Constant speedups are one thing, but if you have a bad algorithm (like blindly searching a list to implement an associative array), the problem will scale poorly no matter how fast your computer is. The only way a futuristic computer running a linear-time algorithm could keep up with another computer running a constant-time algorithm would be if it could somehow compress time.
The good thing about these types of mental exercises is that it helps expose our shared set of (mostly hidden) assumptions. For example, we like to think that we can do array lookup (and by extension, hash lookup) in O(1) time. Geometrically though, RAM is really a tree structure, and we have wait for signals to propogate through O(log n) row and column decoders. But even this is optimistic, because if bits take up a finite volume (and the speed of light is constant), then we're really looking at O(n**(1/3)) time for a lookup.
Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
Read Where should I post X? if you're not absolutely sure you're posting in the right place.
Please read these before you post! —
Posts may use any of the Perl Monks Approved HTML tags:
Outside of code tags, you may need to use entities for some characters:
- a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
Link using PerlMonks shortcuts! What shortcuts can I use for linking?
See Writeup Formatting Tips and other pages linked from there for more info.
| & || & |
| < || < |
| > || > |
| [ || [ |
| ] || ] ||