merge: added Problem 25 to Euler (TheAlgorithms#793)

* added Problem 25

* fixed alert

* fixed alert

* rewrote to improve runtime

* Update Problem025.js

* fixed typo

* added test file for Project-Euler/Problem025.js

* Update Project-Euler/test/Problem025.test.js

Co-authored-by: Rak Laptudirm <raklaptudirm@gmail.com>

* Update Problem025.test.js

Co-authored-by: Rak Laptudirm <raklaptudirm@gmail.com>

Author: byt3h3ad

Project-Euler/Problem025.js

@@ -0,0 +1,45 @@
+/**
+* Problem 25 - 1000-digit Fibonacci number
+*
+* @see {@link https://projecteuler.net/problem=25}
+*
+* The Fibonacci sequence is defined by the recurrence relation:
+* 
+* Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
+* 
+* Hence the first 12 terms will be:
+* 
+* F1 = 1
+* F2 = 1
+* F3 = 2
+* F4 = 3
+* F5 = 5
+* F6 = 8
+* F7 = 13
+* F8 = 21
+* F9 = 34
+* F10 = 55
+* F11 = 89
+* F12 = 144
+* The 12th term, F12, is the first term to contain three digits.
+
+* What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
+*/
+
+// brute force method
+
+function fibonacciIndex(t = 1000) {
+  let digits = 10n**BigInt(t-1),
+      fib0 = BigInt(0),
+      fib1 = BigInt(1),
+      index = 1
+  while (fib1 < digits) {  // using this to compare number of digits instead of .toString() significantly improved run time
+    const tempfib = fib1
+    fib1 = fib1 + fib0
+    fib0 = tempfib
+    index += 1
+  }
+  return(index)
+}
+
+export { fibonacciIndex }

Project-Euler/test/Problem025.test.js

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+import { fibonacciIndex } from '../Problem025'
+
+describe ('Check Problem 25 - 1000 digit Fibonnaci number', () => {
+    it('First term of the Fibonnaci sequence containing 3 digits', () => {
+        expect(fibonacciIndex(3)).toBe(12)
+    })
+
+    it('First term of the Fibonnaci sequence containing 10 digits', () => {
+        expect(fibonacciIndex(10)).toBe(45)
+    })
+
+    it('First term of the Fibonnaci sequence containing 50 digits', () => {
+        expect(fibonacciIndex(50)).toBe(237)
+    })
+
+    it('First term of the Fibonnaci sequence containing 100 digits', () => {
+        expect(fibonacciIndex(100)).toBe(476)
+    })
+
+    it('First term of the Fibonnaci sequence containing 1000 digits', () => {
+        expect(fibonacciIndex(1000)).toBe(4782)
+    })
+    
+    it('First term of the Fibonnaci sequence containing 10000 digits', () => {
+        expect(fibonacciIndex(10000)).toBe(47847)
+    })
+})