Re: question in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg80106] Re: question in mathematica*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 12 Aug 2007 07:26:55 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <fa11b990e477.46baf2d3@bgu.ac.il> <D370EB89-ACFD-4FFF-B4E7-84A25FF267C5@mimuw.edu.pl> <C82B7D4D-6C0B-47E1-8603-DEE030A6E387@mimuw.edu.pl> <f69ab100e04a.46bc3a23@bgu.ac.il> <f9jlql$3pj$1@smc.vnet.net>

Andrzej Kozlowski wrote: > First, please send such question to the MathGroup, > > mathgroup at smc.vnet.net > > not me personally. (I really have desire, tiem or ability to replace > the enitre MathGroup.) > So I have decided to post this question to the MathGroup in case > someone else finds it interesting. > > Also, there is something about this question and the earlier you sent > me that make sme suspicious. What do you say "you need to use > recursion and pattern matching, Select and Join"? This sounds to me > like some sort of test problem so I have decided to answer it but > without using any of these functions (although it may not be the > simplest way to do this). So here is my answer: > > ls = {9, 2, 10, 3, 14, 9}; > > Reverse[Last[Last[Reap[NestWhile[With[{a = First[Ordering[#, -1]]}, > Sow[#[[a]]]; Take[#, a - 1]] &,ls,Length[#] > 0 &]]]]] > > {9, 10, 14} > > > On 10 Aug 2007, at 10:12, Ivan Egorov wrote: > >> I have one more question. >> >> >> >> Write a function maxima[lis_List] which, given a list of numbers, >> produces a list of those >> >> numbers greater than all those that precede them. For example >> >> maxima[{ 9, 2, 10, 3, 14, 9}] returns { 9, 10, 14}. You need to use >> recursion, pattern matching, >> >> Select and Join. Here is another possible answer, which uses some pattern matching. In[1]:= Clear[maxima] maxima[ls_List /; VectorQ[ls, NumberQ]] := Last /@ ((Split[##1, #2 >= #1 & ] & )[ls] /. l : {{__}, ___, {_}} :> Most[l]) ls = {9, 2, 10, 3, 14, 9}; maxima[ls] Out[4]= {9, 10, 14} Below, we have tested the maxima function against some possible cases. In[5]:= ls = {9, 2, 10, 3, 14, 9, 10}; maxima[ls] ls = {9, 11, 2, 10, 3, 14, 9, 10}; maxima[ls] ls = {9, 11, 2, 10, 3, a, 14, 9, 10}; maxima[ls] ls = {9, 11, 2}; maxima[ls] ls = {9, 2}; maxima[ls] ls = {2, 9}; maxima[ls] ls = {2}; maxima[ls] ls = {2, 2, 2, 9}; maxima[ls] ls = {2, 2, 2, 9, 9, 10}; maxima[ls] Out[6]= {9, 10, 14, 10} Out[8]= {11, 10, 14, 10} Out[10]= maxima[{9, 11, 2, 10, 3, a, 14, 9, 10}] Out[12]= {11} Out[14]= {9} Out[16]= {9} Out[18]= {2} Out[20]= {9} Out[22]= {10} -- Jean-Marc