added fibonacci using formula along with test cases (#1358)

* added fibonacci using formula along with test cases

* updated the changes

* added jest's each in test cases

* added jest's each for testing

* returned inline value

* removed redundant comment

* hoisted the variables

* Use shorthand

* considered adding resource of the formula

---------

Co-authored-by: madhuredra <madhuredra.tiwari@zemosolabs.com>
Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com>

Maths/Fibonacci.js

@@ -187,9 +187,20 @@ const FibonacciMatrixExpo = (num) => {
   return F[0][0] * (isNeg ? (-ONE) ** (num + ONE) : ONE)
 }
 
+/*
+  Resource : https://math.hmc.edu/funfacts/fibonacci-number-formula/
+*/
+
+const sqrt5 = Math.sqrt(5)
+const phi = (1 + sqrt5) / 2
+const psi = (1 - sqrt5) / 2
+
+const FibonacciUsingFormula = n => Math.round((phi ** n - psi ** n) / sqrt5)
+
 export { FibonacciDpWithoutRecursion }
 export { FibonacciIterative }
 export { FibonacciGenerator }
 export { FibonacciRecursive }
 export { FibonacciRecursiveDP }
 export { FibonacciMatrixExpo }
+export { FibonacciUsingFormula }

Maths/test/Fibonacci.test.js

@@ -4,7 +4,8 @@ import {
   FibonacciIterative,
   FibonacciGenerator,
   FibonacciRecursive,
-  FibonacciMatrixExpo
+  FibonacciMatrixExpo,
+  FibonacciUsingFormula
 } from '../Fibonacci'
 
 describe('Fibonacci', () => {
@@ -95,4 +96,11 @@ describe('Fibonacci', () => {
     expect(FibonacciMatrixExpo(-5n)).toBe(5n)
     expect(FibonacciMatrixExpo(-6n)).toBe(-8n)
   })
+  it.each([
+    [0, 0],
+    [1, 1],
+    [15, 610]
+  ])('should calculate the correct Fibonacci number for n = %i', (n, expected) => {
+    expect(FibonacciUsingFormula(n)).toBe(expected)
+  })
 })