Java实现LR（1）分析法

在Java中实现LR(1)分析法，可以采用以下步骤：

1. 定义文法：使用Java代码定义给定文法，例如：

String[][] productionRules = {
    {"E", "E + T"},
    {"E", "E - T"},
    {"E", "T"},
    {"T", "T * F"},
    {"T", "T / F"},
    {"T", "F"},
    {"F", "( E )"},
    {"F", "i"}
};

2. 构建LR(1)项集族：根据给定文法，构建LR(1)项集族。

3. 构建LR(1)分析表：根据LR(1)项集族，构建LR(1)分析表。

4. 实现LR(1)分析器：使用Java代码实现LR(1)分析器，并使用LR(1)分析表对输入符号串进行分析。

下面是一个简单的Java实现LR(1)分析法的示例：

import java.util.*;

public class LR1 {
    // 定义文法
    static String[][] productionRules = {
        {"E", "E + T"},
        {"E", "E - T"},
        {"E", "T"},
        {"T", "T * F"},
        {"T", "T / F"},
        {"T", "F"},
        {"F", "( E )"},
        {"F", "i"}
    };

    // 定义LR(1)项
    static class LR1Item {
        String left;
        String[] right;
        String[] lookahead;

        public LR1Item(String left, String[] right, String[] lookahead) {
            this.left = left;
            this.right = right;
            this.lookahead = lookahead;
        }

        public boolean equals(Object obj) {
            if (!(obj instanceof LR1Item)) return false;
            LR1Item item = (LR1Item) obj;
            return left.equals(item.left) && Arrays.equals(right, item.right) && Arrays.equals(lookahead, item.lookahead);
        }

        public int hashCode() {
            return Objects.hash(left, Arrays.hashCode(right), Arrays.hashCode(lookahead));
        }

        public String toString() {
            return left + " -> " + String.join(" ", right) + " , " + String.join(" ", lookahead);
        }
    }

    // 构建LR(1)项集族
    static Map<Set<LR1Item>, Integer> buildLR1ItemSets() {
        Map<Set<LR1Item>, Integer> itemSets = new HashMap<>();
        Queue<Set<LR1Item>> queue = new LinkedList<>();
        int id = 0;

        // 添加起始项 S' -> .E
        Set<LR1Item> startItemSet = new HashSet<>();
        startItemSet.add(new LR1Item("S'", new String[]{"E"}, new String[]{"$"}));
        itemSets.put(startItemSet, id++);
        queue.offer(startItemSet);

        while (!queue.isEmpty()) {
            Set<LR1Item> itemSet = queue.poll();
            Map<String, Set<LR1Item>> itemSetMap = new HashMap<>();

            // 按照圆点后面的符号对项进行分类
            for (LR1Item item : itemSet) {
                if (item.right.length == 0 || item.right[0].equals("#")) {
                    continue;
                }
                String nextSymbol = item.right[item.lookahead.length];
                Set<LR1Item> nextItemSet = itemSetMap.computeIfAbsent(nextSymbol, k -> new HashSet<>());
                nextItemSet.add(new LR1Item(item.left, item.right, Arrays.copyOfRange(item.lookahead, 1, item.lookahead.length)));
            }

            // 对每个分类后的项集构建新的项集
            for (Map.Entry<String, Set<LR1Item>> entry : itemSetMap.entrySet()) {
                Set<LR1Item> nextItemSet = entry.getValue();
                if (itemSets.containsKey(nextItemSet)) {
                    continue;
                }
                itemSets.put(nextItemSet, id++);
                queue.offer(nextItemSet);
            }
        }

        return itemSets;
    }

    // 构建LR(1)分析表
    static Map<Integer, Map<String, Object>> buildLR1AnalysisTable() {
        Map<Integer, Map<String, Object>> analysisTable = new HashMap<>();
        Map<Set<LR1Item>, Integer> itemSets = buildLR1ItemSets();

        // 对于每个项集
        for (Map.Entry<Set<LR1Item>, Integer> entry : itemSets.entrySet()) {
            Set<LR1Item> itemSet = entry.getKey();
            int state = entry.getValue();
            Map<String, Object> stateAction = new HashMap<>();

            // 对于每个 LR(1) 项
            for (LR1Item item : itemSet) {
                if (item.right.length == 0) { // 归约项
                    for (String lookahead : item.lookahead) {
                        stateAction.put(lookahead, "r" + (Arrays.asList(productionRules).indexOf(new String[]{item.left})) + "");
                    }
                } else { // 移进项
                    String nextSymbol = item.right[item.lookahead.length];
                    if (nextSymbol.equals("#")) {
                        nextSymbol = "$";
                    }
                    int nextState = itemSets.get(itemSetMap.get(nextSymbol));
                    stateAction.put(nextSymbol, "s" + nextState);
                }
            }

            analysisTable.put(state, stateAction);
        }

        return analysisTable;
    }

    // 分析符号串
    static boolean analyze(String input, Map<Integer, Map<String, Object>> analysisTable) {
        Stack<Integer> stateStack = new Stack<>();
        Stack<String> symbolStack = new Stack<>();
        stateStack.push(0);
        symbolStack.push("$");

        int i = 0;
        while (i < input.length()) {
            int state = stateStack.peek();
            String symbol = input.charAt(i) + "";
            Map<String, Object> stateAction = analysisTable.get(state);
            Object action = stateAction.get(symbol);
            if (action == null) {
                return false;
            }
            if (action instanceof String) { // 移进操作
                String s = (String) action;
                stateStack.push(Integer.parseInt(s.substring(1)));
                symbolStack.push(symbol);
                i++;
            } else { // 规约操作
                int rule = (int) action;
                String[] production = productionRules[rule];
                for (int j = 0; j < production[1].length(); j++) {
                    stateStack.pop();
                    symbolStack.pop();
                }
                int nextState = stateStack.peek();
                symbolStack.push(production[0]);
                stateStack.push((int) analysisTable.get(nextState).get(production[0]));
            }
        }

        return true;
    }

    public static void main(String[] args) {
        String input = "i+i*i";
        Map<Integer, Map<String, Object>> analysisTable = buildLR1AnalysisTable();
        boolean result = analyze(input, analysisTable);
        System.out.println(result);
    }
}

在以上代码中，LR1Item表示一个LR(1)项，buildLR1ItemSets方法用于构建LR(1)项集族，buildLR1AnalysisTable方法用于构建LR(1)分析表，analyze方法用于实现LR(1)分析器，main方法用于测试分析器。