Re: Re: Pattern Matching in Lists

• To: mathgroup at smc.vnet.net
• Subject: [mg35597] Re: [mg35586] Re: Pattern Matching in Lists
• From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
• Date: Mon, 22 Jul 2002 02:10:53 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I was  too quick with sending my alleged solution , not noticing
immediately that it fails in cases when w is of the form  {0,...,1}. (It
works however if we consider "cyclic" solutions, meaning that {0,1} is
thought to contain one instance of {1,0}!)

Since there seems no way of dealing with this problem without making the
solutions slower, Alan's

Count[Drop[w,-1]-Drop[w,1],1]

is indeed (almost certainly) the fastest solution.

(of course one can still make it faster by compiling:

f = Compile[{{w, _Integer, 1}}, Count[Drop[w, -1] - Drop[w, 1], 1]]

is about 6 times faster on my machine than the uncompiled version).

Andrzej

On Sunday, July 21, 2002, at 04:48  PM, Andrzej Kozlowski wrote:

> Having quickly glanced through the avalanche of proposed solutions I
> did not see following one.(if there was I apologize for claiming it as
> my own):
>
> Count[w - RotateLeft[w], 1]
>
> According to my comparisons it is the fastest so far (the one that I
> sent originally is one of the slowest)
>
>  In[1]:=
> w=Table[Random[Integer],{200000}];
>
> In[2]:=
> Count[Partition[w,2,1],{1,0}]//Timing
>
> Out[2]=
> {0.86 Second,50131}
>
> In[3]:=
> Count[Drop[w,-1]-Drop[w,1],1]//Timing
>
> Out[3]=
> {0.34 Second,50131}
>
> In[5]:=
> Count[w-RotateLeft[w],1]//Timing
>
> Out[5]=
> {0.29 Second,50131}
>
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
>
>
> On Sunday, July 21, 2002, at 02:01  PM, Allan Hayes wrote:
>
>> [second posting in view of reported technical problem]
>>
>> Anthony,
>> Take
>>     w = Table[Random[Integer], {200000}
>>
>> My first thought was, and several posts used this,
>>
>>     Count[Partition[w, 2,1],{1,0}]//Timing
>>
>>         {3.24 Second,49851}
>>
>> Later it occured to me to use arithmetic, which turned out to be twice
>> as
>> fast:
>>
>>      Count[ Drop[w,-1] - Drop[w,1],1]//Timing
>>
>>         {1.49 Second,49851}
>>
>> This is close to Selwyn Hollis's code
>>
>>     Count[Drop[w+2RotateRight[w],1],2]//Timing
>>
>>         {1.6 Second,49851}
>>
>> --
>> Allan
>>
>> ---------------------
>> Allan Hayes
>> Mathematica Training and Consulting
>> Leicester UK
>> www.haystack.demon.co.uk
>> hay at haystack.demon.co.uk
>> Voice: +44 (0)116 271 4198
>> Fax: +44 (0)870 164 0565
>>
>>
>> "Anthony Mendes" <amendes at zeno.ucsd.edu> wrote in message
>> news:ah5qce\$59o\$1 at smc.vnet.net...
>>> Hello,
>>>
>>> Suppose w={1,1,1,0,0,1,0,1,0,0,1,0,0}.
>>>
>>> How can I count the number of occurrences of a 1 in w immediately
>>> followed by a 0 in w?
>>>
>>> I have tried every incarnation of Count[] I can think of; for example,
>>>
>>> Count[w,{___,1,0,___}]
>>>
>>> does not seem to work.  In general, how can I count the number of
>>> occurrences of a 1 followed by a 0 in a list of 1's and 0's?  Thank
>>> you!
>>>
>>>
>>> --
>>> Tony
>>> _____________________
>>> amendes at math.ucsd.edu
>>>
>>>
>>
>>
>>
>>
>>
>>
>>
>>
>

```

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