How to rebuild original data from a histogram?

Question

I have data in form

list of values ex. {5,7,4} list of frequecies ex. {1,2,3}

I would like to obtain the original data from which such a histogram was generated

ex. {5,7,7,4,4,4}

Answer 1

Without looking at performance, but only on understanding: First, you create a function f which takes a value and a count and which reproduces the value exactly count times. In the simplest case

f[val_, count_] := ConstantArray[val, count]

and you can call f[3,4] to get {3,3,3,3}. Now, you combine your input arrays so that you can call f directly for each pair. For this, you can use MapThread. To create you final result, you have to Flatten the output:

Flatten[MapThread[f, {{5, 7, 4}, {1, 2, 3}}]]

This all can of course be combined into one call

vals = {5, 7, 4};
counts = {1, 2, 3};

Flatten[MapThread[ConstantArray, {vals, counts}]]

or

ConstantArray @@@ Transpose[{vals, counts}] // Flatten

or (to simplify kgulers approach)

Inner[ConstantArray, vals, counts, Join]

and many more

Answer 2

 values = RandomSample[Range[100], 5]
 (*{72,75,44,25,60}*)
 counts = RandomInteger[{1, 5}, 5]
 (* {4,3,1,1,1} *)

Inner and Table:

 Inner[Table[#1, {#2}] &, values, counts, Join] (*thanks: Halirutan *)

Inner and ConstantArray:

 Flatten@Inner[ConstantArray, values, counts, List]

both give

 {72, 72, 72, 72, 75, 75, 75, 44, 25, 60}

Update: further variations using Thread, MapIndexed ...

 Table @@@ Thread[{values, List /@ counts}] // Flatten
 #1[[Join @@ MapIndexed[Table[First[#2], {#}] &, #2]]] &[values, counts]
 Module[{f}, Thread[f[values, List /@ counts]] /. f -> Table // Flatten]