diff --git a/Project-Euler/Problem020.js b/Project-Euler/Problem020.js index fc92df4f9..fa67bec80 100644 --- a/Project-Euler/Problem020.js +++ b/Project-Euler/Problem020.js @@ -1,21 +1,39 @@ -/* -Factorial digit sum +/** + * 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! + */ -n! means n × (n − 1) × ... × 3 × 2 × 1 +const factorialDigitSum = function (n = 100) { -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. + // Consider each digit*10^exp separately, right-to-left ([units, tens, ...]). + let digits = [1]; -Find the sum of the digits in the number 100! -*/ + for (let x=2; x<=n; x++) { + let carry = 0; + for (let exp=0; exp 0) { + digits.push(carry%10); + carry = Math.floor(carry/10); + } + } -const findFactorialDigitSum = (num) => { - let result = 0 - const stringifiedNumber = factorize(num).toLocaleString('fullwide', { useGrouping: false }) - stringifiedNumber.split('').map(num => { result += Number(num) }) - return result + // (digits are reversed but we only want the sum so it doesn't matter) + + return digits.reduce((prev, current) => prev + current, 0) } -const factorize = (num) => num === 0 ? 1 : num * factorize(num - 1) +console.log('Factorial digit sum of 100! :', factorialDigitSum()) -console.log(findFactorialDigitSum(100)) +module.exports = factorialDigitSum