to open file " << filename;
        return -1;
    }
    string st = "\0";
    char buf[100];
    while (!inFile.eof()) {
        inFile.getline(buf, 20);
        st = buf;
        if (strlen(buf) == 0 || st == "end") {
            break;
        }
        divide_words(st, match_map);                                        //对每一行文法进行分析找出非终结符和对应的产生式
    }
    inFile.close();
    /*遍历非终结符集合，为每个非终结符寻找first集合*/
    for (set<string>::iterator i = non_terminal.begin(); i != non_terminal.end(); ++i) {
        set<string> the_first;                                              //当前非终结符的first集合
        find_first(*i, the_first);
        first.insert(make_pair(*i, the_first));
    }
    cout << "非终结符" << "\t" << "First集合" << endl;
    for (map<string, set<string>>::iterator i = first.begin(); i != first.end(); i++) {
        cout << "-------------------------" << endl;
        cout << i->first << "\t|\t";
        cout << "{ ";
        //倒序输出first集合中的元素与文法中出现的顺序保持一致
        for (set<string>::reverse_iterator j = (i->second).rbegin(); j != (i->second).rend(); j++) {
            cout << *j << ", ";
        }
        cout << "\b\b }";
        cout << endl;
    }
    cout << endl;
    initial_follow();
    find_follow(follow);
    cout << "非终结符" << "\t" << "Follow集合" << endl;
    for (map<string, set<string>>::iterator i = follow.begin(); i != follow.end(); i++) {
        cout << "------------------------------" << endl;
        cout << i->first << "\t|\t";
        cout << "{ ";
        //倒序输出first集合中的元素与文法中出现的顺序保持一致
        for (set<string>::reverse_iterator j = (i->second).rbegin(); j != (i->second).rend(); j++) {
            cout << *j << ", ";
        }
        cout << "\b\b }";
        cout << endl;
    }

    return 0;
}