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Given a list of (frencuently repeated and unsorted) pairs

{Mode, SubMode}

I want to form the list

{ {COUNT_mode1, COUNT_mode2,...,COUNT_modeN}, {COUNT_mode1_submode1, COUNT_mode1,submode2, ... , COUNT_mdoe1,submodeM1, ... ,COUNT_modeN_submodeNM}, {mode1,mode2,...}, {submode1,submode2,...} }

Here is an example, given:

l = { {"games","minecraft"},{"games","minecraft"},{"games","WoW"}, {"books","book1"},{"books","book1"},{"books","book1"},{"books","book5"},{"other","something"},{"other","book1"}}

MyFunction[l] --> 
{
    {3,4,2},
    {2,1,3,1,1,1},
    {"games","books","other"},
    {"minecraft","WoW","book1","book5","something","book1"}
}
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  • $\begingroup$ I notice that you did not Accept an answer to this question. Is there something that remains to be addressed? $\endgroup$ – Mr.Wizard♦ Oct 18 '14 at 22:32
  • $\begingroup$ @Mr.Wizard I forgot to accept one. $\endgroup$ – José D. Oct 20 '14 at 7:59
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Update: cleaner now and with a v10 alternative.

If I am understanding you I think I would use:

Flatten[Reverse[Tally /@ (l\[Transpose]), 3], {3, 1}]

{
 {3, 4, 2},
 {2, 1, 3, 1, 1, 1},
 {"games", "books", "other"},
 {"minecraft", "WoW", "book1", "book5", "something", "book1"}
}

Alternatively using Counts introduced in Mathematica 10:

Join[Values, Keys][Counts /@ (l\[Transpose])] // Through
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Here is one way.

modes = Transpose[Tally[l[[All, 1]]]]

(* Out[176]= {{"games", "books", "other"}, {3, 4, 2}} *)

submodes = 
 Reverse[Transpose[
   Flatten[Map[Tally, GatherBy[l, First][[All, All, 2]]], 1]]]

(* Out[178]= {{2, 1, 3, 1, 1, 1}, {"minecraft", "WoW", "book1", "book5", 
  "something", "book1"}} *)

Riffle[modes, submodes]

(* Out[179]= {{"games", "books", "other"}, {2, 1, 3, 1, 1, 1}, {3, 4, 
  2}, {"minecraft", "WoW", "book1", "book5", "something", "book1"}} *)
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It clunks a bit, but it generates the specified output for the test input you provided. 

summarize[pairs_] :=
 With[{gathered = GatherBy[pairs, First]},
  {Length /@ gathered,
   Flatten[Tally[#[[All, -1]]][[All, -1]] & /@ gathered],
   gathered[[All, 1, 1]],
   Flatten[DeleteDuplicates /@ gathered[[All, All, -1]], 1]
   }];

summarize[l] === {{3, 4, 2}, {2, 1, 3, 1, 1, 1}, {"games", "books", "other},  
  {"minecraft", "WoW", "book1", "book5", "something", "book1"}}

(* True *)
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Here is one way.

MyFunc[l_] := Block[{t1, t2, res},
   t1 = Tally[l[[All, 1]]];
   t2 = Tally[l[[All, 2]]];
   res = {t1[[All, 2]], t2[[All, 2]], t1[[All, 1]], t2[[All, 1]]};
   Return[res];
];
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  • $\begingroup$ I'd advise against using Block for variable localization. Module is much safer. $\endgroup$ – Leonid Shifrin Apr 17 '14 at 9:22
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An approach using Reap and Sow:

Using:

lst = {{"games", "minecraft"}, {"games", "minecraft"}, {"games", 
   "WoW"}, {"books", "book1"}, {"books", "book1"}, {"books", 
   "book1"}, {"books", "book5"}, {"other", "something"}, {"other", 
   "book1"}}

Then

Join[Transpose[
   Last@Reap[Sow[1, First[#]] & /@ lst, _, {Total@#2, #1} &]],
  Transpose@
   Last@Reap[
     Sow[1, wp[#]] & /@ lst, _, {Total@#2, #1[[1, 2]]} &]][[{1, 3, 2, 
   4}]]

yields:

{{3, 4, 2}, {2, 1, 3, 1, 1, 1}, {"games", "books", 
  "other"}, {"minecraft", "WoW", "book1", "book5", "something", 
  "book1"}}
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