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From: Ian Kelly <ian.g.kelly@gmail.com>
Date: Mon, 2 May 2011 23:46:58 -0600
Subject: Re: Recursion or iteration (was Fibonacci series recursion error)
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On Mon, May 2, 2011 at 11:27 PM, Dan Stromberg <drsalists@gmail.com> wrote:
> But the recursive solution has time complexity of O(logn).=A0 The iterati=
ve
> solution has time complexity of O(n).=A0 That's a significant difference =
for
> large n - a significant benefit of the recursive version.


It's linear as written.  I think you're talking about an
implementation like this one:

def powR(x,n):
  if n < 0:
    return 1.0 / powR(x, -n)
  elif n =3D=3D 0:
    return 1
  else:
    half_n =3D n // 2
    root =3D powR(x, half_n)
    result =3D root * root
    if half_n + half_n =3D=3D n - 1:
      result =3D result * x
    return result

That's O(log n), but it was harder to write, and it could just as
easily be iterative.  In fact it might actually have been a bit
simpler to write it iteratively.