Problem_Generator/src/BracketManager.java

import java.util.List;
import java.util.Random;

/**
 * 负责生成并添加括号
 */
public class BracketManager {
  private static final Random RANDOM = new Random();
  
  /**
   * 根据元素个数选择括号对数
   * 3 -> 80% 1对 20%0对
   * 4 -> 90% 1对 10%2对
   * 5 -> 50% 1对 50%2对
   */
  public int decideParenthesesPairs(int numCount) {
    return switch (numCount) {
      case 3 -> RANDOM.nextDouble() < 0.8 ? 1 : 0;
      case 4 -> RANDOM.nextDouble() < 0.9 ? 1 : 2;
      case 5 -> RANDOM.nextDouble() < 0.5 ? 1 : 2;
      default -> 0;
    };
  }
  
  // 添加括号
  public String addParentheses(String expression, int pairs, List<Integer> numPositions) {
    String[] tokens = expression.split(" ");
    int numCount = numPositions.size();
    boolean[] markLeft = new boolean[numCount];
    boolean[] markRight = new boolean[numCount];
    
    generateBracketPositions(numCount, numPositions, pairs, tokens, markLeft, markRight);
    String result = insertBrackets(tokens, markLeft, markRight);
    return validateParentheses(result) ? result : expression;
  }
  
  //计算生成括号的位置
  private void generateBracketPositions(int numCount, List<Integer> numPositions, int pairs, String[] tokens,
                                        boolean[] markLeft, boolean[] markRight) {
    int attempts = 0;
    for (int p = 0; p < pairs && attempts < 50; p++, attempts++) {
      boolean placed = false;
      for (int tries = 0; tries < 50 && !placed; tries++) {
        int start = RANDOM.nextInt(numCount - 1);
        int end = start + 1 + RANDOM.nextInt(numCount - start - 1);
        if (end >= numCount) end = numCount - 1;
        
        // 20%概率尝试嵌套在已有括号内部
        if (RANDOM.nextDouble() < 0.2) {
          for (int i = 0; i < numCount; i++) {
            if (markLeft[i]) {
              start = i;
              end = i + RANDOM.nextInt(numCount - i);
              break;
            }
          }
        }
        
        if (canPlaceBracket(start, end, markLeft, markRight, numPositions, tokens)) {
          markLeft[start] = true;
          markRight[end] = true;
          placed = true;
        }
      }
    }
  }
  
  //检测添加括号的合法性
  private boolean canPlaceBracket(int start, int end, boolean[] markLeft, boolean[] markRight,
                                  List<Integer> numPositions, String[] tokens) {
    if (isOuterMostBracket(start, end, markLeft.length)) return false;
    if (isInvalidOverlap(start, end, markLeft, markRight)) return false;
    return isValidBracketRange(tokens, numPositions, start, end);
  }
  
  //避免最外层括号
  private boolean isOuterMostBracket(int start, int end, int numCount) {
    return start == 0 && end == numCount - 1;
  }
  
  //允许嵌套但禁止交叉
  private boolean isInvalidOverlap(int start, int end, boolean[] markLeft, boolean[] markRight) {
    for (int i = start; i <= end; i++) {
      // start/end可重合，内部禁止已有左右括号
      if ((i != start && markLeft[i]) || (i != end && markRight[i])) return true;
    }
    return false;
  }
  
  //检测括号是否有意义（优先级）
  private boolean isValidBracketRange(String[] tokens, List<Integer> numPositions, int start, int end) {
    int opStart = numPositions.get(start) + 1;
    int opEnd = numPositions.get(end) - 1;
    String firstOp = null;
    boolean hasHigherOuterOp = false;
    
    for (int i = opStart; i <= opEnd; i += 2) {
      if (!isNumber(tokens[i])) {
        if (firstOp == null) firstOp = tokens[i];
        else if (isDifferentPriority(firstOp, tokens[i])) {
          hasHigherOuterOp = true;
          break;
        }
      }
    }
    return hasHigherOuterOp || firstOp == null;
  }
  
  //比较运算符优先级
  private boolean isDifferentPriority(String op1, String op2) {
    int p1 = (op1.equals("+") || op1.equals("-")) ? 1 : 2;
    int p2 = (op2.equals("+") || op2.equals("-")) ? 1 : 2;
    return p1 != p2;
  }
  
  //插入操作
  private String insertBrackets(String[] tokens, boolean[] markLeft, boolean[] markRight) {
    StringBuilder sb = new StringBuilder();
    int numIndex = 0;
    for (String token : tokens) {
      if (isNumber(token)) {
        if (markLeft[numIndex]) sb.append("( ");
        sb.append(token);
        if (markRight[numIndex]) sb.append(" )");
        numIndex++;
      } else {
        sb.append(" ").append(token).append(" ");
      }
    }
    return sb.toString();
  }
  
  //检查括号是否缺失
  private boolean validateParentheses(String expr) {
    int balance = 0;
    for (char c : expr.toCharArray()) {
      if (c == '(') balance++;
      if (c == ')') balance--;
      if (balance < 0) return false;
    }
    return balance == 0;
  }
  
  private boolean isNumber(String token) {
    try { Integer.parseInt(token); return true; }
    catch (NumberFormatException e) { return false; }
  }
}