MathPaperGenerator/src/Generator.java

import java.util.Random;
import java.util.Set;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.stream.Collectors;

/**
 * 工具类：负责生成不同难度的数学题目。
 */
public class Generator {

  private static final Random RAND = new Random();
  private static final int MAX_ATTEMPTS = 2000;

  /**
   * 内部类：按用户难度等级生成题目。
   */
  static class QuestionGenerator {

    private final Login.Level level;
    private final Set<String> existing;

    QuestionGenerator(Login.Level level, List<String> existingQuestions) {
      this.level = level;
      this.existing = existingQuestions.stream().map(String::trim).collect(Collectors.toSet());
    }

    /**
     * 生成一份试卷。
     *
     * @param n 需要生成的题目数量
     * @return 生成的题目列表
     */
    List<String> generatePaper(int n) {
      Set<String> generated = new LinkedHashSet<>();
      // 防止死循环
      int attempts = 0;

      while (generated.size() < n && attempts < MAX_ATTEMPTS) {
        attempts++;
        String q = generateOneQuestion();
        // 统一去掉题号与多余空白来比对
        String key = normalize(q);
        //与文件内+本次前面生成的查重
        if (!existing.contains(key) && !generated.contains(key)) {
          generated.add(q);
        }
      }

      if (generated.size() < n) {
        System.out.println(
            "注意：无法生成足够的不重复题目，已生成 "
                + generated.size() + " 道题（请求 " + n + " 道）");
      }
      return new ArrayList<>(generated);
    }

    //去空格
    private String normalize(String s) {
      return s.replaceAll("\\s+", "").toLowerCase();
    }

    // 生成单题主逻辑
    private String generateOneQuestion() {
      int operands = RAND.nextInt(5) + 1; // 保证 1..5 个操作数
      int operands_p = RAND.nextInt(4) + 2; // 保证 2..5 个操作数
      return switch (level) {
        case PRIMARY -> genPrimary(operands_p);
        case MIDDLE -> genMiddle(operands);
        case HIGH -> genHigh(operands);
      };
    }

    // 生成小学题（只有 + - * / 和括号）
    private String genPrimary(int operands) {
      if (operands == 1) {
        return String.valueOf(randInt(1, 100));
      }
      List<String> ops = Arrays.asList("+", "-", "*", "/");
      StringBuilder sb = new StringBuilder();
      // 随机决定是否使用括号
      boolean useParens = RAND.nextBoolean();
      if (useParens && operands >= 3 && RAND.nextBoolean()) {
        // 构造 (a op b) op c ...
        sb.append("(");
        sb.append(randInt(1, 100)).append(" ").append(randomChoice(ops)).append(" ")
            .append(randInt(1, 100));
        sb.append(")");
        for (int i = 2; i < operands; i++) {
          sb.append(" ").append(randomChoice(ops)).append(" ").append(randInt(1, 100));
        }
      } else {
        // 直连
        sb.append(randInt(1, 100));
        for (int i = 1; i < operands; i++) {
          sb.append(" ").append(randomChoice(ops)).append(" ").append(randInt(1, 100));
        }
      }
      return sb.toString();
    }

    // 生成初中题：至少包含一个 ^2 或 sqrt()
    private String genMiddle(int operands) {
      // 基本表达式生成，后插入平方或开根号
      String expr = genPrimary(operands); // 基本算术
      // 2选1
      if (RAND.nextBoolean()) {
        // 找一个数字位置并替换为 (x)^2
        expr = applySquare(expr);
      } else {
        expr = applySqrt(expr);
      }
      return expr;
    }

    // 生成高中题：至少包含 sin/cos/tan
    private String genHigh(int operands) {
      String expr = genPrimary(operands);
      expr = applyTrig(expr);
      return expr;
    }

    // 把表达式中某个数字替换为 (x)^2
    private String applySquare(String expr) {
      // 寻找所有数字的片段
      List<int[]> spans = findNumberSpans(expr);
      if (spans.isEmpty()) {
        return expr + "^2";
      }
      int[] s = spans.get(RAND.nextInt(spans.size()));
      String before = expr.substring(0, s[0]);
      String num = expr.substring(s[0], s[1]);
      String after = expr.substring(s[1]);
      return before + "(" + num + ")^2" + after;
    }

    // 把表达式中某个数字替换为 sqrt(x)
    private String applySqrt(String expr) {
      List<int[]> spans = findNumberSpans(expr);
      if (spans.isEmpty()) {
        return "sqrt(" + expr + ")";
      }
      int[] s = spans.get(RAND.nextInt(spans.size()));
      String before = expr.substring(0, s[0]);
      String num = expr.substring(s[0], s[1]);
      String after = expr.substring(s[1]);
      return before + "sqrt(" + num + ")" + after;
    }

    // 把某个数字或子表达式替换为 sin(x)/cos(x)/tan(x)
    private String applyTrig(String expr) {
      List<int[]> spans = findNumberSpans(expr);
      String func = randomChoice(Arrays.asList("sin", "cos", "tan"));
      if (spans.isEmpty()) {
        return func + "(" + expr + ")";
      }
      int[] s = spans.get(RAND.nextInt(spans.size()));
      String before = expr.substring(0, s[0]);
      String num = expr.substring(s[0], s[1]);
      String after = expr.substring(s[1]);
      return before + func + "(" + num + ")" + after;
    }

    // 找出数字位置
    private List<int[]> findNumberSpans(String expr) {
      List<int[]> spans = new ArrayList<>();
      char[] chs = expr.toCharArray();
      int i = 0, n = chs.length;
      while (i < n) {
        if (Character.isDigit(chs[i])) {
          int j = i;
          while (j < n && (Character.isDigit(chs[j]))) {
            j++;
          }
          spans.add(new int[]{i, j});
          i = j;
        } else {
          i++;
        }
      }
      return spans;
    }

    //a..b随机数
    private int randInt(int a, int b) {
      return RAND.nextInt(b - a + 1) + a;
    }

    //抽签功能
    private <T> T randomChoice(List<T> list) {
      return list.get(RAND.nextInt(list.size()));
    }
  }
}