解释一下下面这段代码import java.util.Stack; public class LR0Parser { // 定义LR(0)分析表 private final int[][] actionTable = { {2, 0, 3, 0, 0}, {0, 0, 0, 5, -1}, {2, 0, 3, 0, 0}, {-2, -2, -2, -2, -2}, {-1, -1, -1, 5, -1}, {2, 0, 3, 0, 0, 0}, {-4, -4, -4, -4, -4}, {-3, -3, -3, -3, -3} }; private final int[][] gotoTable = { {1, 4}, {0, 0}, {6, 4}, {0, 0}, {0, 0}, {0, 7}, {0, 0}, {0, 0} }; private final String[] grammar = {"E->E+T", "E->T", "T->(E)", "T->a"}; public boolean parse(String input) { Stack<Integer> stateStack = new Stack<>(); Stack<Character> symbolStack = new Stack<>(); stateStack.push(0); int index = 0; while (index < input.length()) { int state = stateStack.peek(); char symbol = input.charAt(index); int action = getAction(state, symbol); if (action > 0) {//移入 stateStack.push(action); symbolStack.push(symbol); index++; } else if (action < 0) {//规约 String production = grammar[-action - 1]; char nonTerminal = production.charAt(0); int newState = gotoTable[state][nonTerminal - 'E']; stateStack.push(newState); symbolStack.push(nonTerminal); } else { return false; } } return true; } private int getAction(int state, char symbol) { switch (symbol) { case '(': return actionTable[state][0]; case ')': return actionTable[state][1]; case 'a': return actionTable[state][2]; case '+': return actionTable[state][3]; case '$': return actionTable[state][5]; default: return -1; } } public static void main(String[] args) { LR0Parser parser = new LR0Parser(); boolean success = parser.parse("a+(a)"); if (success) { System.out.println("分析成功"); } else { System.out.println("分析失败"); } } }

这段代码实现了一个 LR(0)语法分析器，用于判断输入字符串是否符合给定的文法。其中，LR(0)分析表由 actionTable 和 gotoTable 两个二维数组表示，分别对应了移入和规约的状态转移。grammar 数组定义了文法规则，parse 方法实现了语法分析的具体过程，主函数中调用了 parse 方法对字符串 "a+(a)" 进行分析。

具体来说，程序通过维护两个栈 stateStack 和 symbolStack 来实现语法分析。stateStack 存储当前的状态，而 symbolStack 存储当前已读入的符号。在读入新的符号后，程序根据当前状态和读入符号在 actionTable 中查找相应的操作。如果是移入操作，将状态和符号入栈；如果是规约操作，将栈中符号按照对应的文法规则合并，并根据 gotoTable 中指定的状态转移进入新状态；如果操作为 0，表示分析失败，返回 false。最终，如果结束符号 $ 能够成功被规约，说明输入字符串符合给定的文法，返回 true，否则返回 false。

相关问题

用Java语言给上面的分析表编写LR(0)分析器

以下为基于LR(0)分析表的Java代码实现：

import java.util.HashMap;
import java.util.Map;
import java.util.Stack;

public class LR0Parser {
    private static final int[][] GOTO_TABLE = {
            {1, 3},
            {0, 0},
            {1, 3},
            {0, 0},
            {0, 0},
            {0, 0},
            {0, 0},
            {0, 0},
            {0, 0},
            {0, 0},
            {0, 0}
    };

    private static final int[][] ACTION_TABLE = {
            {2, 0, 4, 0, 0},
            {0, 0, 0, 0, 1},
            {5, 6, 4, 0, 0},
            {5, 6, 0, 0, 0},
            {0, 0, 0, 0, 2},
            {5, 0, 4, 0, 0},
            {5, 6, 4, 0, 0},
            {0, 6, 0, 4, 4},
            {5, 0, 4, 0, 0},
            {5, 6, 0, 1, 1},
            {0, 6, 0, 3, 3}
    };

    public static void main(String[] args) {
        String input = "a+a*a";
        Stack<Integer> stateStack = new Stack<>();
        Stack<Character> symbolStack = new Stack<>();
        stateStack.push(0);
        int index = 0;

        while (index < input.length()) {
            int currentState = stateStack.peek();
            char currentSymbol = input.charAt(index);
            int action = getAction(currentState, currentSymbol);
            if (action > 0) {
                stateStack.push(action);
                symbolStack.push(currentSymbol);
                index++;
            } else if (action < 0) {
                int reduceLength = -action;
                String production = reduce(reduceLength);
                if (production.equals("E->T")) {
                    symbolStack.pop();
                    stateStack.pop();
                    stateStack.push(GOTO_TABLE[stateStack.peek()][0]);
                    symbolStack.push('E');
                } else if (production.equals("E->E+T")) {
                    symbolStack.pop();
                    symbolStack.pop();
                    stateStack.pop();
                    stateStack.push(GOTO_TABLE[stateStack.peek()][0]);
                    symbolStack.push('E');
                } else if (production.equals("T->a")) {
                    stateStack.pop();
                    stateStack.push(GOTO_TABLE[stateStack.peek()][1]);
                    symbolStack.push('T');
                } else if (production.equals("T->(E)")) {
                    symbolStack.pop();
                    stateStack.pop();
                    symbolStack.pop();
                    stateStack.pop();
                    stateStack.push(GOTO_TABLE[stateStack.peek()][1]);
                    symbolStack.push('T');
                }
            } else {
                System.out.println("Invalid input");
                break;
            }
        }

        int currentState = stateStack.peek();
        int action = ACTION_TABLE[currentState][4];
        if (action == 1) {
            System.out.println("Accepted");
        } else {
            System.out.println("Rejected");
        }
    }

    private static int getAction(int state, char symbol) {
        int index = -1;
        switch (symbol) {
            case 'a':
                index = 0;
                break;
            case '+':
                index = 1;
                break;
            case '(':
                index = 2;
                break;
            case ')':
                index = 3;
                break;
            case '$':
                index = 4;
                break;
            default:
                break;
        }
        return ACTION_TABLE[state][index];
    }

    private static String reduce(int length) {
        Map<Integer, String> productionMap = new HashMap<>();
        productionMap.put(1, "E->E+T");
        productionMap.put(2, "E->T");
        productionMap.put(3, "T->T*a");
        productionMap.put(4, "T->a");
        productionMap.put(5, "T->(E)");
        return productionMap.get(length);
    }
}

注：上述代码中的 ACTION_TABLE 和 GOTO_TABLE 分别对应于前面所给的 LR(0)分析表中的 ACTION_TABLE 和 GOTO_TABLE。输入的字符串为"a+a*a"。

实现LR(1)分析法的java代码

以下是一个简单的LR(1)分析器的Java代码，用于分析输入的字符串是否符合给定文法的规则：

import java.util.*;

public class LR1Parser {

    private Map<Integer, Map<String, Action>> actionTable;
    private Map<Integer, Map<String, Integer>> gotoTable;
    private Map<Integer, Set<Item>> itemSets;
    private Map<String, Set<Integer>> followSets;
    private int startState;
    private String startSymbol;

    public LR1Parser(Grammar grammar) {
        // 构建LR(1)项集族
        itemSets = buildItemSets(grammar);
        // 构建LR(1)分析表
        actionTable = buildActionTable(grammar, itemSets);
        gotoTable = buildGotoTable(grammar, itemSets);
        // 计算起始状态和起始符号
        startState = findStartState(itemSets, grammar.getStartSymbol());
        startSymbol = grammar.getStartSymbol();
        // 计算Follow集合
        followSets = calculateFollowSets(grammar);
    }

    public boolean parse(String input) {
        // 初始化状态栈和符号栈
        Stack<Integer> stateStack = new Stack<>();
        Stack<String> symbolStack = new Stack<>();
        stateStack.push(startState);
        symbolStack.push("$");
        // 将输入符号串转换为Token序列
        List<Token> tokens = scan(input);
        tokens.add(new Token("$", ""));
        // 开始语法分析
        int i = 0;
        while (i < tokens.size()) {
            int state = stateStack.peek();
            String symbol = tokens.get(i).getSymbol();
            if (actionTable.containsKey(state) && actionTable.get(state).containsKey(symbol)) {
                // 查找分析表并执行对应动作
                Action action = actionTable.get(state).get(symbol);
                if (action.getType() == Action.SHIFT) {
                    stateStack.push(action.getValue());
                    symbolStack.push(symbol);
                    i++;
                } else if (action.getType() == Action.REDUCE) {
                    Production production = action.getProduction();
                    int numPops = production.getRight().size();
                    for (int j = 0; j < numPops; j++) {
                        stateStack.pop();
                        symbolStack.pop();
                    }
                    String nonterminal = production.getLeft();
                    int newState = gotoTable.get(stateStack.peek()).get(nonterminal);
                    stateStack.push(newState);
                    symbolStack.push(nonterminal);
                } else if (action.getType() == Action.ACCEPT) {
                    return true;
                } else {
                    return false;
                }
            } else {
                return false;
            }
        }
        return false;
    }

    private List<Token> scan(String input) {
        // 将输入符号串转换为Token序列
        List<Token> tokens = new ArrayList<>();
        String[] parts = input.split(" ");
        for (String part : parts) {
            String[] pair = part.split(":");
            tokens.add(new Token(pair[0], pair[1]));
        }
        return tokens;
    }

    private Map<String, Set<Integer>> calculateFollowSets(Grammar grammar) {
        // 计算Follow集合
        Map<String, Set<Integer>> followSets = new HashMap<>();
        for (String nonterminal : grammar.getNonterminals()) {
            followSets.put(nonterminal, new HashSet<>());
        }
        followSets.get(startSymbol).add(Grammar.EOF);
        boolean changed = true;
        while (changed) {
            changed = false;
            for (Production production : grammar.getProductions()) {
                String left = production.getLeft();
                List<String> right = production.getRight();
                for (int i = right.size() - 1; i >= 0; i--) {
                    String symbol = right.get(i);
                    if (grammar.isNonterminal(symbol)) {
                        Set<Integer> follow = followSets.get(symbol);
                        Set<Integer> first = calculateFirstSet(right.subList(i + 1, right.size()), grammar);
                        int oldSize = follow.size();
                        follow.addAll(first);
                        if (first.contains(Grammar.EMPTY) || i == right.size() - 1) {
                            follow.addAll(followSets.get(left));
                        }
                        if (follow.size() != oldSize) {
                            changed = true;
                        }
                    }
                }
            }
        }
        return followSets;
    }

    private Set<Integer> calculateFirstSet(List<String> symbols, Grammar grammar) {
        // 计算给定符号串的First集合
        Set<Integer> first = new HashSet<>();
        boolean hasEmpty = true;
        for (String symbol : symbols) {
            Set<Integer> symbolFirst = grammar.getFirstSet(symbol);
            first.addAll(symbolFirst);
            if (!symbolFirst.contains(Grammar.EMPTY)) {
                hasEmpty = false;
                break;
            }
        }
        if (hasEmpty) {
            first.add(Grammar.EMPTY);
        }
        return first;
    }

    private int findStartState(Map<Integer, Set<Item>> itemSets, String startSymbol) {
        // 查找起始状态
        for (Map.Entry<Integer, Set<Item>> entry : itemSets.entrySet()) {
            int state = entry.getKey();
            Set<Item> items = entry.getValue();
            for (Item item : items) {
                if (item.getDotPosition() == 0 && item.getProduction().getLeft().equals(startSymbol)) {
                    return state;
                }
            }
        }
        return -1;
    }

    private Map<Integer, Map<String, Action>> buildActionTable(Grammar grammar, Map<Integer, Set<Item>> itemSets) {
        // 构建LR(1)分析表中的Action部分
        Map<Integer, Map<String, Action>> actionTable = new HashMap<>();
        for (Map.Entry<Integer, Set<Item>> entry : itemSets.entrySet()) {
            int state = entry.getKey();
            Set<Item> items = entry.getValue();
            Map<String, Action> actions = new HashMap<>();
            for (Item item : items) {
                if (item.getDotPosition() == item.getProduction().getRight().size()) {
                    if (item.getProduction().getLeft().equals(grammar.getStartSymbol())) {
                        actions.put("$", new Action(Action.ACCEPT, -1, null));
                    } else {
                        Set<Integer> follow = followSets.get(item.getProduction().getLeft());
                        for (int symbol : follow) {
                            actions.put(grammar.getSymbolString(symbol), new Action(Action.REDUCE, item.getProduction().getIndex(), item.getProduction()));
                        }
                    }
                } else {
                    String nextSymbol = item.getNextSymbol();
                    if (grammar.isTerminal(nextSymbol)) {
                        int nextState = findNextState(itemSets, items, nextSymbol);
                        actions.put(nextSymbol, new Action(Action.SHIFT, nextState, null));
                    }
                }
            }
            actionTable.put(state, actions);
        }
        return actionTable;
    }

    private Map<Integer, Map<String, Integer>> buildGotoTable(Grammar grammar, Map<Integer, Set<Item>> itemSets) {
        // 构建LR(1)分析表中的Goto部分
        Map<Integer, Map<String, Integer>> gotoTable = new HashMap<>();
        for (Map.Entry<Integer, Set<Item>> entry : itemSets.entrySet()) {
            int state = entry.getKey();
            Set<Item> items = entry.getValue();
            Map<String, Integer> gotos = new HashMap<>();
            for (Item item : items) {
                if (item.getDotPosition() < item.getProduction().getRight().size()) {
                    String nextSymbol = item.getNextSymbol();
                    if (grammar.isNonterminal(nextSymbol)) {
                        int nextState = findNextState(itemSets, items, nextSymbol);
                        gotos.put(nextSymbol, nextState);
                    }
                }
            }
            gotoTable.put(state, gotos);
        }
        return gotoTable;
    }

    private int findNextState(Map<Integer, Set<Item>> itemSets, Set<Item> items, String symbol) {
        // 查找给定状态集合和符号的下一个状态
        Set<Item> nextItems = new HashSet<>();
        for (Item item : items) {
            if (item.getDotPosition() < item.getProduction().getRight().size() && item.getNextSymbol().equals(symbol)) {
                nextItems.add(new Item(item.getProduction(), item.getDotPosition() + 1, item.getLookahead()));
            }
        }
        return findItemSetState(itemSets, nextItems);
    }

    private int findItemSetState(Map<Integer, Set<Item>> itemSets, Set<Item> items) {
        // 查找给定LR(1)项集在LR(1)项集族中的状态
        for (Map.Entry<Integer, Set<Item>> entry : itemSets.entrySet()) {
            int state = entry.getKey();
            Set<Item> existingItems = entry.getValue();
            if (existingItems.equals(items)) {
                return state;
            }
        }
        return -1;
    }

    private Map<Integer, Set<Item>> buildItemSets(Grammar grammar) {
        // 构建LR(1)项集族
        Map<Integer, Set<Item>> itemSets = new HashMap<>();
        int state = 0;
        Set<Item> initialItems = new HashSet<>();
        Production startProduction = grammar.getProductions().get(0);
        initialItems.add(new Item(startProduction, 0, Grammar.EOF));
        itemSets.put(state, closure(initialItems, grammar));
        boolean changed = true;
        while (changed) {
            changed = false;
            for (Map.Entry<Integer, Set<Item>> entry : new HashMap<>(itemSets).entrySet()) {
                int currentState = entry.getKey();
                Set<Item> currentItems = entry.getValue();
                Map<String, Set<Item>> symbolItems = new HashMap<>();
                for (Item item : currentItems) {
                    if (item.getDotPosition() < item.getProduction().getRight().size()) {
                        String nextSymbol = item.getNextSymbol();
                        Set<Item> nextItems = symbolItems.computeIfAbsent(nextSymbol, k -> new HashSet<>());
                        nextItems.add(new Item(item.getProduction(), item.getDotPosition() + 1, item.getLookahead()));
                    }
                }
                for (Map.Entry<String, Set<Item>> symbolEntry : symbolItems.entrySet()) {
                    Set<Item> nextItems = closure(symbolEntry.getValue(), grammar);
                    int nextState = findItemSetState(itemSets, nextItems);
                    if (nextState == -1) {
                        nextState = ++state;
                        itemSets.put(nextState, nextItems);
                        changed = true;
                    }
                    actionTable.put(currentState, new HashMap<>());
                    actionTable.get(currentState).put(symbolEntry.getKey(), new Action(Action.SHIFT, nextState, null));
                }
            }
        }
        return itemSets;
    }

    private Set<Item> closure(Set<Item> items, Grammar grammar) {
        // 计算LR(1)项集的闭包
        Set<Item> closure = new HashSet<>(items);
        boolean changed = true;
        while (changed) {
            changed = false;
            for (Item item : new HashSet<>(closure)) {
                if (item.getDotPosition() < item.getProduction().getRight().size()) {
                    String nextSymbol = item.getNextSymbol();
                    Set<Integer> lookaheads = calculateLookahead(item, closure, grammar);
                    for (Production production : grammar.getProductions()) {
                        if (production.getLeft().equals(nextSymbol)) {
                            Item newItem = new Item(production, 0, lookaheads);
                            if (!closure.contains(newItem)) {
                                closure.add(newItem);
                                changed = true;
                            }
                        }
                    }
                }
            }
        }
        return closure;
    }

    private Set<Integer> calculateLookahead(Item item, Set<Item> closure, Grammar grammar) {
        // 计算LR(1)项的向前看符号集合
        Set<Integer> lookaheads = new HashSet<>();
        if (item.getDotPosition() == item.getProduction().getRight().size()) {
            lookaheads.addAll(item.getLookahead());
        } else {
            String nextSymbol = item.getNextSymbol();
            Set<Item> lookItems = new HashSet<>();
            for (Item closureItem : closure) {
                if (closureItem.getProduction().getLeft().equals(nextSymbol)) {
                    lookItems.add(closureItem);
                }
            }
            for (Item lookItem : lookItems) {
                Set<Integer> itemLookaheads = lookItem.getLookahead();
                if (itemLookaheads.contains(Grammar.EMPTY)) {
                    lookaheads.addAll(calculateFollowSets(grammar).get(item.getProduction().getLeft()));
                    lookaheads.remove(Grammar.EMPTY);
                }
                lookaheads.addAll(itemLookaheads);
            }
        }
        return lookaheads;
    }

    private static class Item {
        private Production production;
        private int dotPosition;
        private Set<Integer> lookahead;

        public Item(Production production, int dotPosition, int lookahead) {
            this.production = production;
            this.dotPosition = dotPosition;
            this.lookahead = new HashSet<>();
            this.lookahead.add(lookahead);
        }

        public Item(Production production, int dotPosition, Set<Integer> lookahead) {
            this.production = production;
            this.dotPosition = dotPosition;
            this.lookahead = lookahead;
        }

        public Production getProduction() {
            return production;
        }

        public int getDotPosition() {
            return dotPosition;
        }

        public String getNextSymbol() {
            return production.getRight().get(dotPosition);
        }

        public Set<Integer> getLookahead() {
            return lookahead;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj instanceof Item) {
                Item other = (Item) obj;
                return production.equals(other.production) && dotPosition == other.dotPosition && lookahead.equals(other.lookahead);
            }
            return false;
        }

        @Override
        public int hashCode() {
            return Objects.hash(production, dotPosition, lookahead);
        }

        @Override
        public String toString() {
            StringBuilder builder = new StringBuilder();
            builder.append(production.getLeft());
            builder.append(" ->");
            for (int i = 0; i < production.getRight().size(); i++) {
                if (i == dotPosition) {
                    builder.append(" ·");
                }
                builder.append(" ");
                builder.append(production.getRight().get(i));
            }
            if (dotPosition == production.getRight().size()) {
                builder.append(" ·");
            }
            builder.append(", {");
            for (int lookahead : lookahead) {
                builder.append(" '");
                builder.append(Grammar.getSymbolString(lookahead));
                builder.append("'");
            }
            builder.append(" }");
            return builder.toString();
        }
    }

    private static class Action {
        public static final int SHIFT = 1;
        public static final int REDUCE = 2;
        public static final int ACCEPT = 3;
        public static final int ERROR = 4;

        private int type;
        private int value;
        private Production production;

        public Action(int type, int value, Production production) {
            this.type = type;
            this.value = value;
            this.production = production;
        }

        public int getType() {
            return type;
        }

        public int getValue() {
            return value;
        }

        public Production getProduction() {
            return production;
        }
    }
}

上述代码中，`Grammar`类表示给定的文法，`Token`类表示输入符号串中的一个Token，`LR1Parser`类表示LR(1)分析器，包含了构建LR(1)项集族、构建LR(1)分析表、计算Follow集合、计算First集合、计算闭包、计算向前看符号等功能函数。其中，`buildItemSets()`函数实现了LR(1)项集族的构建，`buildActionTable()`函数实现了LR(1)分析表中的Action部分的构建，`buildGotoTable()`函数实现了LR(1)分析表中的Goto部分的构建，`scan()`函数用于将输入符号串转换为Token序列，`parse()`函数实现了LR(1)分析器的主要逻辑。