feat: add Automorphic Numbers and tests in Math (#1496)

* feat: add automorphic number and tests

* fix: add spaces

* fix: merge tests with test.each

Maths/AutomorphicNumber.js

@@ -0,0 +1,40 @@
+/**
+ * @function isAutomorphic
+ * @author [SilverDragonOfR] (https://github.com/SilverDragonOfR)
+ *
+ * @see [Automorphic] (https://en.wikipedia.org/wiki/Automorphic_number)
+ * @description This script will check whether a number is Automorphic or not
+ * @description A number n is said to be a Automorphic number if the square of n ends in the same digits as n itself.
+ *
+ * @param {Integer} n - the n for nth Catalan Number
+ * @return {Integer} - the nth Catalan Number
+ * @complexity Time: O(log10(n)) , Space: O(1)
+ *
+ * @convention We define Automorphic only for whole number integers. For negetive integer we return False. For float or String we show error.
+ * @examples 0, 1, 5, 6, 25, 76, 376, 625, 9376 are some Automorphic numbers
+ */
+
+// n is the number to be checked
+export const isAutomorphic = (n) => {
+  if (typeof n !== 'number') {
+    throw new Error('Type of n must be number')
+  }
+  if (!Number.isInteger(n)) {
+    throw new Error('n cannot be a floating point number')
+  }
+  if (n < 0) {
+    return false
+  }
+
+  // now n is a whole number integer >= 0
+  let n_sq = n * n
+  while (n > 0) {
+    if (n % 10 !== n_sq % 10) {
+      return false
+    }
+    n = Math.floor(n / 10)
+    n_sq = Math.floor(n_sq / 10)
+  }
+  
+  return true
+}

Maths/test/AutomorphicNumber.test.js

@@ -0,0 +1,28 @@
+import { isAutomorphic } from '../AutomorphicNumber'
+
+describe('AutomorphicNumber', () => {
+  it('should throw Error when n is String', () => {
+    expect(() => isAutomorphic('qwerty')).toThrow()
+  })
+  it('should throw Error when n is floating point', () => {
+    expect(() => isAutomorphic(13.6)).toThrow()
+  })
+
+  test.each([
+    { n: -3 , expected: false },
+    { n: -25 , expected: false },
+  ])('should return false when n is negetive', ({ n, expected }) => {
+    expect(isAutomorphic(n)).toBe(false)
+  })
+
+  test.each([
+    { n: 7 , expected: false },
+    { n: 83 , expected: false },
+    { n: 0 , expected: true },
+    { n: 1 , expected: true },
+    { n: 376 , expected: true },
+    { n: 90625 , expected: true },
+  ])('should return $expected when n is $n', ({ n, expected }) => {
+    expect(isAutomorphic(n)).toBe(expected)
+  })
+})