Project Euler - Problem 16 #745

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		* [Problem013](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem013.js)
		* [Problem014](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem014.js)
		* [Problem015](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem015.js)
	* [Problem016](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem016.js)
		* [Problem020](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem020.js)
		* [Problem1](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem1.js)
		* [Problem10](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem10.js)
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45 changes: 45 additions & 0 deletions Project-Euler/Problem016.js

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	/**
	* Problem 16 - Power digit sum
	*
	* @see {@link https://projecteuler.net/problem=16}
	*
	* 215 = 32768 and the sum of its digits is 3 +たす 2 +たす 7 +たす 6 +たす 8 =わ 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)
	}

	console.log('Power digit sum of 2^1000 :', powerDigitSum())
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	module.exports = powerDigitSum
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16 changes: 16 additions & 0 deletions Project-Euler/test/Problem016.test.js

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	const powerDigitSum = require('../Problem016')
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	describe('Check Problem 16 - Power digit sum', () => {
	it('Power digit sum of 2^15', () => {
	expect(powerDigitSum(2, 15)).toBe(26)
	})

	it('Power digit sum of 2^1000', () => {
	expect(powerDigitSum()).toBe(1366)
	expect(powerDigitSum(2, 1000)).toBe(1366)
	})

	it('Power digit sum of 3^5000', () => {
	expect(powerDigitSum(3, 5000)).toBe(11097)
	})
	})

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