JavaScript Memoization with Multiple Arguments

Memoization is a powerful optimization technique used to speed up function calls by caching the results of expensive function calls and returning the cached result when the same inputs occur again. This challenge focuses on implementing a generic memoization function that can handle functions with multiple arguments.

Problem Description

Your task is to create a JavaScript function called memoize that takes a function fn as an argument and returns a new, memoized version of fn. The memoized function should:

• Cache the results of fn based on the arguments it receives.
• If fn is called with arguments that have been seen before, return the cached result instead of re-executing fn.
• If fn is called with new arguments, execute fn, cache its result, and then return the result.
• Handle functions with any number of arguments.

Examples

Example 1:

const factorial = (n) => {
  console.log('Calculating factorial for:', n);
  if (n <= 1) return 1;
  return n * factorial(n - 1);
};

const memoizedFactorial = memoize(factorial);

memoizedFactorial(5); // Output: Calculating factorial for: 5, Calculating factorial for: 4, Calculating factorial for: 3, Calculating factorial for: 2, Calculating factorial for: 1. Returns 120.
memoizedFactorial(5); // Output: Returns 120 (no console logs from factorial).
memoizedFactorial(3); // Output: Returns 6 (no console logs from factorial).

Explanation: The first call to memoizedFactorial(5) executes the original factorial function and caches the result. Subsequent calls with 5 or 3 retrieve the cached results without re-computation.

Example 2:

const greet = (greeting, name) => {
  console.log('Greeting:', greeting, 'for:', name);
  return `${greeting}, ${name}!`;
};

const memoizedGreet = memoize(greet);

memoizedGreet('Hello', 'Alice'); // Output: Greeting: Hello for: Alice. Returns "Hello, Alice!".
memoizedGreet('Hello', 'Alice'); // Output: Returns "Hello, Alice!" (no console log from greet).
memoizedGreet('Hi', 'Bob');     // Output: Greeting: Hi for: Bob. Returns "Hi, Bob!".
memoizedGreet('Hello', 'Alice'); // Output: Returns "Hello, Alice!" (no console log from greet).

Explanation: The memoizedGreet function correctly caches results based on the combination of both arguments. Calling with the same ('Hello', 'Alice') pair retrieves the cached result.

Example 3:

const complexOperation = (a, b, c) => {
  console.log('Performing complex operation with:', a, b, c);
  return a * b + c;
};

const memoizedComplex = memoize(complexOperation);

memoizedComplex(2, 3, 4); // Output: Performing complex operation with: 2 3 4. Returns 10.
memoizedComplex(2, 3, 4); // Output: Returns 10 (no console log from complexOperation).
memoizedComplex(5, 1, 2); // Output: Performing complex operation with: 5 1 2. Returns 7.
memoizedComplex(2, 3, 4); // Output: Returns 10 (no console log from complexOperation).
memoizedComplex(2, '3', 4); // Output: Performing complex operation with: 2 3 4. Returns 10. (Note: String '3' is coerced to number 3 by JS arithmetic, this might be a consideration for strict memoization).

Explanation: This example demonstrates memoization with three arguments. It also highlights how JavaScript's type coercion might affect cache hits if not handled carefully (though for this challenge, standard JavaScript behavior is acceptable).

Constraints

• The memoize function must accept a single argument: the function to be memoized.
• The memoized function should handle an arbitrary number of arguments passed to it.
• Arguments can be of any JavaScript type (primitives, objects, arrays).
• The cache should be managed internally within the memoize function's closure.
• Performance is a consideration; the goal is to avoid unnecessary re-computation.

Notes

• Consider how to uniquely identify a set of arguments for caching purposes. A simple approach might involve stringifying arguments, but be mindful of its limitations with complex objects.
• Think about the scope of the cache. It should persist across calls to the memoized function.
• The original function fn should be called with its original arguments (apply or spread syntax can be useful here).
• Edge cases like functions with no arguments or functions that return undefined should be handled gracefully.