Merge pull request #160 from 2knal/master

Create fastDoublingNthFibonacci.py

* https://www.hackerearth.com/pt-br/practice/notes/fast-doubling-method-to-find-nth-fibonacci-number/

* https://www.hackerearth.com/pt-br/practice/notes/abhinav92003/why-output-the-answer-modulo-109-7/

* https://www.quora.com/What-is-the-concept-of-taking-modulo-by-1000000007

math/fibonacci/python/fastDoublingNthFibonacci.py

@@ -0,0 +1,23 @@
+'''
+Fast Doubling method: https://www.hackerearth.com/practice/notes/fast-doubling-method-to-find-nth-fibonacci-number/
+
+Fibonacci series: 0 1 1 2 3 ...
+NthFibonacci(n, mod) -> int
+mod: We find modulo of number (usually with 1e9+7), as it is too big.
+'''
+
+def NthFibonacci(n, mod):
+	return int(NthFibonacciHelper(n, mod)[0])
+
+def NthFibonacciHelper(n, mod):
+	if not n:
+		return (0, 1)
+	else:
+		a, b = NthFibonacciHelper(n // 2, mod)
+		c = (a%mod * ((b*2)%mod - a%mod))%mod
+		d = ((a%mod * a%mod)%mod + (b%mod * b%mod)%mod)%mod
+
+		if not n&1:
+			return (c, d)
+		else:
+			return (d, c + d)