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lis={"#49:5"->"#61:7", "#49:5"->"#62:5", "#49:6"->"#61:8", "#49:6"->"#62:4", "#49:7"->"#61:10", "#49:7"->"#62:3", "#49:8"->"#61:9", "#49:8"->"#62:6"}

I would like to partition this list of rules into a number of sublists that is based on value string patterns #61:x, #62:y,.... #6n:z

clusters=Flatten@DeleteDuplicates@StringCases[Values@mrules,"#"~~cluster__~~":"->cluster]

Out= {61,62}

Therefore this list of rules can be split into two sublists (ordering is not required here):

 {{"#49:5"->"#61:7", "#49:6"->"#61:8", "#49:7"->"#61:10", "#49:8"->"#61:9"}, {"#49:5"->"#62:5", "#49:6"->"#62:4", "#49:7"->"#62:3", "#49:8"->"#62:6"}}

I can also take the list of values sorted

Sort@Values@lis

Out = {"#61:10", "#61:7", "#61:8", "#61:9", "#62:3", "#62:4", "#62:5", "#62:6"}

Then I experimented with Cases, Split, Select, StringMatchQ, etc without any luck.

Could you please assist me with this problem ?

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2 Answers 2

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One way:

label[_ -> s_] := StringReplace[s, "#" ~~ n__ ~~ ":" ~~ __ :> n]
GatherBy[lis, label]

(* Out: {{"#49:5" -> "#61:7", "#49:6" -> "#61:8", "#49:7" -> "#61:10", 
  "#49:8" -> "#61:9"}, {"#49:5" -> "#62:5", "#49:6" -> "#62:4", 
  "#49:7" -> "#62:3", "#49:8" -> "#62:6"}} *)
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  • $\begingroup$ A very clever and elegant solution indeed, thank you C.E. $\endgroup$ May 31, 2016 at 1:44
  • $\begingroup$ For those who want to avoid ToExpression[]: GatherBy[lis, StringCases[Last[#], "#" ~~ d : DigitCharacter .. ~~ __ :> d] &] $\endgroup$ May 31, 2016 at 10:44
  • $\begingroup$ @J.M. You posting this made me realize that ToExpression was superfluous in the first place, because they're just labels. They're not used for anything other than checking for equality. So I removed it in the answer. $\endgroup$
    – C. E.
    May 31, 2016 at 12:05
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Just for another approach (based on grouping by "#6n". Using GroupBy:

lis = {"#49:5" -> "#61:7", "#49:5" -> "#62:5", "#49:6" -> "#61:8", 
   "#49:6" -> "#62:4", "#49:7" -> "#61:10", "#49:7" -> "#62:3", 
   "#49:8" -> "#61:9", "#49:8" -> "#62:6"};
gp = GroupBy[lis, StringTake[#[[2]], {2, 3}] &, Rule @@@ # &];
v = Values[gp]

To sort by rule value:

f = ToExpression[StringSplit[StringDrop[#, 1], ":"]] &;
SortBy[#, f@#[[2]] &] & /@ v

yields:

{{"#49:5" -> "#61:7", "#49:6" -> "#61:8", "#49:8" -> "#61:9",
"#49:7" -> "#61:10"}, {"#49:7" -> "#62:3", "#49:6" -> "#62:4",
"#49:5" -> "#62:5", "#49:8" -> "#62:6"}}

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  • $\begingroup$ Thank you, always eager to learn new things ;-) $\endgroup$ May 31, 2016 at 6:00
  • $\begingroup$ @Athanassios Παρακαλώ. I voted for C.E. I just wanted to show another way. Mma is versatile. I learn a lot from the creativity of the users on this site myself. :) $\endgroup$
    – ubpdqn
    May 31, 2016 at 6:04
  • $\begingroup$ Hi, I studied a bit your code. I noticed that the third argument of GroupBy, i.e. (Rule @@@ # &) can be omitted ??? And I am trying hard to understand this SortBy. Would you be kind enough to provide some analysis, e.g. rewrite it in a more comprehensible way. This f@#[[2]]& is really too difficult to grasp. Thank you $\endgroup$ Jun 4, 2016 at 8:51
  • $\begingroup$ I can see that : f /@ Values /@ Values@gp {{{61, 7}, {61, 8}, {61, 10}, {61, 9}}, {{62, 5}, {62, 4}, {62, 3}, {62, 6}}} But I cannot understand how this f@#[[2]]& is applied on Values@gp $\endgroup$ Jun 4, 2016 at 8:57
  • $\begingroup$ @Athanassios f@#[[2]& is just using the function fon the second part of the argument. In this case the second argument is the value of the rule. The value is a string (a pair of numbers separate by ':'). f converts this into an expression (numerical) that SortBy can use to order. I hope this is clearer. # is just a placeholder and & is used for completion pure functions.:) $\endgroup$
    – ubpdqn
    Jun 4, 2016 at 8:57

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