运用java语言 构造识别活前缀的DFA (即LR(0)项目集规范族的构造)

下面是一个示例Java代码，用于构造LR(0)项目集规范族并生成识别活前缀的DFA：

import java.util.*;

public class LR0Parser {
    private final Map<Integer, Map<String, Integer>> transitions;
    private final Map<Integer, Map<String, String>> actions;

    public LR0Parser(Grammar grammar) {
        // 构造LR(0)项目集规范族
        List<Set<Item>> canonicalCollection = buildCanonicalCollection(grammar);

        // 构造DFA
        transitions = new HashMap<>();
        actions = new HashMap<>();
        int state = 0;
        for (Set<Item> items : canonicalCollection) {
            Map<String, Integer> transition = new HashMap<>();
            Map<String, String> action = new HashMap<>();
            for (Item item : items) {
                if (item.isReduce()) {
                    String production = item.getProduction().toString();
                    if (item.getProduction().getLeft().equals(grammar.getStart())) {
                        action.put("$", "accept");
                    } else {
                        for (String lookahead : item.getLookaheads()) {
                            action.put(lookahead, production);
                        }
                    }
                } else {
                    String symbol = item.getNextSymbol();
                    int target = getGoto(items, symbol, canonicalCollection);
                    if (grammar.isTerminal(symbol)) {
                        action.put(symbol, "shift " + target);
                    } else {
                        transition.put(symbol, target);
                    }
                }
            }
            transitions.put(state, transition);
            actions.put(state, action);
            state++;
        }
    }

    // 构造LR(0)项目集规范族
    private List<Set<Item>> buildCanonicalCollection(Grammar grammar) {
        List<Set<Item>> canonicalCollection = new ArrayList<>();
        Set<Item> startItemSet = closure(Collections.singleton(new Item(grammar.getStartProduction(), 0, "$")));
        canonicalCollection.add(startItemSet);

        boolean changed = true;
        while (changed) {
            changed = false;
            for (int i = 0; i < canonicalCollection.size(); i++) {
                Set<Item> itemSet = canonicalCollection.get(i);
                Map<String, Set<Item>> transitions = new HashMap<>();
                for (Item item : itemSet) {
                    if (!item.isReduce()) {
                        String symbol = item.getNextSymbol();
                        Set<Item> targetSet = closure(item.moveDot());
                        transitions.computeIfAbsent(symbol, k -> new HashSet<>()).addAll(targetSet);
                    }
                }
                for (Map.Entry<String, Set<Item>> entry : transitions.entrySet()) {
                    Set<Item> targetSet = entry.getValue();
                    if (!canonicalCollection.contains(targetSet)) {
                        canonicalCollection.add(targetSet);
                        changed = true;
                    }
                }
            }
        }

        return canonicalCollection;
    }

    // 计算一个项目集的闭包
    private Set<Item> closure(Set<Item> itemSet) {
        Set<Item> closure = new HashSet<>(itemSet);
        boolean changed = true;
        while (changed) {
            changed = false;
            Set<Item> newItems = new HashSet<>();
            for (Item item : closure) {
                if (!item.isReduce()) {
                    String symbol = item.getNextSymbol();
                    if (!item.getProduction().isNullable() && symbol != null && !newItems.contains(item.moveDot())) {
                        newItems.add(item.moveDot());
                    }
                }
            }
            if (!newItems.isEmpty()) {
                closure.addAll(newItems);
                changed = true;
            }
        }
        return closure;
    }

    // 计算一个项目集在给定符号下的转移
    private int getGoto(Set<Item> itemSet, String symbol, List<Set<Item>> canonicalCollection) {
        Set<Item> targetSet = new HashSet<>();
        for (Item item : itemSet) {
            if (!item.isReduce() && item.getNextSymbol().equals(symbol)) {
                targetSet.add(item.moveDot());
            }
        }
        return canonicalCollection.indexOf(closure(targetSet));
    }

    // 解析输入串
    public boolean parse(String input) {
        Deque<Integer> stateStack = new ArrayDeque<>();
        Deque<String> symbolStack = new ArrayDeque<>();
        stateStack.push(0);
        symbolStack.push("$");
        int index = 0;
        while (true) {
            int state = stateStack.peek();
            String symbol = index < input.length() ? String.valueOf(input.charAt(index)) : "$";
            if (!actions.get(state).containsKey(symbol)) {
                return false;
            }
            String action = actions.get(state).get(symbol);
            if (action.equals("accept")) {
                return true;
            } else if (action.startsWith("shift")) {
                int target = Integer.parseInt(action.substring(6));
                stateStack.push(target);
                symbolStack.push(symbol);
                index++;
            } else {
                Production production = Production.fromString(action);
                for (int i = 0; i < production.getRight().size(); i++) {
                    stateStack.pop();
                    symbolStack.pop();
                }
                String nonterminal = production.getLeft();
                state = stateStack.peek();
                stateStack.push(transitions.get(state).get(nonterminal));
                symbolStack.push(nonterminal);
            }
        }
    }
}

这段代码中，LR0Parser类代表了LR(0)分析器，它接受一个文法作为参数，并构造了LR(0)项目集规范族及其对应的DFA。在构造DFA时，对于每个LR(0)项目集，我们使用transitions和actions两个Map来分别存储转移函数和动作表。在解析输入串时，我们使用两个栈来模拟分析栈和符号栈的变化过程。