| --- Log opened Mon Oct 27 00:00:51 2008 |
| 00:07 | | * Finerty shoots number theory in the bitch. |
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| 00:17 | <@ToxicFrog> | Ding 1! |
| 00:17 | <@ToxicFrog> | I am now a tetrahedron! |
| 00:17 | <@Finerty> | Yay! |
| 00:18 | | * Finerty pokes at 21. |
| 00:18 | <@Finerty> | ...oh, duh. that one's not hard, I have the divisor function written. |
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| 00:25 | | * ToxicFrog finally gets around to building the lua bignum library |
| 00:34 | | * Serah nibbles on TF. |
| 00:39 | <@ToxicFrog> | meep |
| 00:39 | | * ToxicFrog licks Serah |
| 00:46 | <@Finerty> | ..okay what? |
| 00:47 | <@Finerty> | Problem 21. For some reason, I am not getting one of the five pairs of amicable numbers under 10,000. |
| 00:49 | <@Finerty> | ...it's getting 986 for 1210's restricted divisor function. why is this? |
| 00:50 | <@Finerty> | ....because my factorization thing was wrong and stopped when left with a square of a prime. |
| 00:50 | | * Finerty fixes that so it filters using <= instead of <. |
| 00:57 | <@ToxicFrog> | 24: 1 minute 7 using a non-memoized, iterator-based permuter. |
| 01:00 | <@ToxicFrog> | Let's see how it does if I change that to list based with memoization. |
| 01:11 | <@ToxicFrog> | As it turns out, not really worth it. |
| 01:11 | <@ToxicFrog> | Iterators: 1:07, 100KB |
| 01:11 | <@ToxicFrog> | Memoized lists: 0:56, 470MB |
| 01:12 | <@ToxicFrog> | As speed/size tradeoffs go, that one's not really worth it. |
| 01:12 | | * Finerty knows how to do that one better; the trick is to use a variable-base number system. |
| 01:13 | <@GeekSoldier> | haha. |
| 01:15 | <@ToxicFrog> | o.O |
| 01:15 | <@ToxicFrog> | Do tell. |
| 01:15 | <@Finerty> | Okay, so, you know how many permutations of k elements there are, right? |
| 01:16 | <@ToxicFrog> | Yes. |
| 01:16 | <@ToxicFrog> | k!, IIRC |
| 01:16 | <@Finerty> | Okay, so you know, from that, how many permuations of k+1 elements there are that start with each element, right? |
| 01:17 | <@ToxicFrog> | Yes. |
| 01:17 | <@Finerty> | So for instance there's 24 permutations of 1,2,3,4, and 24 permutations of 1,2,3,4,5 that start with 1. |
| 01:18 | <@Finerty> | Therefore, we know that the fifth digit from the right has a place value of 24. |
| 01:20 | <@ToxicFrog> | If I followed that right, the placevalues from right to left of the first five digits would be 0, 1, 2, 6, 24? |
| 01:20 | <@Finerty> | yep. |
| 01:20 | <@ToxicFrog> | And by "variable base" you mean "each digit is in a different base"? |
| 01:20 | <@Finerty> | Yep. |
| 01:23 | <@ToxicFrog> | And thus, the problem now becomes "express 1e7 in this format"? |
| 01:23 | <@Finerty> | So what you can then do is go through, pick the 'digit' with an appropriate value, use that as an index into an array, pop that item from the array and place it in the appropriate location. |
| 01:24 | <@ToxicFrog> | waitwaitwait |
| 01:24 | <@ToxicFrog> | "with an appropriate value"? |
| 01:24 | <@Finerty> | Using The Price Is Right |
| 01:25 | <@Finerty> | Starting on the left: find the largest number which, when multiplied by that place value, will give a number no larger than the target value. |
| 01:25 | <@ToxicFrog> | Right. |
| 01:25 | <@ToxicFrog> | Ok, makes sense. |
| 01:27 | <@ToxicFrog> | That just leaves the digit => symbol map. |
| 01:27 | <@Finerty> | Which is what you use the array popper for. |
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| 01:31 | <@ToxicFrog> | I think it's just symbol(place, value) == inputstring[place+value], zero-indexed |
| 01:32 | <@Finerty> | Nope. |
| 01:33 | <@ToxicFrog> | ...what is it, then? |
| 01:33 | <@Finerty> | Starting at the left: symbol[place] = inputstring.pop(value[place]) |
| 01:33 | <@ToxicFrog> | ('place' is from the left here, BTW - place 0 is the MSB) |
| 01:33 | <@Finerty> | You have to remove used symbols |
| 01:33 | <@ToxicFrog> | Oooh right |
| 01:39 | <@Finerty> | so you're getting 2 6 6 2 5 1 2 2 0 0 as your indexes (that last one you'll be dividing by zero, but there's only one possibility anyway)... |
| 01:40 | <@Finerty> | Which obviously has duplicates in it. |
| 01:40 | <@Finerty> | mmm, except this is zero-indexed stuff, so the real number is 999999 |
| 01:41 | <@Finerty> | 2 6 6 2 5 1 2 1 1 0 |
| 01:46 | <@Finerty> | All this is nine divmods and ten array pops, which is absurd speed. |
| 01:55 | <@Finerty> | ...probably better to do right-to-left, that way you don't have to calculate the factorial all the way out. A little trickier, though - you have to mod with the place value above to see your excess, and the divmod stuff doesn't work out exactly as hoped. |
| 01:56 | <@Finerty> | ...because it's actually easier, and you use smaller numbers. holy shit that's cool. |
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| 05:08 | | * Vornicus tries to figure out how to do 23 in less time. |
| 05:52 | <@Serah> | Twentythree? |
| 05:53 | <@Vornicus> | Project Euler, problem 23 |
| 05:54 | <@Vornicus> | Consider the Abundant Numbers: numbers for which the sum of their proper divisors (for 24: 1 2 3 4 6 8 12 are proper divisors) is greater than the number itself. |
| 05:55 | <@Vornicus> | Now, it has been shown that only some numbers below 20,000 or so cannot be expressed as the sum of two abundant numbers |
| 05:55 | <@Vornicus> | The problem asks you to figure out what those numbers are. |
| 05:56 | <@Vornicus> | With 6,000 abundant numbers in that range, though, trying a brute force method is a bit of a pain - 36,000,000 results from the minkovsky sum, then reduced drastically as you filter duplicates. |
| 05:57 | <@Serah> | Bit of pain + computer + patience = olution! |
| 05:57 | <@Vornicus> | Yeah, but these problems are all suppsoed to be solvable in under a minute or so of computer work, and this feels like a lot more than a minute. |
| 06:00 | <@Serah> | More powerful CPU? |
| 06:01 | <@Vornicus> | I can probably filter in a couple directions to halve or quarter the number of things to look at. |
| 06:03 | <@Vornicus> | (currently I test a + b; I could restrict to a < b, and a + b < limit, which adds additional checks to the generation of trials, but can reduce the field drastically if I sort the items.) |
| 06:09 | <@Serah> | Yeah, can't you also sort out all odd numbers? |
| 06:10 | <@Vornicus> | Why would I be able to do that? |
| 06:11 | <@Serah> | No wait, the above was an example. |
| 06:11 | <@Serah> | I thought for a minute 1, 2, three, 4, 6, 8, and 12 was the only legal divisors. |
| 06:11 | <@Serah> | Nevermind. |
| 06:12 | <@Serah> | Actually you should be able to eliminate some divisors which are less likely to produce the desired result. |
| 06:13 | <@Serah> | Although we want certain not less likely. |
| 06:13 | <@Serah> | This is the sort of thing that requires me having slept. |
| 06:14 | <@Serah> | Although I would likely brute force it. |
| 06:14 | <@Serah> | With my old box, when I slept. |
| 06:14 | <@Serah> | But I will sleepflee now. |
| 06:14 | <@Serah> | Byes Vorn! |
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| 06:15 | <@Vornicus> | Yeah, brute forcing is probably the answer, but I should probably break out bisect and see if I can't drastically reduce the number of trials; at a guess I can hit 1/4 the number of things. |
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| 16:19 | <@gnolam> | Reasons to Buy an EEE PC, #7: Telling people you're going downtown to buy some 'EEE'. |
| 16:19 | <@Shoukanjuu> | >__> |
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| 20:19 | | * gnolam hates on Firefox. |
| 20:19 | <@Shoukanjuu> | Oh no you didn't! |
| 20:21 | <@gnolam> | Oh yes I did. Piece of crap software. :P |
| 20:23 | <@gnolam> | Hah, success! |
| 20:23 | | * gnolam can has regular KDE on the EEE PC. |
| 20:25 | <@gnolam> | Now, for a suitably offensive background picture... |
| 20:29 | <@Shoukanjuu> | :P |
| 20:35 | < Vash> | ... |
| 20:35 | < Vash> | Interesting. |
| 20:35 | <@AnnoDomini> | gnolam: Going to 4chan, eh? |
| 20:36 | <@Shoukanjuu> | AD: What |
| 20:37 | | * Vash goes ponder some more about what cookies to make later |
| 20:37 | <@gnolam> | Try SYN cookies. I hear they're tasty. |
| 20:37 | <@AnnoDomini> | Shoukanjuu: Offensive pictures. 4chan. |
| 20:37 | <@Shoukanjuu> | 4chan isn't *all* offensive pictures. |
| 20:38 | <@Shoukanjuu> | there's still the rare sane person there, who posts on topic, is a sniper who is credit to the team, and never touches the offensive portions of the site :P |
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| 21:04 | <@gnolam> | I think I'll have to put xubuntu on this thing. |
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| 21:05 | <@McMartin> | gnolam: Might as well wait three days and get the latest edition. |
| 21:06 | <@gnolam> | ? |
| 21:07 | <@McMartin> | 8.10 comes out in three days. |
| 21:07 | <@gnolam> | Ah. |
| 21:08 | <@McMartin> | (I don't know if Xubuntu gets a full spin each release or not, but I *think* it does.) |
| 21:12 | | * gnolam pokes Chernobyl with a spoon. |
| 21:13 | <@AnnoDomini> | Have you gotten to finishing that report site of yours? |
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| 21:22 | <@gnolam> | Nyet, tovarishch. |
| 21:22 | <@gnolam> | (I went with http://www.lysator.liu.se/~gnolam/temp/CoASoviet-1024-600.png as a wallpaper, BTW) |
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| 21:23 | <@gnolam> | I did write a bit on it, but I haven't published any of it yet. |
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| 23:07 | | * gnolam discovers WiFi signal strength maps of his campus. |
| 23:07 | <@gnolam> | Neat! |
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| --- Log closed Tue Oct 28 00:00:50 2008 |