JavaScript Code Optimizer: Minimizing Operations

Code optimization is a crucial aspect of software development, especially when dealing with performance-sensitive applications. This challenge asks you to build a simple code optimizer that analyzes a sequence of mathematical operations and attempts to reduce the number of operations required to achieve the same result. The goal is to identify and eliminate redundant or unnecessary calculations.

Problem Description

You are tasked with creating a JavaScript function called optimizeOperations that takes a string representing a sequence of mathematical operations as input. The input string will consist of numbers and operators (+, -, *, /) separated by spaces. The function should parse this string, analyze the operations, and return a new string representing an optimized sequence with fewer operations, while ensuring the result remains the same. The optimization strategy should focus on simplifying expressions like a + 0, a - 0, a * 1, a / 1, a - a, a + a and similar trivial cases.

Key Requirements:

• Input: A string representing a mathematical expression (e.g., "2 + 3 * 4 - 1").
• Output: A string representing the optimized mathematical expression.
• Simplification Rules:
  • a + 0 should be simplified to a.
  • a - 0 should be simplified to a.
  • a * 1 should be simplified to a.
  • a / 1 should be simplified to a.
  • a - a should be simplified to 0.
  • a + a should be simplified to 2 * a.
• Order of Operations: The optimizer should respect the standard order of operations (PEMDAS/BODMAS). While full parsing isn't required, be mindful of how simplification might affect the overall expression.
• Error Handling: The function should handle invalid input gracefully (e.g., non-numeric values, invalid operators) by returning the original input string unchanged.

Expected Behavior:

The function should iteratively apply the simplification rules to the input string until no further simplifications are possible. The output string should be a valid mathematical expression that yields the same result as the original expression.

Edge Cases to Consider:

• Expressions with parentheses (not required to handle, return original input).
• Expressions with negative numbers.
• Expressions with floating-point numbers (not required to handle, return original input).
• Empty input string.
• Input string containing only numbers.
• Input string containing only operators.

Examples

Example 1:

Input: "2 + 3 * 4 - 1"
Output: "2 + 3 * 4 - 1"
Explanation: No simplifications apply.

Example 2:

Input: "5 + 0"
Output: "5"
Explanation:  `5 + 0` is simplified to `5`.

Example 3:

Input: "10 - 0"
Output: "10"
Explanation: `10 - 0` is simplified to `10`.

Example 4:

Input: "7 * 1"
Output: "7"
Explanation: `7 * 1` is simplified to `7`.

Example 5:

Input: "8 / 1"
Output: "8"
Explanation: `8 / 1` is simplified to `8`.

Example 6:

Input: "3 - 3"
Output: "0"
Explanation: `3 - 3` is simplified to `0`.

Example 7:

Input: "4 + 4"
Output: "2 * 4"
Explanation: `4 + 4` is simplified to `2 * 4`.

Example 8:

Input: "2 + 3 * 4 - 1 + 0"
Output: "2 + 3 * 4 - 1"
Explanation: The `+ 0` is simplified.

Constraints

• Input String Length: The input string will have a maximum length of 256 characters.
• Number Format: Numbers will be integers.
• Operator Set: Only the operators +, -, *, and / are allowed.
• Performance: The function should complete within 100ms for any valid input string.
• No External Libraries: You are not allowed to use external libraries for parsing or evaluation.

Notes

• You can split the input string into an array of tokens (numbers and operators) to make processing easier.
• Iterative simplification is a good approach. Apply the simplification rules repeatedly until no further changes occur.
• Be careful about the order of operations when applying simplifications. While full parsing isn't required, consider how simplification might affect the expression's meaning.
• Focus on the core simplification rules first. More complex optimizations can be added later if time permits.
• Consider using regular expressions for tokenizing the input string. However, be mindful of performance implications.
• The goal is to minimize the number of operations, not necessarily the length of the string. 2 * 4 is preferable to 4 + 4 in terms of operation count.