Re: Find count of binary number pattern within concatenated number

• To: mathgroup at smc.vnet.net
• Subject: [mg91129] Re: Find count of binary number pattern within concatenated number
• From: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
• Date: Thu, 7 Aug 2008 04:38:08 -0400 (EDT)
• References: <g7bqom\$moc\$1@smc.vnet.net> <489992F3.4070802@gmail.com>

```On Wed, Aug 6, 2008 at 2:54 PM, Diana Mecum <diana.mecum at gmail.com> wrote:
> Jean,
>
> Thank you. A question. I count four non-overlapping repititions of the
> pattern with n = 13 ?

Correct. Indeed, the "Non-Overlapping" is too restrictive and does not
produce the desired result. Please, just disregard it.

What I mean by overlapping is that for a sequence such as {1, 1, 0, 1,
1, 0, 1} the function will count 2 subsequence 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}

Regards,
- Jean-Marc

> Diana
>
> On Wed, Aug 6, 2008 at 5:02 AM, 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}

```

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