Comments for niche computing science

Comment on A Survey of Binary Search by Shin

Shin — Sat, 27 Feb 2010 17:09:31 +0000

You are right. I wasn't being clear: the >>> operator is available only in Java, and the last line (m = ((unsigned int)l + (unsigned int)r)) >> 1;) is for C/C++. I've added some comments to clarify that. Thanks!

Comment on A Survey of Binary Search by Michael

Michael — Sat, 27 Feb 2010 16:40:14 +0000

Java does not have unsigned types. Joshua Bloch's proposed alternatives in Java for avoiding overflow of the middle value are either int mid = low + ((high - low) / 2); or int mid = (low + high) >>> 1;.

Comment on A Survey of Binary Search by Shin

Shin — Sat, 27 Feb 2010 13:24:34 +0000

Thanks! I’ve got to be careful next time. :)

Comment on A Survey of Binary Search by Dirk Gerrits

Dirk Gerrits — Sat, 27 Feb 2010 08:28:30 +0000

The last name of “Netty van Gasteren” is “Van Gasteren”, not “Gasteren”.

Comment on Determining List Steepness in a Homomorphism by Mark Essel

Mark Essel — Tue, 14 Jul 2009 18:37:17 +0000

Just had time to scan the top few paragraphs, I’m interested enough to come back and do some homework. In a world with no free time, we still find time to have some fun :D

Comment on Determining List Steepness in a Homomorphism by cmcq

cmcq — Sat, 11 Jul 2009 09:03:40 +0000

1) No, because s>=(2^n-1)c where n is the list length. For negative c this puts a lower bound on n. For example [-8,-4,-2,-1] has s=-15, c=-1, so -15>=(2^n-1)*(-1), which gives n>=4.

A technique based on fixed-length inverses is very restricted: they can’t compute length!

2) You don’t need rationals ever: for sumcaps of two element lists you can use g(s,c)=[s-c,c]. Though personally I would not hesitate to extend the ring of numbers if it gave a simpler proof! Isn’t that what proof irrelevance is all about?

Comment on Determining List Steepness in a Homomorphism by Shin

Shin — Sat, 11 Jul 2009 04:30:18 +0000

Thanks for the encouragement! I've been relying on WordPress to generate the RSS (was this the link you tried?). What error message did you see? I'll check whether other WordPress users had the same problem.

Comment on Determining List Steepness in a Homomorphism by Shin

Shin — Sat, 11 Jul 2009 04:27:44 +0000

Thanks for the interesting comments, cmcq. Indeed it is harder than it looks. The first guess of mine (and some students here) was: g (s, c) = [(s+c)/2, (s-c)/2]. Not only was that wrong (it fails for, e.g, (8,8), output of sumcap [8]), but also forces us to move from integer to rational (that was why I was vague about the type of "numbers" in the post). I've been thinking: 1) is it possible to find an inverse that produces a constant-length list? 2) Can we stay within Int, if the input is Int? Goal 1) is essential for deriving ⊚, and 2) is desirable because the ⊚ that eventually worked does operate on integers only. You seem to have shown that goal 1) is hard to achieve. Well, perhaps the construction of list homomorphism by inverses is just not as widely applicable as we've expected.

Comment on Determining List Steepness in a Homomorphism by Matías Giovannini

Matías Giovannini — Sat, 11 Jul 2009 00:35:40 +0000

Great post! Shin-Cheng, your RSS feed is broken. I’d love to subscribe, but unfortunately the XML parser in Firefox 3.0.x complains.

Comment on Determining List Steepness in a Homomorphism by cmcq

cmcq — Fri, 10 Jul 2009 11:35:26 +0000

Wordpress ate my definition of g:
For s<3c<0, pick n such that s<=(2^n-1)c and use g(s,c)=[s+2^(n-1)c, 2^(n-2)c, ..., 2c, c].