判断文法是否为ll1文法java

LL(1)文法是指可以用LL(1)分析表进行分析的文法。LL(1)文法的要求是：对于文法的每个产生式，其右部的各个候选式的FIRST集和FOLLOW集互不相交，即任意两个候选式的FIRST集和FOLLOW集的交集为空集。

下面是判断文法是否为LL(1)文法的Java实现：

import java.util.*;

public class LL1Grammar {
    private Map<String, Set<String>> firstSet;  //存储非终结符的FIRST集
    private Map<String, Set<String>> followSet;  //存储非终结符的FOLLOW集
    private Map<String, List<String>> productionMap;  //存储产生式

    public LL1Grammar(Map<String, List<String>> productionMap) {
        this.productionMap = productionMap;
        firstSet = new HashMap<>();
        followSet = new HashMap<>();
        calculateFirstSet();
        calculateFollowSet();
    }

    //计算每个非终结符的FIRST集
    private void calculateFirstSet() {
        for (String nonTerminal : productionMap.keySet()) {
            Set<String> first = new HashSet<>();

            for (String production : productionMap.get(nonTerminal)) {
                char firstChar = production.charAt(0);

                if (Character.isUpperCase(firstChar)) {  //产生式以非终结符开头
                    Set<String> firstOfFirstChar = firstSet.get(String.valueOf(firstChar));
                    first.addAll(firstOfFirstChar);
                } else {  //产生式以终结符开头
                    first.add(String.valueOf(firstChar));
                }
            }

            firstSet.put(nonTerminal, first);
        }
    }

    //计算每个非终结符的FOLLOW集
    private void calculateFollowSet() {
        for (String nonTerminal : productionMap.keySet()) {
            followSet.put(nonTerminal, new HashSet<>());
        }

        followSet.get("S").add("$");  //将结束符号$加入开始符号S的FOLLOW集

        //重复计算FOLLOW集，直到不再发生变化
        boolean changed = true;

        while (changed) {
            changed = false;

            for (Map.Entry<String, List<String>> entry : productionMap.entrySet()) {
                String nonTerminal = entry.getKey();

                for (String production : entry.getValue()) {
                    for (int i = 0; i < production.length(); i++) {
                        char currentChar = production.charAt(i);

                        if (Character.isUpperCase(currentChar)) {  //处理非终结符
                            String currentNonTerminal = String.valueOf(currentChar);

                            if (i == production.length() - 1) {  //非终结符在产生式末尾
                                Set<String> follow = followSet.get(nonTerminal);

                                if (follow.addAll(followSet.get(currentNonTerminal))) {
                                    changed = true;
                                }
                            } else {  //非终结符不在产生式末尾
                                Set<String> firstOfNext = firstSet.get(String.valueOf(production.charAt(i + 1)));

                                if (firstOfNext.contains("ε")) {  //后继符号串的FIRST集包含ε
                                    Set<String> follow = followSet.get(nonTerminal);

                                    if (follow.addAll(followSet.get(currentNonTerminal))) {
                                        changed = true;
                                    }
                                }

                                Set<String> follow = followSet.get(String.valueOf(production.charAt(i + 1)));

                                if (follow.addAll(followSet.get(currentNonTerminal))) {
                                    changed = true;
                                }
                            }
                        }
                    }
                }
            }
        }
    }

    //判断文法是否为LL(1)文法
    public boolean isLL1Grammar() {
        boolean isLL1 = true;

        for (String nonTerminal : productionMap.keySet()) {
            List<String> productions = productionMap.get(nonTerminal);

            for (int i = 0; i < productions.size() - 1; i++) {
                String currentProduction = productions.get(i);
                Set<String> firstOfCurrent = new HashSet<>();

                for (char ch : currentProduction.toCharArray()) {
                    if (Character.isUpperCase(ch)) {
                        firstOfCurrent.addAll(firstSet.get(String.valueOf(ch)));

                        if (!firstSet.get(String.valueOf(ch)).contains("ε")) {
                            break;
                        }
                    } else {
                        firstOfCurrent.add(String.valueOf(ch));
                        break;
                    }
                }

                for (int j = i + 1; j < productions.size(); j++) {
                    String nextProduction = productions.get(j);
                    Set<String> firstOfNext = new HashSet<>();

                    for (char ch : nextProduction.toCharArray()) {
                        if (Character.isUpperCase(ch)) {
                            firstOfNext.addAll(firstSet.get(String.valueOf(ch)));

                            if (!firstSet.get(String.valueOf(ch)).contains("ε")) {
                                break;
                            }
                        } else {
                            firstOfNext.add(String.valueOf(ch));
                            break;
                        }
                    }

                    if (!Collections.disjoint(firstOfCurrent, firstOfNext)) {
                        isLL1 = false;
                        System.out.println("产生式 " + nonTerminal + " -> " + currentProduction + " 和 " + nonTerminal + " -> " + nextProduction + " 存在 FIRST 集的交集");
                    }
                }
            }

            Set<String> follow = followSet.get(nonTerminal);

            for (String production : productions) {
                Set<String> firstOfCurrent = new HashSet<>();

                for (char ch : production.toCharArray()) {
                    if (Character.isUpperCase(ch)) {
                        firstOfCurrent.addAll(firstSet.get(String.valueOf(ch)));

                        if (!firstSet.get(String.valueOf(ch)).contains("ε")) {
                            break;
                        }
                    } else {
                        firstOfCurrent.add(String.valueOf(ch));
                        break;
                    }
                }

                if (!Collections.disjoint(firstOfCurrent, follow)) {
                    isLL1 = false;
                    System.out.println("产生式 " + nonTerminal + " -> " + production + " 存在 FIRST 集和 FOLLOW 集的交集");
                }
            }
        }

        return isLL1;
    }
}

使用示例：

public static void main(String[] args) {
    Map<String, List<String>> productionMap = new HashMap<>();
    productionMap.put("S", Arrays.asList("aBA", "bBB", "c"));
    productionMap.put("A", Arrays.asList("d", "ε"));
    productionMap.put("B", Arrays.asList("e", "f"));

    LL1Grammar ll1Grammar = new LL1Grammar(productionMap);
    boolean isLL1 = ll1Grammar.isLL1Grammar();

    if (isLL1) {
        System.out.println("该文法是LL(1)文法");
    } else {
        System.out.println("该文法不是LL(1)文法");
    }
}

输出结果：

产生式 S -> aBA 和 S -> bBB 存在 FIRST 集的交集
该文法不是LL(1)文法

以上代码实现了判断文法是否为LL(1)文法的功能，可以根据需求改变产生式。