Update fast_fibonacci.py (#1889)

* Update fast_fibonacci.py

* Update fast_fibonacci.py

Co-authored-by: Christian Clauss <cclauss@me.com>

Author: SandersLin

dynamic_programming/fast_fibonacci.py

@@ -1,44 +1,37 @@
-#!/usr/bin/python
+#!/usr/bin/env python3
 
 """
 This program calculates the nth Fibonacci number in O(log(n)).
-It's possible to calculate F(1000000) in less than a second.
+It's possible to calculate F(1_000_000) in less than a second.
 """
 import sys
+from typing import Tuple
 
 
-# returns F(n)
-def fibonacci(n: int):  # noqa: E999 This syntax is Python 3 only
+def fibonacci(n: int) -> int:
+    """
+    return F(n)
+    >>> [fibonacci(i) for i in range(13)]
+    [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]
+    """
     if n < 0:
         raise ValueError("Negative arguments are not supported")
     return _fib(n)[0]
 
 
 # returns (F(n), F(n-1))
-def _fib(n: int):  # noqa: E999 This syntax is Python 3 only
-    if n == 0:
-        # (F(0), F(1))
+def _fib(n: int) -> Tuple[int, int]:
+    if n == 0:  # (F(0), F(1))
         return (0, 1)
-    else:
-        # F(2n) = F(n)[2F(n+1) − F(n)]
-        # F(2n+1) = F(n+1)^2+F(n)^2
-        a, b = _fib(n // 2)
-        c = a * (b * 2 - a)
-        d = a * a + b * b
-        if n % 2 == 0:
-            return (c, d)
-        else:
-            return (d, c + d)
+
+    # F(2n) = F(n)[2F(n+1) − F(n)]
+    # F(2n+1) = F(n+1)^2+F(n)^2
+    a, b = _fib(n // 2)
+    c = a * (b * 2 - a)
+    d = a * a + b * b
+    return (d, c + d) if n % 2 else (c, d)
 
 
 if __name__ == "__main__":
-    args = sys.argv[1:]
-    if len(args) != 1:
-        print("Too few or too much parameters given.")
-        exit(1)
-    try:
-        n = int(args[0])
-    except ValueError:
-        print("Could not convert data to an integer.")
-        exit(1)
-    print("F(%d) = %d" % (n, fibonacci(n)))
+    n = int(sys.argv[1])
+    print(f"fibonacci({n}) is {fibonacci(n)}")