Re: Element Extraction

• To: mathgroup at smc.vnet.net
• Subject: [mg19272] Re: [mg19240] Element Extraction
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 12 Aug 1999 01:24:25 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```>Hello everyone,
>I have a problem extracting list of list.
>Given some list, consisting of elements (not all of them distinct) with
>the same length and some target list of the same length, for example:
>In[26]:=
>someList={{0,0,0},{0,0,1},{0,0,2},{0,1,0},{0,1,1},{0,1,2},{0,2,0},{0,2,1},{0,
>2,2},{1,0,0},{1,0,1},{1,0,2},{1,1,0},{1,1,1},{1,1,2},{1,2,0},{1,2,1},{1,
>2,2},{2,0,0},{2,0,1},{2,0,2},{2,1,0},{2,1,1},{2,1,2},{2,2,0},{2,2,1},{2,
>      2,2}};
>
>In[27]:=
>target={0,0,1};
>
>Hamming distance between two bit strings means the number of bit
>positions in which they differ. For example consecutive elements of the
>Gray code list have Hamming distance = 1.
>I need to extract these cases(elements of someList) which differ from
>target in one coordinate (Hamming distance = 1) or less (the
>element===target itself//Hamming distance=0), so the answer should be:
>
>In[33]:=
>
>How could I achieve the extraction efficiently?
>Thank you in advance for any suggestions.
>Eugene
>

Eugene,

This is one approach:

hammtest[p : {_, _, _}, t : {_, _, _}] := Count[Abs[t - p], 0] > 1;
Select[someList, hammtest[#, {0, 0, 1}] &]
{{0, 0, 0}, {0, 0, 1}, {0, 0, 2}, {0, 1, 1}, {0, 2, 1}, {1, 0, 1}, {2, 0, 1}}

On this test list:

testlist =
Table[{Random[Integer, {0, 2}], Random[Integer, {0, 2}],
Random[Integer, {0, 2}]}, {10000}];

and on a Pentium 166 MH PC, the timing was

Select[testlist, hammtest[#, {0, 0, 1}] &]; // Timing
{5.82 Second, Null}

David Park