Project Euler - Problem 20 (fix + test)

Project-Euler/Problem020.js

@@ -1,21 +1,38 @@
-/*
-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 = (n = 100) => {
+  // Consider each digit*10^exp separately, right-to-left ([units, tens, ...]).
+  const digits = [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.
+  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)
+    }
+  }
 
-Find the sum of the digits in the number 100!
-*/
+  // (digits are reversed but we only want the sum so it doesn't matter)
 
-const findFactorialDigitSum = (num) => {
-  let result = 0
-  const stringifiedNumber = factorize(num).toLocaleString('fullwide', { useGrouping: false })
-  stringifiedNumber.split('').map(num => { result += Number(num) })
-  return result
+  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

Project-Euler/test/Problem020.test.js

@@ -0,0 +1,16 @@
+const factorialDigitSum = require('../Problem020')
+
+describe('Check Problem 20 - Factorial digit sum', () => {
+  it('Factorial digit sum of 10!', () => {
+    expect(factorialDigitSum(10)).toBe(27)
+  })
+
+  it('Factorial digit sum of 100!', () => {
+    expect(factorialDigitSum()).toBe(648)
+    expect(factorialDigitSum(100)).toBe(648)
+  })
+
+  it('Factorial digit sum of 1000!', () => {
+    expect(factorialDigitSum(1000)).toBe(10539)
+  })
+})