Incremental Computation Engine in JavaScript

This challenge asks you to build a JavaScript engine capable of performing calculations incrementally. Instead of recomputing an entire result from scratch when a single input changes, the engine should efficiently update the result based on the change. This is particularly useful in scenarios like financial modeling, data dashboards, or any application where calculations are complex and frequently updated with small changes to input data.

Problem Description

You are tasked with creating a JavaScript class called IncrementalCalculator. This class should be able to:

1. Accept an initial set of input values: These inputs will be stored internally.
2. Define a calculation function: This function takes the stored input values as arguments and returns a calculated result.
3. Provide an update method: This method accepts a single input value and its new value. The IncrementalCalculator should then efficiently recompute the result, only recalculating the parts of the calculation that depend on the updated input.
4. Provide a getValue method: This method returns the current calculated result.

The core challenge lies in minimizing the computational effort required by the update method. You should aim for an efficient update strategy that avoids unnecessary recalculations. A naive approach of recomputing the entire result on every update will not be sufficient.

Key Requirements:

• The IncrementalCalculator class must be implemented.
• The update method must accept the input name and the new value.
• The getValue method must return the current calculated result.
• The engine should be able to handle multiple inputs.
• The calculation function should be flexible and able to perform any valid JavaScript calculation.

Expected Behavior:

• When initialized, the IncrementalCalculator should compute the initial result using the provided calculation function and store the input values.
• When update is called, the engine should identify the dependencies between inputs and the result, and only recalculate the necessary parts of the calculation.
• getValue should always return the most up-to-date calculated result.

Edge Cases to Consider:

• What happens if an input is updated multiple times in a row?
• What happens if an input is updated with the same value it already has?
• How should the engine handle invalid input values (e.g., non-numeric values when numeric calculations are expected)? (While error handling isn't strictly required, consider how you might approach it.)
• What if the calculation function relies on external dependencies (e.g., a library function)?

Examples

Example 1:

Input:
initialInputs = { a: 10, b: 5 }
calculation = (a, b) => a * b;

const calculator = new IncrementalCalculator(initialInputs, calculation);

Output:
calculator.getValue(); // Returns 50

calculator.update('a', 15);

Output:
calculator.getValue(); // Returns 75

Explanation: The initial calculation is 10 * 5 = 50. When 'a' is updated to 15, only the multiplication needs to be recomputed: 15 * 5 = 75.

Example 2:

Input:
initialInputs = { x: 2, y: 3, z: 4 }
calculation = (x, y, z) => (x + y) * z;

const calculator = new IncrementalCalculator(initialInputs, calculation);

Output:
calculator.getValue(); // Returns 20

calculator.update('y', 5);

Output:
calculator.getValue(); // Returns 24

Explanation: The initial calculation is (2 + 3) * 4 = 20. When 'y' is updated to 5, only the addition and multiplication need to be recomputed: (2 + 5) * 4 = 28.

Example 3: (Edge Case - No Change)

Input:
initialInputs = { price: 100, quantity: 2 }
calculation = (price, quantity) => price * quantity;

const calculator = new IncrementalCalculator(initialInputs, calculation);

Output:
calculator.getValue(); // Returns 200

calculator.update('quantity', 2);

Output:
calculator.getValue(); // Returns 200

Explanation: Updating 'quantity' to its existing value should not trigger any recalculation.

Constraints

• The input values will be primitive JavaScript types (numbers, strings, booleans).
• The calculation function will be a pure function (no side effects).
• The number of inputs will be relatively small (less than 10).
• The calculation function should be reasonably efficient (avoiding extremely complex or computationally expensive operations).
• The update method should ideally take less than O(n) time, where n is the number of inputs, in most common scenarios. (A full recalculation would be O(n) but is not the goal).

Notes

• Consider using memoization or caching to store intermediate results and avoid redundant calculations.
• Think about how to efficiently track the dependencies between inputs and the result. A dependency graph might be helpful.
• The focus is on the incremental update logic, not on creating a general-purpose expression parser. You can assume the calculation function is well-formed and valid.
• While error handling is not explicitly required, consider how you might handle invalid input or calculation errors gracefully.
• Prioritize clarity and maintainability of your code. Well-structured and commented code will be appreciated.