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