feat: add Automorphic Numbers and tests in Math

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 +1,34 @@
+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()
+ })
+ it('should return false when n is negetive', () => {
+ expect(isAutomorphic(-3)).toBeFalsy()
+ })
+ it('should return false when n is negetive', () => {
+ expect(isAutomorphic(-25)).toBeFalsy()
+ })
+ it('should return false when n is 7', () => {
+ expect(isAutomorphic(7)).toBeFalsy()
+ })
+ it('should return false when n is 83', () => {
+ expect(isAutomorphic(83)).toBeFalsy()
+ })
+ it('should return true when n is 0', () => {
+ expect(isAutomorphic(0)).toBeTruthy()
+ })
+ it('should return true when n is 1', () => {
+ expect(isAutomorphic(1)).toBeTruthy()
+ })
+ it('should return true when n is 376', () => {
+ expect(isAutomorphic(376)).toBeTruthy()
+ })
+ it('should return true when n is 90625', () => {
+ expect(isAutomorphic(90625)).toBeTruthy()
+ })
+})