How to Do Factorial with Memoization in JavaScript

Factorial can be defined with a recursive function in JavaScript with a single line in the following way:

const factorial = n => n <= 1 ? 1 : n * factorial(n - 1)

// The above is equivalent to:
const factorial = (n) => {
    if (n <= 1) {
        return 1
    }

    return n * factorial(n - 1)
}

// Returns 3628800
factorial(10)

This means that if the passed number is less than or equal to 1, then the output will be 1, otherwise, it will be n * factorial(n-1). Based on the formula, we can define factorial as:

n! = n * (n - 1) * ... * 1

or

n! = n ∗ factorial (n − 1)

To memoize a factorial function in JavaScript, we need to create an array to store previously calculated values inside it and return the value that already exists in the array (cache) rather than recalculating it.

const factorialCache = []
const factorialWithMemoization = n => {
    if (!factorialCache[n]) {
  	factorialCache[n] = n <= 1 ? 1 : n * factorial(n - 1)
    }

    return factorialCache[n]
}

in case the value doesn't exist in the cache, we can create it at the given index, and return the cached value during the next call. This means that if we call the function with 10 again, the cache will be equal to the following:

(11) [empty × 10, 3628800]

To compare the performance difference between the two factorial functions, check out the benchmark created on jsben.ch.

Make sure you never prematurely optimize code in JavaScript. Optimize when performance issues arise.

Want to learn more about how memoization works in JavaScript? Check out how you can create a memoize decorator in JavaScript in the following tutorial:

The Decorator Design Pattern in JavaScriptBenchmark and optimize your code with the help of decoratorsLearn how you can use decorators in JavaScript, to wrap a method or a property into another function to extends its original functionality...Learn More