chore: Merge pull request TheAlgorithms#799 from VinWare/master

Extended Eucliedian Algorithm added to Maths folder

Author: raklaptudirm

Conversions/MeterToFeetConversion.js

@@ -1,10 +1,10 @@
 // Foot: https://en.wikipedia.org/wiki/Foot_(unit)
 const feetToMeter = (feet) => {
- return feet*0.3048;
+ return feet * 0.3048
 }
 
 const meterToFeet = (meter) => {
- return meter/0.3048;
+ return meter / 0.3048
 }
 
-export { feetToMeter, meterToFeet }
+export { feetToMeter, meterToFeet }

Conversions/test/MeterToFeetConversion.test.js

@@ -1,4 +1,4 @@
-import { meterToFeet, feetToMeter } from "../MeterToFeetConversion";
+import { meterToFeet, feetToMeter } from '../MeterToFeetConversion'
 
 describe('Testing conversion of Meter to Feet', () => {
  it('with feet value', () => {
@@ -10,4 +10,4 @@ describe('Testing conversion of Feet to Meter', () => {
  it('with feet value', () => {
  expect(feetToMeter(10)).toBe(3.048)
  })
-})
+})

Dynamic-Programming/MaxProductOfThree.js

@@ -5,15 +5,15 @@
  * @param {number[]} arrayItems
  * @returns number
  */
-export function maxProductOfThree(arrayItems) {
+export function maxProductOfThree (arrayItems) {
  // if size is less than 3, no triplet exists
- let n = arrayItems.length
+ const n = arrayItems.length
  if (n < 3) throw new Error('Triplet cannot exist with the given array')
- let max1 = arrayItems[0],
-  max2 = -1,
-  max3 = -1,
-  min1 = arrayItems[0],
-   min2 = -1
+ let max1 = arrayItems[0]
+ let max2 = -1
+ let max3 = -1
+ let min1 = arrayItems[0]
+ let min2 = -1
  for (let i = 1; i < n; i++) {
  if (arrayItems[i] > max1) {
  max3 = max2
@@ -32,7 +32,7 @@ export function maxProductOfThree(arrayItems) {
  min2 = arrayItems[i]
  }
  }
- let prod1 = max1 * max2 * max3,
-   prod2 = max1 * min1 * min2
+ const prod1 = max1 * max2 * max3
+ const prod2 = max1 * min1 * min2
  return Math.max(prod1, prod2)
 }

Maths/ExtendedEuclideanGCD.js

@@ -0,0 +1,71 @@
+/**
+ * Problem statement and explanation: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
+ *
+ * This algorithm plays an important role for modular arithmetic, and by extension for cyptography algorithms
+ * 
+ * Basic explanation:
+ * The Extended Euclidean algorithm is a modification of the standard Euclidean GCD algorithm.
+ * It allows to calculate coefficients x and y for the equation:
+ * ax + by = gcd(a,b)
+ * 
+ * This is called Bézout's identity and the coefficients are called Bézout coefficients
+ * 
+ * The algorithm uses the Euclidean method of getting remainder:
+ * r_i+1 = r_i-1 - qi*ri
+ * and applies it to series s and t (with same quotient q at each stage)
+ * When r_n reaches 0, the value r_n-1 gives the gcd, and s_n-1 and t_n-1 give the coefficients
+ * 
+ * This implementation uses an iterative approach to calculate the values
+ */
+
+/**
+ *
+ * @param {Number} arg1 first argument
+ * @param {Number} arg2 second argument
+ * @returns Array with GCD and first and second Bézout coefficients
+ */
+const extendedEuclideanGCD = (arg1, arg2) => {
+ if (typeof arg1 !== 'number' || typeof arg2 !== 'number') throw new TypeError('Not a Number')
+ if (arg1 < 1 || arg2 < 1) throw new TypeError('Must be positive numbers')
+
+ // Make the order of coefficients correct, as the algorithm assumes r0 > r1
+ if (arg1 < arg2) {
+ const res = extendedEuclideanGCD(arg2, arg1)
+ const temp = res[1]
+ res[1] = res[2]
+ res[2] = temp
+ return res
+ }
+
+ // At this point arg1 > arg2
+
+ // Remainder values
+ let r0 = arg1
+ let r1 = arg2
+
+ // Coefficient1 values
+ let s0 = 1
+ let s1 = 0
+
+ // Coefficient 2 values
+ let t0 = 0
+ let t1 = 1
+
+ while (r1 !== 0) {
+ const q = Math.floor(r0 / r1)
+
+ const r2 = r0 - r1 * q
+ const s2 = s0 - s1 * q
+ const t2 = t0 - t1 * q
+
+ r0 = r1
+ r1 = r2
+ s0 = s1
+ s1 = s2
+ t0 = t1
+ t1 = t2
+ }
+ return [r0, s0, t0]
+}
+
+export { extendedEuclideanGCD }

Maths/FigurateNumber.js

@@ -1,20 +1,19 @@
 /**
- Problem Statment and Explanation : 
+ Problem Statment and Explanation :
  Triangular => https://en.wikipedia.org/wiki/Triangular_number
  Tetrahedral => https://en.wikipedia.org/wiki/Tetrahedral_number
  Pentatope => https://en.wikipedia.org/wiki/Pentatope_number
 
-
- Example: 
+ Example:
  Triangular => (0, 1, 3, 6, 10, 15, 21, 28, 36, 45)
  Tetrahedral => (1, 4, 10, 20, 35, 56, 84, 120, 165,)
  Pentatope => (1, 5, 15, 35, 70, 126, 210, 330, 495)
  */
 
 /**
- * 
- * @param {*} number 
- * @returns 
+ *
+ * @param {*} number
+ * @returns
  */
 const isTriangular = (number) => {
  for (let i = 0; i <= number; i++) {
@@ -28,9 +27,9 @@ const isTriangular = (number) => {
 }
 
 /**
- * 
- * @param {*} number 
- * @returns 
+ *
+ * @param {*} number
+ * @returns
  */
 const isTetrahedral = (number) => {
  for (let i = 1; i <= number; i++) {
@@ -43,9 +42,9 @@ const isTetrahedral = (number) => {
  return false
 }
 /**
- * 
- * @param {*} number 
- * @returns 
+ *
+ * @param {*} number
+ * @returns
  */
 const isPentatope = (number) => {
  for (let i = 1; i <= number; i++) {
@@ -59,11 +58,11 @@ const isPentatope = (number) => {
 }
 
 /**
- * 
- * @param {*} number 
- * @returns 
+ *
+ * @param {*} number
+ * @returns
  */
-let checkAll = (number) => {
+const checkAll = (number) => {
  return {
  isTriangular: isTriangular(number),
  isTetrahedral: isTetrahedral(number),

Maths/test/ExtendedEuclideanGCD.test.js

@@ -0,0 +1,16 @@
+import { extendedEuclideanGCD } from '../ExtendedEuclideanGCD'
+
+describe('extendedEuclideanGCD', () => {
+ it('should return valid values in order for positive arguments', () => {
+ expect(extendedEuclideanGCD(240, 46)).toMatchObject([2, -9, 47])
+ expect(extendedEuclideanGCD(46, 240)).toMatchObject([2, 47, -9])
+ })
+ it('should give error on non-positive arguments', () => {
+ expect(() => extendedEuclideanGCD(0, 240)).toThrowError(new TypeError('Must be positive numbers'))
+ expect(() => extendedEuclideanGCD(46, -240)).toThrowError(new TypeError('Must be positive numbers'))
+ })
+ it('should give error on non-numeric arguments', () => {
+ expect(() => extendedEuclideanGCD('240', 46)).toThrowError(new TypeError('Not a Number'))
+ expect(() => extendedEuclideanGCD([240, 46])).toThrowError(new TypeError('Not a Number'))
+ })
+})

Maths/test/FigurateNumber.test.js

@@ -54,15 +54,15 @@ describe('FigurateNumber', () => {
  })
  /** End */
 
- it('Check All : should return all true',() => {
+ it('Check All : should return all true', () => {
  expect(checkAll(1)).toEqual({
  isTriangular: true,
  isTetrahedral: true,
  isPentatope: true
  })
  })
 
- it('Check All : should return all true,true,false',() => {
+ it('Check All : should return all true,true,false', () => {
  expect(checkAll(15)).toEqual({
  isTriangular: true,
  isTetrahedral: false,