Added fastfibonacci.py

dynamic_programming/fastfibonacci.py

@@ -0,0 +1,42 @@
+"""
+This program calculates the nth Fibonacci number in O(log(n)).
+It's possible to calculate F(1000000) in less than a second.
+"""
+import sys
+
+
+# returns F(n)
+def fibonacci(n: int):
+    if n < 0:
+        raise ValueError("Negative arguments are not supported")
+    return _fib(n)[0]
+
+
+# returns (F(n), F(n-1))
+def _fib(n: 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)
+
+
+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)))