Merge pull request #550 from sandyboypraper/master

Added EulersTotientFunction function to the Maths Folder

Maths/EulersTotientFunction.js

@@ -0,0 +1,28 @@
+/*
+    author sandyboypraper
+
+    Here is the EulerTotientFunction.
+    it is also represented by phi
+
+    so EulersTotientFunction(n) (or phi(n)) is the count of numbers in {1,2,3,....,n} that are relatively
+    prime to n, i.e., the numbers whose GCD (Greatest Common Divisor) with n is 1.
+*/
+
+const gcdOfTwoNumbers = (x, y) => {
+  // x is smaller than y
+  // let gcd of x and y is gcdXY
+  // so it devides x and y completely
+  // so gcdXY should also devides y%x (y = gcdXY*a and x = gcdXY*b and y%x = y - x*k so y%x = gcdXY(a - b*k))
+  // and gcd(x,y) is equals to gcd(y%x , x)
+  return x === 0 ? y : gcdOfTwoNumbers(y % x, x)
+}
+
+const eulersTotientFunction = (n) => {
+  let countOfRelativelyPrimeNumbers = 1
+  for (let iterator = 2; iterator <= n; iterator++) {
+    if (gcdOfTwoNumbers(iterator, n) === 1) countOfRelativelyPrimeNumbers++
+  }
+  return countOfRelativelyPrimeNumbers
+}
+
+export { eulersTotientFunction }

Maths/test/EulersTotientFunction.test.js

@@ -0,0 +1,11 @@
+import { eulersTotientFunction } from '../EulersTotientFunction'
+
+describe('eulersTotientFunction', () => {
+  it('is a function', () => {
+    expect(typeof eulersTotientFunction).toEqual('function')
+  })
+  it('should return the phi of a given number', () => {
+    const phiOfNumber = eulersTotientFunction(10)
+    expect(phiOfNumber).toBe(4)
+  })
+})

package-lock.json

@@ -9625,4 +9625,4 @@
       }
     }
   }
-}
+}

package.json

@@ -27,4 +27,4 @@
     "jest": "^26.4.2",
     "standard": "^14.3.4"
   }
-}
+}