tag:blogger.com,1999:blog-8993901435573921786.post5034700203970894994..comments2017-06-13T07:38:48.434-07:00Comments on Pin Dancing: The repertoire method in "Concrete Mathematics"Ravihttp://www.blogger.com/profile/03630087669712445498noreply@blogger.comBlogger17125tag:blogger.com,1999:blog-8993901435573921786.post-43543705919359833772014-07-12T17:03:42.189-07:002014-07-12T17:03:42.189-07:00@raul
Did you ever figure it out? I would love to...@raul<br /><br />Did you ever figure it out? I would love to know the answer as I'm stuck on this as well.Unknownhttps://www.blogger.com/profile/10676269993726313540noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-59244704408690588522013-07-24T21:25:08.921-07:002013-07-24T21:25:08.921-07:00In the post you say:
The seat-of-pants example is...In the post you say:<br /><br /><i>The seat-of-pants example is actually enough if A(n),B(n) and C(n) are <b>all</b> worked out with the repertoire method.</i><br /><br />Do you mean, if all three component functions are <b>each</b> worked out? It's an important distinction. I'm still struggling with it a bit, but isn't the underlying principle similar to how you solve set of three parallel equations in three variables? <br /><br />I apologize if I'm way off base!AimlessInLAhttps://www.blogger.com/profile/09718152552754457700noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-1493781686917506462013-07-24T19:54:26.422-07:002013-07-24T19:54:26.422-07:00Only a few days ago I learned the interesting fact...Only a few days ago I learned the interesting fact that an early appearance in print by Donald Knuth, if not the earliest, was in 1957 in <i>Mad Magazine</i>! As a 19-year-old student he sent in "The Potrezbie System of Measurement", and it was published.<br /><br />As for the explanation, I haven't gone through it yet but I certainly will. I've been struggling with this for a long time, and it's all the more frustrating because I was immediately able to follow the authors' eyeball-the-table/spot-the-pattern/prove-by-induction derivation of the original problem.<br />AimlessInLAhttps://www.blogger.com/profile/09718152552754457700noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-17225427512980787282013-04-23T10:59:21.077-07:002013-04-23T10:59:21.077-07:00f(x) = 1 for all x,including x = n, 2n+1, 2n-1, w...f(x) = 1 for all x,including x = n, 2n+1, 2n-1, whatever else you can think of. <br /><br />f(x) always returns 1 irrespective of the value of the parameter. On a graph, it would be a horizontal line at y = 1Ravihttps://www.blogger.com/profile/03630087669712445498noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-19960408684095500972013-04-23T10:49:08.975-07:002013-04-23T10:49:08.975-07:00Thanks for the article. It has really helped me. I...Thanks for the article. It has really helped me. I have one doubt though.<br /><br />"I guess (the authors do too) that f(n) = 1. <br /><br />Rationale for the guess: f(n) = constant is the simplest possible formulation of f(n) (just for fun you might want to try f(n) = 0)<br /><br />Let us try substituting this in [1]<br /><br />f(1) = alpha becomes 1 = alpha (since f(n) is 1 for any n). <br /><br />similarly <br /><br />f(2n) = 2*f(n) + beta becomes 1 = 2*1 + beta so beta = -1<br />f(2n + 1) = 2*f(n) + gamma becomes 1 = 2*1 + gamma so gamma = -1"<br /><br>Here, since f(n)=1, how are we replacing f(2n) and f(2n+1) for 1 on the LHS of the equation?Kunalhttps://www.blogger.com/profile/17649915080279231096noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-82223053367688612832012-11-24T06:27:09.754-08:002012-11-24T06:27:09.754-08:00Awesome, really helpful, Thanks much!!Awesome, really helpful, Thanks much!!galib2145https://www.blogger.com/profile/07957516437507460116noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-22586667708128507932012-01-19T01:29:36.119-08:002012-01-19T01:29:36.119-08:00@Miguel,
"We "guess" f(n) = 1. f(n...@Miguel,<br /><br />"We "guess" f(n) = 1. f(n) is obviously NOT 1"<br /><br />umm in this case, f(n) *is* 1, for a specific set of values of alpha, beta gamma *and n*. We are just going backwards here. Think about it. <br /><br />In the general case, if the graph of the final answer function doesn't pass through your 'guess point' you won't get valid values for alpha, beta, gamma, A(n) etc.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-37286017868567145052011-12-16T15:31:10.360-08:002011-12-16T15:31:10.360-08:00Hi Ravi,
Do you have any ideas about wh...Hi Ravi,<br /> Do you have any ideas about what to read to start mapping maths to our programming problems in areas other than AI ? I mean that many of our common mundane tasks will have more elegant solutions if one knows the proper maths. So one need not only focus on AI. <br /><br />MohanMohan Radhakrishnanhttps://www.blogger.com/profile/08457140016320542845noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-24831131661586913522011-09-11T08:47:20.945-07:002011-09-11T08:47:20.945-07:00What I can't wrap my head around is why you...What I can't wrap my head around is why you're allowed to plug in guesses for f(n) in the first place. They're merely guesses, right? How do we know our results would be consistent with the real answer?<br /><br />ie: We "guess" f(n) = 1. f(n) is obviously NOT 1, so why are we allowed to work with the results that we obtained from plugging that in?Miguelhttps://www.blogger.com/profile/15936727617025003142noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-49211330867604221172011-08-25T13:35:38.118-07:002011-08-25T13:35:38.118-07:00Thanks! This clears up the first chapter a lot.Thanks! This clears up the first chapter a lot.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-43583861202475180312011-08-17T16:16:28.956-07:002011-08-17T16:16:28.956-07:00Can anyone write the calculations for f(n) = 2^m a...Can anyone write the calculations for f(n) = 2^m and f(n) = k???<br /><br />I don't know how to do it... I can't get to A(n) = 2^m and C(n) = k<br /><br />thx!Raulnoreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-82546176572993515572011-08-08T09:33:15.824-07:002011-08-08T09:33:15.824-07:00That was crucial for me to understand. Really the ...That was crucial for me to understand. Really the writing of this books gets confusing some times. Perhaps you should write your own!! Are u facebook or some other social network. Its good to know people who seek knowlenge.Vaioshttps://www.blogger.com/profile/12877706810451008666noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-89070192797674478472011-07-18T05:52:30.872-07:002011-07-18T05:52:30.872-07:00Thanks a lot for this explanation. I reckon that i...Thanks a lot for this explanation. I reckon that it saved me quite a lot of time. ;-)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-6010877736284456022011-06-02T03:50:34.367-07:002011-06-02T03:50:34.367-07:00Thanks a lot for the post. It was helpful !Thanks a lot for the post. It was helpful !rahulhttp://researchweb.iiit.ac.in/~srahul/noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-20070098499270124532011-02-06T14:49:06.286-08:002011-02-06T14:49:06.286-08:00hah lucky me, I got confused by this just two days...hah lucky me, I got confused by this just two days after you made this post. <br /><br />Appreciate it.Moussa Cidibenoreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-71452130610971086452011-02-05T08:55:48.943-08:002011-02-05T08:55:48.943-08:00@himanshu,
I was referring to the clarity of my w...@himanshu,<br /><br />I was referring to the clarity of my writing (and its possible inadequacies in explaining mathematics) not the content, which (as you rightly point out) is fairly simple. <br /><br />This confusion is a good indicator that I need to improve my writing further.Ravihttps://www.blogger.com/profile/03630087669712445498noreply@blogger.comtag:blogger.com,1999:blog-8993901435573921786.post-63261286675228496422011-02-05T08:38:52.120-08:002011-02-05T08:38:52.120-08:00"...What follows will make no sense to you if..."...What follows will make no sense to you if you are not working through CM..."<br /><br />I don't think prerequisite is that strict. People can make sense out of this as long as they are, in some way, familiar with recurrence relations :)himanshuhttps://www.blogger.com/profile/02909790425038294533noreply@blogger.com