solution: Project Euler 35 (#1201)

* [CREATE] Problem 28 solution for Project Euler

* [UPDATE] Added an explanation for the formula used in the algorithm

* [CREATE] Added Problem 35 for Project-Euler

* [UPDATE] Little typo in the error string

* [UPDATE] Some algorithm changes

* [UPDATE] Fix test string

* [UPDATE] Change prime numbers generator to import a standard sieve
algorithm.

* [UPDATE] Change sieve algorithm implementation and now the solution
works well. Also added some optimizations

Project-Euler/Problem035.js

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+/**
+ * Problem 35 - Circular primes
+ *
+ * @see {@link https://projecteuler.net/problem=35}
+ *
+ * The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.
+ * There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.
+ * How many circular primes are there below one million?
+ *
+ * @author ddaniel27
+ */
+import { sieveOfEratosthenes } from '../Maths/SieveOfEratosthenesIntArray'
+
+function problem35 (n) {
+  if (n < 2) {
+    throw new Error('Invalid input')
+  }
+  const list = sieveOfEratosthenes(n).filter(prime => !prime.toString().match(/[024568]/)) // Get a list of primes without 0, 2, 4, 5, 6, 8
+
+  const result = list.filter((number, _idx, arr) => {
+    const str = String(number)
+    for (let i = 0; i < str.length; i++) { // Get all rotations of the number
+      const rotation = str.slice(i) + str.slice(0, i)
+      if (!arr.includes(Number(rotation))) { // Check if the rotation is prime
+        return false
+      }
+    }
+    return true // If all rotations are prime, then the number is circular prime
+  })
+
+  return result.length + 1 // Add 2 to the result because 2 is a circular prime
+}
+
+export { problem35 }

Project-Euler/test/Problem035.test.js

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+import { problem35 } from '../Problem035.js'
+
+describe('checking circular primes', () => {
+  it('should be invalid input if number is negative', () => {
+    expect(() => problem35(-3)).toThrowError('Invalid input')
+  })
+  it('should be invalid input if number is 0', () => {
+    expect(() => problem35(0)).toThrowError('Invalid input')
+  })
+  // Project Euler Condition Check
+  test('if the number is equal to 100 result should be 13', () => {
+    expect(problem35(100)).toBe(13)
+  })
+  // Project Euler Challenge Check
+  test('if the number is equal to one million result should be 55', () => {
+    expect(problem35(1000000)).toBe(55)
+  })
+})