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Is there a command to insert an item into a list such that they form pairs? In other words to take 

InsertObject[{a,b,c},d]

which will output

{{a,d},{b,d},{c,d}}    ?

This would be equivalent to the function,

Table[{{a,b,c}[[i]],d},{i,1,3}]

This way works just fine, but it doesn't seem to be the "Mathematica way" of doing things. Is there a built in command this?

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3 Answers 3

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Few more alternatives:

{#, d} & /@ {a, b, c}
Tuples[{{a, b, c}, {d}}]
Join[{#}, {d}] & /@ {a, b, c}
Table[{i, d}, {i, {a, b, c}}]
Append[{#}, d] & /@ {a, b, c}
Prepend[{d}, #] & /@ {a, b, c}
Riffle[{#}, {d}] & /@ {a, b, c}
Distribute[{{a, b, c}, d}, List]
Insert[{#}, d, -1] & /@ {a, b, c}
Replace[{a, b, c}, x_ :> {x, d}, 1]
PadRight[List /@ {a, b, c}, {3, 2}, d]
ArrayPad[List /@ {a, b, c}, {0, {0, 1}}, d]
Partition[Riffle[{a, b, c}, d, {2, -1, 2}], 2]
Transpose[{{a, b, c}, ConstantArray[d, {3}]}]
Transpose[{{a, b, c}, Table[d, {3}]}]

Timings:

f1[lst_, elem_] := Map[{#, elem} &, lst]
f2[lst_, elem_] := Tuples[{lst, {elem}}]
f3[lst_, elem_] := Thread[{lst, elem}]
f4[lst_, elem_] := Join[{#}, {elem}] & /@ lst
f5[lst_, elem_] := Table[{i, elem}, {i, lst}]
f6[lst_, elem_] := Append[{#}, elem] & /@ lst
f7[lst_, elem_] := Prepend[{elem}, #] & /@ lst
f8[lst_, elem_] := Riffle[{#}, {elem}] & /@ lst
f9[lst_, elem_] := Distribute[{lst, elem}, List]
f10[lst_, elem_] := Insert[{#}, elem, -1] & /@ lst
f11[lst_, elem_] := Replace[lst, x_ :> {x, elem}, 1]
f12[lst_, elem_] := PadRight[List /@ lst, {Length@lst, 2}, elem]
f13[lst_, elem_] := ArrayPad[List /@ lst, {0, {0, 1}}, elem]
f14[lst_, elem_] := Partition[Riffle[lst, elem, {2, -1, 2}], 2]
f15[lst_, elem_] := Transpose[{lst, ConstantArray[elem, {Length@lst}]}]
f16[lst_, elem_] := Transpose[{lst, Table[elem, {Length@lst}]}]

funcs = {f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12, f13, f14,  f15, f16};
labels = ToString /@ {Map, Tuples, Thread, Join, Table, Append,
                    Prepend, Riffle, Distribute, Insert, Replace, PadRight, ArrayPad, 
                    Partition, TransposeConstantArray, TransposeTable};
res = ConstantArray[0, {16}];

testdata = RandomInteger[10, {10000000}];
Grid[Table[{i, labels[[i]],  First@Timing[res[[i]] = funcs[[i]][testdata, 20];]},
            {i,  Range[16]}], 
     Dividers -> All]

enter image description here

And@@(res[[1]] == # & /@ Rest[res])
(* True *)
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7
  • $\begingroup$ @eldo, thanks for the vote. I am sure there is at least half a dozen more ways -- e.g. Through[{a, b, c}[d]] /. x_[y_] :> {x, y} or {a, b, c} d /. Times -> List :) $\endgroup$
    – kglr
    Jul 15, 2014 at 3:07
  • $\begingroup$ +1 I lol'd at wall of ways and the readers digest large print edition benchmark chart ;-) $\endgroup$
    – ciao
    Jul 15, 2014 at 4:37
  • $\begingroup$ @rasher, thank you -- fontsize does indeed look like readers digest style even for my generation:) Still expecting some BitXor magic from you though to update the chart:) $\endgroup$
    – kglr
    Jul 15, 2014 at 5:39
  • $\begingroup$ They say imitation is the sincerest form of flattery. I'm feeling flattered. :^) $\endgroup$
    – Mr.Wizard
    Jul 15, 2014 at 8:29
  • $\begingroup$ @Mr.W indeed! As we have all learned to expect, a totally unexpected idiom is due soon now that this question got your attention :) $\endgroup$
    – kglr
    Jul 15, 2014 at 9:00
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Indeed there is:

Thread[List[{a, b, c}, d]]
(* {{a, d}, {b, d}, {c, d}} *)

or if you like Thread[{{a, b, c}, d}] but I thought the first version shows more which function is threaded.

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2
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Thanks to kguler.

Here are few more.

list = {a, b, c};
{list[[#]], d} & /@ Range[3]
{Pick[list, #, 1][[1]], d} & /@ IdentityMatrix[3]
{Extract[list, #], d} & /@ Range[3]
{Take[list, {#}][[1]], d} & /@ Range[3]
Flatten@ReplacePart[{#}, 1 -> {#, d}] & /@ list
Array[{list[[#]], d} &, 3]
{#, d} & @@@ (Transpose@{list})
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