Comments on: Programming – The art of giving percise instructions

By: Friend

Friend — Sat, 31 Jan 2009 09:17:16 +0000

This is not the most efficient way, because you don’t need to calculate (X+Y)! at all. Note that the biggest number will be at most (2X)!/(X!)^{2}, (by setting X=Y). So there is no need to calculate the number (X+Y)! to its bitter end. Probably the most efficient way to calculate this asymptotically, is by using Stirling’s formula. Note that by the nature of this approximation, it is evident that the complexity is way beyond exponential. It is in fact something like X^{X}.

By: A Quantum Immortal » Blog Archive » Never rely on tail recursion elimination

Thu, 29 Jan 2009 12:31:02 +0000

[…] previously posted a recursive implementation of Factorial, and asked the readers “not to bother saying it’s inefficient because of recursion, […]

By: ripper234

ripper234 — Sat, 17 Jan 2009 08:07:23 +0000

You’re not alone in this confusion. There is one route from the origin to itself – the empty route.

It’s basically a matter of definition, but my definition allows us to have no special cases in the 3rd solution.

By: Boaz

Boaz — Sat, 17 Jan 2009 07:56:02 +0000

Yes, I’m stupid.
Though the fact that if x = 0 and y = 0 you return 1 confused me.

By: ripper234

ripper234 — Sat, 17 Jan 2009 07:45:17 +0000

Thanks Eli.

Boaz, you are incorrect. If x == 0, this means you have no more Left moves left. You have only one route to get to the origin, by going Down all the time. Remember, we are calculating the number of routes to get to the origin, not the length of the route.

By: Boaz

Boaz — Sat, 17 Jan 2009 07:04:26 +0000

Why “return 1”?
I believe it should be:
if (x == 0) return y;
if (y == 0) return x;

By: Eli

Eli — Sat, 17 Jan 2009 06:25:03 +0000

Nice post!