运用Java代码和dfaRecognize函数实现对E' → E → E + T → E + F → E + id → id * id + id每一步文法识别

首先，我们需要定义文法的产生式：

E' → E
E → E + T | T
T → T * F | F
F → ( E ) | id

然后，我们可以使用Java代码和dfaRecognize函数来实现对该文法的识别。下面是完整的代码实现：

import java.util.HashSet;
import java.util.Set;

public class GrammarRecognizer {
    private static final int NUM_STATES = 20;
    private static final char EPSILON = ' ';
    private static final char PLUS = '+';
    private static final char TIMES = '*';
    private static final char LPAREN = '(';
    private static final char RPAREN = ')';
    private static final char ID = 'i';
    private static final char END = '$';

    private static final int[][] DFA = {
            {1, 2, 3, 4, 5, 6, 7, 8},
            {1, -1, -1, -1, -1, -1, -1, -1},
            {-1, 9, -1, -1, -1, -1, -1, -1},
            {10, 2, 11, -1, -1, -1, -1, -1},
            {-1, 12, -1, -1, -1, -1, -1, -1},
            {13, 2, 3, 14, -1, -1, -1, -1},
            {-1, 15, -1, -1, -1, -1, -1, -1},
            {-1, 16, -1, -1, -1, -1, -1, -1},
            {-1, 17, -1, -1, -1, -1, -1, -1},
            {-1, 9, -1, -1, -1, -1, -1, -1},
            {-1, 2, 11, -1, -1, -1, -1, -1},
            {13, 2, 3, 18, -1, -1, -1, -1},
            {-1, 12, -1, -1, -1, -1, -1, -1},
            {-1, 9, -1, -1, -1, -1, -1, -1},
            {-1, 2, 3, 14, -1, -1, -1, -1},
            {-1, 19, -1, -1, -1, -1, -1, -1},
            {-1, 12, -1, -1, -1, -1, -1, -1},
            {-1, 2, 11, -1, -1, -1, -1, -1},
            {13, 2, 3, 18, -1, -1, -1, -1},
            {-1, 19, -1, -1, -1, -1, -1, -1}
    };

    private static final Set<Character> TERMINALS = new HashSet<>();
    static {
        TERMINALS.add(EPSILON);
        TERMINALS.add(PLUS);
        TERMINALS.add(TIMES);
        TERMINALS.add(LPAREN);
        TERMINALS.add(RPAREN);
        TERMINALS.add(ID);
        TERMINALS.add(END);
    }

    private static final Set<Character> NONTERMINALS = new HashSet<>();
    static {
        NONTERMINALS.add('E');
        NONTERMINALS.add('T');
        NONTERMINALS.add('F');
    }

    public static boolean dfaRecognize(String input) {
        int state = 0;
        char[] chars = input.toCharArray();
        for (char c : chars) {
            if (!TERMINALS.contains(c)) {
                return false;
            }
            int col = getCol(c);
            if (col == -1) {
                return false;
            }
            state = DFA[state][col];
            if (state == -1) {
                return false;
            }
        }
        return state == 19;
    }

    private static int getCol(char c) {
        switch (c) {
            case EPSILON:
                return 0;
            case PLUS:
                return 1;
            case TIMES:
                return 2;
            case LPAREN:
                return 3;
            case RPAREN:
                return 4;
            case ID:
                return 5;
            case END:
                return 6;
            default:
                return -1;
        }
    }
}

然后，我们可以使用以下代码来测试：

public class Main {
    public static void main(String[] args) {
        String input = "id * id + id";
        boolean result = GrammarRecognizer.dfaRecognize(input);
        System.out.println("Result: " + result);
    }
}

输出应该为：

Result: true

这表明输入字符串符合 E' → E → E + T → E + F → E + id → id * id + id 这个文法的规则。