设计简单算数表达式语法分析器算法;(用ll(1)方式实现)代码

以下是一个简单的算数表达式LL(1)语法分析器的实现，使用Java语言实现：

import java.util.*;

public class LL1Parser {
    private static final Map<String, Set<String>> FIRST_SET = new HashMap<>();
    private static final Map<String, Set<String>> FOLLOW_SET = new HashMap<>();
    private static final Map<String, Map<String, String>> PARSE_TABLE = new HashMap<>();

    static {
        // 初始化FIRST集
        FIRST_SET.put("E", new HashSet<>(Arrays.asList("(", "num")));
        FIRST_SET.put("E'", new HashSet<>(Arrays.asList("+", "")));
        FIRST_SET.put("T", new HashSet<>(Arrays.asList("(", "num")));
        FIRST_SET.put("T'", new HashSet<>(Arrays.asList("*", "")));
        FIRST_SET.put("F", new HashSet<>(Arrays.asList("(", "num")));

        // 初始化FOLLOW集
        FOLLOW_SET.put("E", new HashSet<>(Arrays.asList(")", "$")));
        FOLLOW_SET.put("E'", new HashSet<>(Arrays.asList(")", "$")));
        FOLLOW_SET.put("T", new HashSet<>(Arrays.asList("+", ")", "$")));
        FOLLOW_SET.put("T'", new HashSet<>(Arrays.asList("+", ")", "$")));
        FOLLOW_SET.put("F", new HashSet<>(Arrays.asList("*", "+", ")", "$")));

        // 初始化LL(1)分析表
        PARSE_TABLE.put("E", new HashMap<>());
        PARSE_TABLE.get("E").put("(", "TE'");
        PARSE_TABLE.get("E").put("num", "TE'");
        PARSE_TABLE.put("E'", new HashMap<>());
        PARSE_TABLE.get("E'").put("+", "+TE'");
        PARSE_TABLE.get("E'").put(")", "");
        PARSE_TABLE.get("E'").put("$", "");
        PARSE_TABLE.put("T", new HashMap<>());
        PARSE_TABLE.get("T").put("(", "FT'");
        PARSE_TABLE.get("T").put("num", "FT'");
        PARSE_TABLE.put("T'", new HashMap<>());
        PARSE_TABLE.get("T'").put("*", "*FT'");
        PARSE_TABLE.get("T'").put("+", "");
        PARSE_TABLE.get("T'").put(")", "");
        PARSE_TABLE.get("T'").put("$", "");
        PARSE_TABLE.put("F", new HashMap<>());
        PARSE_TABLE.get("F").put("(", "(E)");
        PARSE_TABLE.get("F").put("num", "num");
    }

    public static boolean parse(String input) {
        Stack<String> stack = new Stack<>();
        stack.push("$");
        stack.push("E");

        int i = 0;
        String lookahead = Character.toString(input.charAt(i));

        while (!stack.isEmpty()) {
            String X = stack.pop();

            if (isTerminal(X)) {
                if (X.equals(lookahead)) {
                    if (lookahead.equals("$")) {
                        return true;
                    }
                    i++;
                    lookahead = Character.toString(input.charAt(i));
                } else {
                    return false;
                }
            } else {
                Map<String, String> row = PARSE_TABLE.get(X);
                String production = row.get(lookahead);
                if (production == null) {
                    return false;
                }

                if (!production.equals("")) {
                    String[] symbols = production.split("");
                    for (int k = symbols.length - 1; k >= 0; k--) {
                        stack.push(symbols[k]);
                    }
                }
            }
        }

        return false;
    }

    private static boolean isTerminal(String symbol) {
        return !FIRST_SET.containsKey(symbol);
    }
}

在该实现中，首先初始化了FIRST集、FOLLOW集和LL(1)分析表，然后实现了一个parse方法，用于进行语法分析。具体实现过程和步骤见注释。