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