Re: Delete elements from list..

*To*: mathgroup at smc.vnet.net*Subject*: [mg116752] Re: Delete elements from list..*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Sat, 26 Feb 2011 06:06:56 -0500 (EST)

It's possible the OP really wants the "longest increasing subsequence". In that case, this is simple and fast for large lists: lisLS[x_List] := Tally[#][[All, 1]] &@LongestCommonSequence[x, Union@x]; lisLS@{1, 9, 2, 3, 4, 5, 6, 7, 8} {1, 2, 3, 4, 5, 6, 7, 8} largestTst = RandomInteger[{1, 35000}, 40000]; Length@(one = lisLS[largestTst]) // Timing {0.067601, 393} That's due to Leonid Shifrin, I think. Bobby On Fri, 25 Feb 2011 05:36:31 -0600, Ray Koopman <koopman at sfu.ca> wrote: > On Feb 24, 3:29 am, "Maarten van der Burgt" <Maarten.VanDerBu...@kla- > tencor.com> wrote: >> Hallo, >> >> Thanks everybody who replied to my questions. >> >> The real problem I have is just a bit more complex than my >> simplified example. My list is in fact a numerical 2D list like >> mylist1 == {{x_0, y_0}, {x_1,y_1},... {x_i, y_i}, ...{x_N, y_N}}. >> The xi are strictly increasing and the yi should be as well. >> Due to some measurement errors it can happen that this is not the >> case. I simply want to delete the {xi, yi} pairs where >> y_i <== y_i-1. That way I end up with a list, mylist2, >> where also the y_i are strictly increasing. >> (that way I can make an Interpolation[Reverse/@mylist2] >> in order to have a function x_i(y_i)). >> >> I have not had the time to study your answers in this view, >> but from a first look and the variety of the answers it seems >> that there is definitely something which should help. >> >> Thanks for your help. >> >> Maarten > > Your rule would you reduce {1, 9, 2, 3, 4, 5, 6, 7, 8} to {1, 9} > which I don't think you would want to do. > > Wouldn't it make more sense to delete only the 9? > > (If we work from right to left instead of left to right, > deleting the current y if it's >= min[all previous kept y_i], > we do delete only the 9.) > > Shouldn't the question be more like "What is the smallest set of > points that must be deleted to make y monotone increasing in x?" > > Or, considering that all the y_i may contain error, you could find > the vector z that is closest to y (in some sense that depends on the > assumed nature of the errors) and is also monotone increasing in x, > and then do inverse interpolation. > -- DrMajorBob at yahoo.com