tag:blogger.com,1999:blog-1953325079793449971.post5355477831353302235..comments2024-02-15T20:32:59.333+01:00Comments on Algorithms Weekly by Petr Mitrichev: Power towers solutionPetr Mitrichevhttp://www.blogger.com/profile/00138130656174416711noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-1953325079793449971.post-86351328791769391572023-10-18T14:26:22.686+02:002023-10-18T14:26:22.686+02:00I remember trying to solve this at SMU years back ...I remember trying to solve this at SMU years back using that logic. Never did manage to figure it out hahaAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1953325079793449971.post-5704492320126415742021-03-18T14:17:01.651+01:002021-03-18T14:17:01.651+01:00(if my reasoning were correct, the whole boasting ...(if my reasoning were correct, the whole boasting 'this problem is too easy so it's not going on the real icpc' in the dress rehearsal problem description makes sense...i'm not laughing though.)halfmoonthrottlehttps://www.blogger.com/profile/14722922321743903773noreply@blogger.comtag:blogger.com,1999:blog-1953325079793449971.post-37625052396921477402021-03-18T14:14:34.205+01:002021-03-18T14:14:34.205+01:00this has also troubled me for a long time, as ther...this has also troubled me for a long time, as there are published solutions on kattis but no published solution anywhere on the internet, only a dangling topcoder discussion thread. (your solution seems to use a similar technique) but...as i was browsing wolfram alpha today, i came across the g function on this page: https://mathworld.wolfram.com/PowerTower.html (blogger doesn't accept screenshots it seems) and i think i can use that to create a recursion, roughly the next four lines after the g function's definition, and one can build the recursion via glng=lnx. i'd probably type it up if i got time. <br /><br />if this were the solution, one dude at my uni came very close as he used logarithm on top of the power tower instead of at the bottom. but i feel like the math checks out. <br /><br />seriously it's been years, i first came across this on my first year of icpc and now i've already graduated. i'd probably type this solution on kattis if i got time. halfmoonthrottlehttps://www.blogger.com/profile/14722922321743903773noreply@blogger.comtag:blogger.com,1999:blog-1953325079793449971.post-20202984418682420182019-10-30T22:21:20.080+01:002019-10-30T22:21:20.080+01:00What to do if log(log(ch1)) and log(log(ch2)) both...What to do if log(log(ch1)) and log(log(ch2)) both >=300, but difference is less than 10? Andrey Misnikhttps://www.blogger.com/profile/06755375789746599591noreply@blogger.comtag:blogger.com,1999:blog-1953325079793449971.post-21114607890598056732019-09-21T12:46:18.340+02:002019-09-21T12:46:18.340+02:00it's almost 4 months since you posted @petr.Ea...it's almost 4 months since you posted @petr.Each time you end posts with "check back next week".... i've been checking for 12 weeks now :(... waiting for you to post ....sk28https://www.blogger.com/profile/06629806194204510437noreply@blogger.comtag:blogger.com,1999:blog-1953325079793449971.post-105243474798450622019-06-09T15:18:30.224+02:002019-06-09T15:18:30.224+02:00Given that we're already reaching the limits o...Given that we're already reaching the limits of floating-point types with values up to 100, at this point I doubt that solving it with values up to 1000000 is possible at all. Do you have grounds to believe that problem is solvable in those constraints? (for example, did a well-known problemsetter set it?..)Petr Mitrichevhttps://www.blogger.com/profile/00138130656174416711noreply@blogger.comtag:blogger.com,1999:blog-1953325079793449971.post-53311485504335542902019-06-09T06:54:30.801+02:002019-06-09T06:54:30.801+02:00https://uva.onlinejudge.org/external/131/13143.pdf...https://uva.onlinejudge.org/external/131/13143.pdf<br /><br />But can you solve this harder problem? Power Towers Longest Path in Graph problem?<br />Lucashttps://uva.onlinejudge.org/external/131/13143.pdfnoreply@blogger.comtag:blogger.com,1999:blog-1953325079793449971.post-48732240742411690672019-06-08T21:53:25.539+02:002019-06-08T21:53:25.539+02:00Neat! This is a blast from the past. I really li...Neat! This is a blast from the past. I really like your Expand idea to determine how many "interesting" tower powers there are.<br /><br />You're right that the leap of faith is what kept this in a Practice round instead of a Finals set. Realistically, solving this in a contest would require you to estimate roughly what level of precision (and what KIND of precision) is required, like you did with your logs of logs. But if you submitted and got WA, it'd be hard to know whether a) you've got a bug, or b) there's some mathematical construction (or coincidence) that produces tower powers that come closer than you'd expect.<br /><br />I'm something of a closet fan of Googology, the study of big numbers. In addition to this problem, I also wrote an MIT Mystery Hunt puzzle that required you to sort even crazier numbers: http://web.mit.edu/puzzle/www/2016/puzzle/identify_sort_index_solve/ (Whoops, looks like the Mathjax on that page broke. Oh well.)SnapDragonnoreply@blogger.comtag:blogger.com,1999:blog-1953325079793449971.post-38474550412043850932019-06-08T12:10:32.555+02:002019-06-08T12:10:32.555+02:00your maths is very very strong. your maths is very very strong. FanofPetrnoreply@blogger.comtag:blogger.com,1999:blog-1953325079793449971.post-45470440439654048502019-06-08T12:09:29.142+02:002019-06-08T12:09:29.142+02:00your maths is very very strong.your maths is very very strong.Anonymoushttps://www.blogger.com/profile/18409198011346767092noreply@blogger.com