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Re: Find count of binary number pattern within concatenated number
*To*: mathgroup at smc.vnet.net
*Subject*: [mg91131] Re: Find count of binary number pattern within concatenated number
*From*: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
*Date*: Thu, 7 Aug 2008 04:38:31 -0400 (EDT)
*References*: <g7bqom$moc$1@smc.vnet.net> <489992F3.4070802@gmail.com>
On Wed, Aug 6, 2008 at 2:02 PM, Jean-Marc Gulliet
<jeanmarc.gulliet at gmail.com> wrote:
> Diana wrote:
>
>> Can someone tell me how to find the count of the occurrences of "1101"
>> within "11011100101110111100010011010101111001101" generated with the
>> FromDigits statements below? I will be increasing "n".
>>
>> n=13
>>
>> FromDigits[Flatten[IntegerDigits[Range[n],2]]]
>>
>> 11011100101110111100010011010101111001101.
>>
>> FromDigits[IntegerDigits[n, 2]]
>>
>> 1101
>
> Here is two almost identical versions of the counting function: the first
> one seeks for overlapping sequences, the second looks only for
> non-overlapping sequences. Of course the results might be very different for
> a same number.
>
> (* Overlapping sequences *)
> myCount[n_Integer] :=
> Module[{nb2 = IntegerDigits[n, 2]},
> Flatten[Position[
> Partition[Flatten[IntegerDigits[Range[n], 2]], Length[nb2], 1],
> nb2]]]
>
> myCount[13]
>
> {1, 12, 25, 38}
>
> (* Non-Overlapping sequences *)
> myCount[n_Integer] :=
> Module[{nb2 = IntegerDigits[n, 2]},
> Flatten[Position[
> Partition[Flatten[IntegerDigits[Range[n], 2]], Length[nb2]],
> nb2]]]
>
> myCount[13]
>
> {1, 7}
Please, disregard this nonsense about the "Non-Overlapping" function:
it is too restrictive and does not produce the desired result.
The first fucntion does work correctly -- at least as far as I can
tell. What I mean by overlapping is that for a sequence such as {1, 1,
0, 1, 1, 0, 1} the function will count 2 subsequences 1101 starting at
1 and 4, respectively. (Note that the beginning of the second sequence
is also the end of the first sequence.)
StringPosition["1101101", "1101"]
{{1, 4}, {4, 7}}
Another possible approach is to convert the numbers into strings and
use the string search functions.
myCount[n_Integer] :=
StringPosition[
ToString[FromDigits[Flatten[IntegerDigits[Range[n], 2]]]],
ToString[FromDigits[IntegerDigits[n, 2]]]][[All, 1]]
myCount[13]
{1, 12, 25, 38}
Sorry for the confusion,
-- Jean-Marc
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