如何判断字符串中数学表达式的结果是否正确？

function isMathExpressionValid(expression) {
  // Step 1: 检查表达式中是否只包含合法字符

  // 正则表达式匹配非法字符
  const illegalChars = /[^0-9+\-*/()\s]/;
  if (illegalChars.test(expression)) {
    return false;
  }

  // Step 2: 检查括号匹配

  const stack = [];
  for (let i = 0; i < expression.length; i++) {
    if (expression[i] === '(') {
      stack.push('(');
    } else if (expression[i] === ')') {
      if (stack.length === 0) {
        return false; // 右括号多于左括号
      }
      stack.pop();
    }
  }
  if (stack.length !== 0) {
    return false; // 左括号多于右括号
  }

  // Step 3: 将中缀表达式转换为后缀表达式

  const operators = {
    '+': 1,
    '-': 1,
    '*': 2,
    '/': 2,
  };

  const outputQueue = [];
  const operatorStack = [];

  const tokens = expression.split(/\s+/); // 按空格分割表达式

  for (let i = 0; i < tokens.length; i++) {
    const token = tokens[i];
    if (!isNaN(token)) {
      outputQueue.push(token); // 数字直接输出
    } else if (token in operators) {
      while (
        operatorStack.length > 0 &&
        operators[token] <= operators[operatorStack[operatorStack.length - 1]]
      ) {
        outputQueue.push(operatorStack.pop());
      }
      operatorStack.push(token);
    } else if (token === '(') {
      operatorStack.push(token);
    } else if (token === ')') {
      while (operatorStack.length > 0 && operatorStack[operatorStack.length - 1] !== '(') {
        outputQueue.push(operatorStack.pop());
      }
      operatorStack.pop(); // 弹出左括号
    }
  }

  while (operatorStack.length > 0) {
    outputQueue.push(operatorStack.pop());
  }

  // Step 4: 计算后缀表达式

  const stack = [];
  for (let i = 0; i < outputQueue.length; i++) {
    const token = outputQueue[i];
    if (!isNaN(token)) {
      stack.push(parseFloat(token));
    } else if (token in operators) {
      const b = stack.pop();
      const a = stack.pop();
      let result;
      switch (token) {
        case '+':
          result = a + b;
          break;
        case '-':
          result = a - b;
          break;
        case '*':
          result = a * b;
          break;
        case '/':
          if (b === 0) {
            return false; // 除零错误
          }
          result = a / b;
          break;
      }
      stack.push(result);
    }
  }

  if (stack.length !== 1) {
    return false; // 表达式错误
  }

  // Step 5: 返回结果

  return true;
}

// 示例用法
const expression = '3 + 4 * (2 - 1)';
const isValid = isMathExpressionValid(expression);
console.log(isValid); // 输出: true