Memoize a recursive Fibonacci function

Question

I created a withMemo function that returns a memoized version of the provided function.

const memoizedFn = withMemo(fn)

How can I memoize this fibonacci function that works with recursion ?

const fibo = (n) => {

  if (n <= 1) return 1
  
  return fibo(n - 2) + fibo(n - 1)
}

Indeed withMemo(fibo) doesn't improve performance since the recursive calls inside fibo still point to the unmemoized version...

So I have to alter the declaration of fibo to make momoization work:

    const momoizableFibo = memoizer => {
      const fibo = (n) => {
    
        if (n <= 1) return 1
      
        return memoizer(fibo)(n - 2) + memoizer(fibo)(n - 1)
      }
      
      return memoizer(fibo)
    }
// momoizableFibo(withMemo)(50) // takes a ms 

Is there a way to memoize fibo (or any other recursive function for that matter) without altering it's declaration in the way I did ?

Answer 1

You can use let fibo instead of const fibo. Then replace the fibo variable with a memoized version. By updating fibo the nested call will now refer to the memoized fibo function instead of the original.

let fibo = (n) => {
  console.log(n); // <- show original fibo calls
  if (n <= 1) return 1;
  return fibo(n - 2) + fibo(n - 1);
}
// update fibo variable so the nested fibo call calls the memoized version
fibo = withMemo(fibo);

console.log("fibo(3)", "//=>", fibo(3));
console.log("fibo(5)", "//=>", fibo(5));
console.log("fibo(2)", "//=>", fibo(2));


// simplified memoize function, only works for serializable parameters
function withMemo(fn) {
  const cache = new Map();
  return function (...args) {
    const key = JSON.stringify(args);
    if (cache.has(key)) return cache.get(key);
    const result = fn(...args);
    cache.set(key, result);
    return result;
  }
}