math-learing/src/main/java/com/personalproject/service/MathExpressionEvaluator.java

package com.personalproject.service;

import java.util.HashMap;
import java.util.Map;
import java.util.Stack;
import java.util.function.DoubleUnaryOperator;
import java.util.regex.Pattern;

/**
 * 可处理基本算术运算的数学表达式求值器.
 */
public final class MathExpressionEvaluator {

  private static final Pattern NUMBER_PATTERN = Pattern.compile("-?\\d+(\\.\\d+)?");
  private static final Map<Character, Integer> PRECEDENCE = new HashMap<>();
  private static final Map<String, DoubleUnaryOperator> FUNCTIONS = new HashMap<>();

  static {
    PRECEDENCE.put('+', 1);
    PRECEDENCE.put('-', 1);
    PRECEDENCE.put('*', 2);
    PRECEDENCE.put('/', 2);
    PRECEDENCE.put('^', 3);

    FUNCTIONS.put("sin", angle -> Math.sin(Math.toRadians(angle)));
    FUNCTIONS.put("cos", angle -> Math.cos(Math.toRadians(angle)));
    FUNCTIONS.put("tan", angle -> Math.tan(Math.toRadians(angle)));
    FUNCTIONS.put("sqrt", Math::sqrt);
  }

  private MathExpressionEvaluator() {
    // 防止实例化此工具类
  }

  /**
   * 计算数学表达式字符串的结果.
   *
   * @param expression 要计算的数学表达式
   * @return 计算结果
   * @throws IllegalArgumentException 如果表达式无效
   */
  public static double evaluate(String expression) {
    if (expression == null) {
      throw new IllegalArgumentException("Expression cannot be null");
    }

    expression = expression.replaceAll("\\s+", ""); // 移除空白字符
    if (expression.isEmpty()) {
      throw new IllegalArgumentException("Expression cannot be empty");
    }

    // 将表达式拆分为记号
    String[] tokens = tokenize(expression);

    // 使用调度场算法将中缀表达式转换为后缀表达式
    String[] postfix = infixToPostfix(tokens);

    // 计算后缀表达式
    return evaluatePostfix(postfix);
  }

  /**
   * 将表达式拆分为数字与运算符的记号.
   *
   * @param expression 待拆分的表达式
   * @return 记号数组
   */
  private static String[] tokenize(String expression) {
    java.util.List<String> tokens = new java.util.ArrayList<>();
    StringBuilder currentNumber = new StringBuilder();

    for (int i = 0; i < expression.length(); i++) {
      char c = expression.charAt(i);

      if (Character.isDigit(c) || c == '.') {
        currentNumber.append(c);
      } else if (Character.isLetter(c)) {
        if (currentNumber.length() > 0) {
          tokens.add(currentNumber.toString());
          currentNumber.setLength(0);
        }
        StringBuilder functionBuilder = new StringBuilder();
        functionBuilder.append(c);
        while (i + 1 < expression.length() && Character.isLetter(expression.charAt(i + 1))) {
          functionBuilder.append(expression.charAt(++i));
        }
        String function = functionBuilder.toString();
        if (!isFunction(function)) {
          throw new IllegalArgumentException("Unsupported function: " + function);
        }
        tokens.add(function);
      } else if (c == '(' || c == ')') {
        if (currentNumber.length() > 0) {
          tokens.add(currentNumber.toString());
          currentNumber.setLength(0);
        }
        tokens.add(String.valueOf(c));
      } else if (isOperator(c)) {
        if (currentNumber.length() > 0) {
          tokens.add(currentNumber.toString());
          currentNumber.setLength(0);
        }

        // 处理一元负号
        if (c == '-' && (i == 0 || expression.charAt(i - 1) == '(')) {
          currentNumber.append(c);
        } else {
          tokens.add(String.valueOf(c));
        }
      } else {
        throw new IllegalArgumentException("Invalid character in expression: " + c);
      }
    }

    if (currentNumber.length() > 0) {
      tokens.add(currentNumber.toString());
    }

    return tokens.toArray(new String[0]);
  }

  /**
   * 检查字符是否为运算符.
   *
   * @param c 待检查的字符
   * @return 若字符是运算符则返回 true，否则返回 false
   */
  private static boolean isOperator(char c) {
    return c == '+' || c == '-' || c == '*' || c == '/' || c == '^';
  }

  private static boolean isFunction(String token) {
    return FUNCTIONS.containsKey(token);
  }

  /**
   * 使用调度场算法将中缀表达式转换为后缀表达式.
   *
   * @param tokens 中缀表达式的记号数组
   * @return 后缀表达式的记号数组
   */
  private static String[] infixToPostfix(String[] tokens) {
    java.util.List<String> output = new java.util.ArrayList<>();
    Stack<String> operators = new Stack<>();

    for (String token : tokens) {
      if (isNumber(token)) {
        output.add(token);
      } else if (isFunction(token)) {
        operators.push(token);
      } else if (token.equals("(")) {
        operators.push(token);
      } else if (token.equals(")")) {
        while (!operators.isEmpty() && !operators.peek().equals("(")) {
          output.add(operators.pop());
        }
        if (!operators.isEmpty()) {
          operators.pop(); // 移除 "("
        }
        if (!operators.isEmpty() && isFunction(operators.peek())) {
          output.add(operators.pop());
        }
      } else if (isOperator(token.charAt(0))) {
        while (!operators.isEmpty()
            && isOperator(operators.peek().charAt(0))
            && PRECEDENCE.get(operators.peek().charAt(0)) >= PRECEDENCE.get(token.charAt(0))) {
          output.add(operators.pop());
        }
        operators.push(token);
      }
    }

    while (!operators.isEmpty()) {
      String operator = operators.pop();
      if (operator.equals("(") || operator.equals(")")) {
        throw new IllegalArgumentException("Mismatched parentheses in expression");
      }
      output.add(operator);
    }

    return output.toArray(new String[0]);
  }

  /**
   * 计算后缀表达式的值.
   *
   * @param postfix 后缀表达式的记号数组
   * @return 计算结果
   */
  private static double evaluatePostfix(String[] postfix) {
    Stack<Double> values = new Stack<>();

    for (String token : postfix) {
      if (isNumber(token)) {
        values.push(Double.parseDouble(token));
      } else if (isOperator(token.charAt(0))) {
        if (values.size() < 2) {
          throw new IllegalArgumentException("Invalid expression: insufficient operands");
        }

        double b = values.pop();
        double a = values.pop();
        double result = performOperation(a, b, token.charAt(0));
        values.push(result);
      } else if (isFunction(token)) {
        if (values.isEmpty()) {
          throw new IllegalArgumentException(
              "Invalid expression: insufficient operands for function");
        }
        double value = values.pop();
        values.push(applyFunction(token, value));
      } else {
        throw new IllegalArgumentException("Unknown token: " + token);
      }
    }

    if (values.size() != 1) {
      throw new IllegalArgumentException("Invalid expression: too many operands");
    }

    return values.pop();
  }

  /**
   * 对两个操作数执行指定运算.
   *
   * @param a        第一个操作数
   * @param b        第二个操作数
   * @param operator 要应用的运算符
   * @return 运算结果
   */
  private static double performOperation(double a, double b, char operator) {
    switch (operator) {
      case '+':
        return a + b;
      case '-':
        return a - b;
      case '*':
        return a * b;
      case '/':
        if (b == 0) {
          throw new ArithmeticException("Division by zero");
        }
        return a / b;
      case '^':
        return Math.pow(a, b);
      default:
        throw new IllegalArgumentException("Unknown operator: " + operator);
    }
  }

  private static double applyFunction(String function, double value) {
    DoubleUnaryOperator operator = FUNCTIONS.get(function);
    if (operator == null) {
      throw new IllegalArgumentException("Unknown function: " + function);
    }
    return operator.applyAsDouble(value);
  }

  /**
   * 检查记号是否为数字.
   *
   * @param token 待检查的记号
   * @return 若为数字则返回 true，否则返回 false
   */
  private static boolean isNumber(String token) {
    return NUMBER_PATTERN.matcher(token).matches();
  }
}