add way of computing fibonacci sequence by O(1) in Python3

math/fibonacci/python/fibonacci_by_formula.py

@@ -0,0 +1,20 @@
+import math
+
+# The code below calculates N-th fibonacci number by O(1)
+# Such speed is achieved by using the Binet's formula which is
+# fib(n) = (phi^n - psi^n) / sqrt(5)
+# where
+# phi = (1 + sqrt(5)) / 2 and psi = (1 - sqrt(5)) / 2
+# But in code we compute fib(n) as
+# fib(n) = round(phi^n) / sqrt(5)
+# because when n -> inf: abs(psi^n) -> 0
+# When n is small this formula is innacurate because
+# we are computing in double and float and they aren't the exact values that we have in Math
+# Because of the same reasons we may have slightly innacurate values with small n.
+
+def fib(n):
+	phi = (1 + math.sqrt(5)) / 2
+	return int(round(phi**n / math.sqrt(5)))
+
+n = 50
+print(fib(50))