/**

* Problem 16 - Power digit sum

*

* @see {@link https://projecteuler.net/problem=16}

*

* 2¹⁵ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

*

* What is the sum of the digits of the number 2¹⁰⁰⁰ ?

*/

/**

* Returns the power digit sum of n^pow.

*

* @param {number} [n=2]

* @param {number} [pow=1000]

* @returns {number}

*/

const powerDigitSum = function (n = 2, pow = 1000) {

// The idea is to consider each digit (d*10^exp) separately, right-to-left.

// digits = [units, tens, ...]

const digits = [n]

let p = 1

while (++p <= pow) {

let carry = 0

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

const prod = digits[exp] * n + 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 { powerDigitSum }