Update Problem001.js (#1536)

* Update Problem001.js

* Update Problem001.js

* Update Problem001.js

* Update Problem001.js

* Update Problem001.js

Author: imrahulkb

Diff for: Project-Euler/Problem001.js

@@ -1,20 +1,23 @@
 // https://projecteuler.net/problem=1
-/*    Multiples of 3 and 5
-    If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
+/* Multiples of 3 and 5
+If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6, and 9. The sum of these multiples is 23.
 Find the sum of all the multiples of 3 or 5 below the provided parameter value number.
 */
 
+// This method uses the nSum function to add the nSum for 3 and 5. However, it needs to subtract the nSum for 15 once to avoid double counting.
 const multiplesThreeAndFive = (num) => {
   if (num < 1) throw new Error('No natural numbers exist below 1')
+  num -= 1
+  let sum = 0
 
-  let total = 0
-  // total for calculating the sum
-  for (let i = 1; i < num; i++) {
-    if (i % 3 === 0 || i % 5 === 0) {
-      total += i
-    }
-  }
-  return total
+  // The nSum function calculates the sum of the first n numbers in the sequence with a common difference of num.
+  // Here, n is denoted as frequency.
+  const nSum = (num, frequency) => (frequency * (frequency + 1) * num) >> 1
+
+  sum += nSum(3, Math.floor(num / 3))
+  sum += nSum(5, Math.floor(num / 5))
+  sum -= nSum(15, Math.floor(num / 15))
+  return sum
 }
 
 export { multiplesThreeAndFive }