/**

* Problem 20 - Factorial digit sum

*

* @see {@link https://projecteuler.net/problem=20}

*

* n! means n × (n − 1) × ... × 3 × 2 × 1

*

* For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,

* and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27

*

* Find the sum of the digits in the number 100!

*/

const factorialDigitSum = (n = 100) => {

// Consider each digit*10^exp separately, right-to-left ([units, tens, ...]).

const digits = [1]

for (let x = 2; x <= n; x++) {

let carry = 0

for (let exp = 0; exp < digits.length; exp++) {

const prod = digits[exp] * x + carry

carry = Math.floor(prod / 10)

digits[exp] = prod % 10

}

while (carry > 0) {

digits.push(carry % 10)

carry = Math.floor(carry / 10)

}

}

// (digits are reversed but we only want the sum so it doesn't matter)

return digits.reduce((prev, current) => prev + current, 0)

}

export { factorialDigitSum }