Simple Expression Compiler in Vue.js with TypeScript

This challenge asks you to build a basic compiler within a Vue.js component. The compiler will take a simple mathematical expression as a string input and evaluate it, displaying the result in the component. This exercise combines front-end development with a simplified compiler concept, demonstrating how to handle user input, parse it, and perform calculations within a Vue application.

Problem Description

You need to create a Vue.js component that accepts a mathematical expression as input from the user (via a text input field) and displays the result of evaluating that expression. The component should include:

1. Input Field: A text input field where the user can enter the mathematical expression.
2. Calculate Button: A button that, when clicked, triggers the compilation and evaluation of the expression.
3. Result Display: A designated area (e.g., a <div>) to display the calculated result.
4. Error Handling: The component should gracefully handle invalid expressions (e.g., syntax errors, division by zero) and display an appropriate error message in the result display area.

The expressions will be limited to basic arithmetic operations: addition (+), subtraction (-), multiplication (*), and division (/). They can include integers and floating-point numbers. Parentheses are not required for this simplified compiler.

Key Requirements:

• The compiler should be implemented within a Vue.js component using TypeScript.
• The expression evaluation should be performed using JavaScript's eval() function (for simplicity in this exercise – note the security implications of eval() in production environments, discussed in the Notes section).
• The component should update the result display whenever the user enters a new expression and clicks the "Calculate" button.
• The component should display an error message if the expression is invalid or results in an error during evaluation.

Expected Behavior:

• When the user enters a valid expression and clicks "Calculate," the component should display the result of the expression.
• When the user enters an invalid expression, the component should display an error message (e.g., "Invalid Expression").
• When the expression results in an error during evaluation (e.g., division by zero), the component should display an error message (e.g., "Error: Division by zero").
• The input field should be cleared after a successful calculation or an error.

Edge Cases to Consider:

• Empty input string.
• Expressions containing only whitespace.
• Expressions with invalid characters (e.g., letters, symbols other than +, -, *, /).
• Division by zero.
• Expressions with leading or trailing spaces.

Examples

Example 1:

Input: "2 + 3 * 4"
Output: 14
Explanation: The expression is evaluated as 2 + (3 * 4) = 2 + 12 = 14.

Example 2:

Input: "10 / 2 - 1"
Output: 4
Explanation: The expression is evaluated as (10 / 2) - 1 = 5 - 1 = 4.

Example 3:

Input: "5 + a"
Output: Invalid Expression
Explanation: The expression contains an invalid character 'a'.

Example 4:

Input: "10 / 0"
Output: Error: Division by zero
Explanation: The expression results in division by zero, which is an error.

Example 5:

Input: ""
Output: Invalid Expression
Explanation: The input is an empty string.

Constraints

• The expressions will consist of integers and floating-point numbers, and the operators +, -, *, and /.
• Parentheses are not allowed.
• The component must be implemented using Vue.js 3 and TypeScript.
• The component should be reasonably performant for simple expressions (evaluation time should be negligible).
• The input string length should not exceed 256 characters.

Notes

• Security Considerations of eval(): Using eval() can be dangerous in production environments if the input is not carefully sanitized, as it allows arbitrary code execution. For a real-world compiler, you would use a safer parsing and evaluation method (e.g., a custom parser and abstract syntax tree). This challenge uses eval() for simplicity and to focus on the Vue.js component implementation.
• Error Handling: Implement robust error handling to catch potential exceptions during expression evaluation. Use try...catch blocks to handle errors gracefully.
• Input Sanitization: While not strictly required for this simplified challenge, consider adding basic input sanitization to remove potentially harmful characters.
• Component Structure: Think about how to structure your Vue.js component to keep the code organized and maintainable. Consider using data properties for the input expression, the result, and any error messages.
• Testing: While not explicitly required, consider how you would test your component to ensure it handles various inputs correctly.