Gathering of list

Question

Problem statement

The following challenge was recently posted to the J language programming forum by Skip Cave (http://jsoftware.com/pipermail/programming/2016-March/044561.html):

"The animal control officer wants to keep track of the animals in a city. The officer tags all the animals with a serial number. He keeps a list of all the animals he has tagged, along with each serial number."

In Mathematica form, the given list is:

    data = {{"bird", 1}, {"cow", 2}, {"cow", 3}, {"dog", 4}, {"cow", 5},   
            {"cow", 6}, {"cow", 7}, {"bird", 8}, {"dog", 9}, {"cat", 10},   
            {"dog", 11}, {"pig", 12}, {"dog", 13}, {"bird", 14}, {"pig", 15}};

"The officer now wants to make a second list showing each type of animal along with all the serial numbers tagged for each animal."

In Mathematica form, the desired output is:

    {{"bird", {1, 8, 14}}, {"cow", {2, 3, 5, 6, 7}}, 
     {"dog", {4, 9, 11, 13}}, {"cat", {10}}, {"pig", {12, 15}}}

The challenge is to transform the given input data into that output form in as simple a way as possible. (As phrased in the J Programming forum post, the challenge was to do so in as short an expression as possible.)

My solution so far:

    creatures = Union[First /@ data]
    gathered = GatherBy[data, First]
    serials = Map[Last, #] & /@ gathered
    Transpose[{creatures, serials}]

Naturally, multiple steps may be combined, e.g.:

    serials = Map[Last, #] & /@ GatherBy[data, First]

In fact, all steps could be combined into one long expression:

    Transpose[{Union[First /@ data], Map[Last, #] & /@ GatherBy[data, First]}]

Moreover, the list serials of lists of serial numbers could be formed using patterned replacement:

    serials = gathered /. {animal_, n_Integer} -> n

Question

Is there some significantly shorter or simpler way to do this?

Notes

1. The original data and desired output could have been cast into the form of associations, but I suspect the operations required to go from data to output would be essentially the same.

2. Probably the output should be fed into SortBy[#, First]& so as to rearrange the output list to be sorted alphabetically by animal name.

P.S.

Can you suggest a better, but succinct, title for my post?

Answer 1

As requested by the OP:

Normal[GroupBy[data, First -> Last]] /. Rule -> List
   {{"bird", {1, 8, 14}}, {"cow", {2, 3, 5, 6, 7}}, {"dog", {4, 9, 11, 13}},
    {"cat", {10}}, {"pig", {12, 15}}}

The handy bit here is the second argument of GroupBy[]:

GroupBy[data, First -> Last]
   <|"bird" -> {1, 8, 14}, "cow" -> {2, 3, 5, 6, 7}, "dog" -> {4, 9, 11, 13},
     "cat" -> {10}, "pig" -> {12, 15}|>

which transforms the values associated with the keys into the desired list of numbers. Contrast this with a plain GroupBy[data, First].

As noted by multiple people, a more compact version is

List @@@ Normal[GroupBy[data, First -> Last]]

Tom in a comment below gives a slicker version:

KeyValueMap[List, GroupBy[data, First -> Last]]

---

The GatherBy[] approach presented by the OP can also be written as

Append[Union[#[[All, 1]]], #[[All, 2]]] & /@ GatherBy[data, First]

or as

Append @@ MapAt[Union, Transpose[#], 1] & /@ GatherBy[data, First]

Answer 2

I think this is one of the simplest here, both conceptually and in code:

Reap[Sow @@@ Reverse[data, {2}], _, List][[2]]

Answer 3

MapAt[#[[1]]&, Transpose/@ GatherBy[data, First], {;; , 1}]

{{"bird", {1, 8, 14}}, {"cow", {2, 3, 5, 6, 7}}, {"dog", {4, 9, 11, 13}}, {"cat", {10}}, {"pig", {12, 15}}}

Edit Corrected by murray, aka OP:

MapAt[Last, Transpose/@ GatherBy[data, First], {;; , 1}]

Edit2 Just for the ad hoc case with specific numeration PositionIndex:

List @@@ Normal @ PositionIndex[data[[All, 1]]]