From ee749bde471d19df65f336d7107a71a08c1345d2 Mon Sep 17 00:00:00 2001
From: sandyboypraper <sandyboyraper@gmail.com>
Date: Mon, 14 Dec 2020 00:33:55 +0530
Subject: [PATCH] Added EulersTotientFunction function to the Maths Folder

---
 Maths/EulersTotientFunction.js           | 28 ++++++++++++++++++++++++
 Maths/test/EulersTotientFunction.test.js | 11 ++++++++++
 package-lock.json                        |  2 +-
 package.json                             |  2 +-
 4 files changed, 41 insertions(+), 2 deletions(-)
 create mode 100644 Maths/EulersTotientFunction.js
 create mode 100644 Maths/test/EulersTotientFunction.test.js

diff --git a/Maths/EulersTotientFunction.js b/Maths/EulersTotientFunction.js
new file mode 100644
index 000000000..ca8bafc0e
--- /dev/null
+++ b/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 gcd_two_numbers = (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 : gcd_two_numbers(y%x , x);
+}
+
+const EulersTotientFunction = (n) => {
+    let countOfRelativelyPrimeNumbers = 1;
+    for(let iterator = 2; iterator<=n; iterator++)
+        if(gcd_two_numbers(iterator , n) == 1)countOfRelativelyPrimeNumbers++;
+    
+    return countOfRelativelyPrimeNumbers;
+}
+
+export {EulersTotientFunction}
diff --git a/Maths/test/EulersTotientFunction.test.js b/Maths/test/EulersTotientFunction.test.js
new file mode 100644
index 000000000..d58d57c4b
--- /dev/null
+++ b/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)
+  })
+})
diff --git a/package-lock.json b/package-lock.json
index d8c7400ba..f051f1f03 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -9625,4 +9625,4 @@
       }
     }
   }
-}
\ No newline at end of file
+}
diff --git a/package.json b/package.json
index 3adff89e6..729e6f71b 100644
--- a/package.json
+++ b/package.json
@@ -27,4 +27,4 @@
     "jest": "^26.4.2",
     "standard": "^14.3.4"
   }
-}
\ No newline at end of file
+}