Is there a method for sampling from a poplulation of n objects, without replacement, to generate k random partitions that doesn't use Reap/Sow?
I want to sample from a poplulation of n objects, without replacement, to generate k random partitions (eg, in a Multinomial sense). So far, the only non-procedural methods I've come up with use Reap/Sow. Is it possible to do this without using Reap/Sow? I don't have a problem with using Reap/Sow. I'm only curious if that is the only way to implement this other than using a procedural method. There may even be a built-in command that does this?
Here is an example of a functional implementation that I wrote that uses Reap/Sow:
In[1]:= randomPartitionsFunctional[pop_List, partLength_Integer] :=
With[{samp = RandomSample[pop, partLength]},
DeleteCases[pop, Alternatives @@ Sow[samp]]
]
In[2]:= randomPartitionsFunctional[pop_List,
partLengths_?(VectorQ[#1, NumericQ] &)] :=
Flatten[Reap[
Fold[randomPartitionsFunctional[#1, #2] &, pop, partLengths]],
2] /; Length[pop] == Total[partLengths]
In[3]:= randomPartitionsFunctional[Range[15], {3, 2, 3, 3, 4}]
Out[3]= {{15, 10, 9}, {14, 4}, {6, 1, 7}, {2, 12, 13}, {3, 11, 8, 5}}
In[4]:= With[{pop = CharacterRange["a", "l"]},
randomPartitionsFunctional[pop, #] & /@
IntegerPartitions[Length[pop], {2}]]
Out[4]= {{{"g", "l", "i", "a", "h", "c", "j", "d", "e", "f",
"b"}, {"k"}}, {{"b", "j", "e", "c", "d", "f", "g", "i", "k",
"h"}, {"l", "a"}}, {{"b", "j", "i", "l", "d", "k", "a", "e",
"h"}, {"c", "g", "f"}}, {{"d", "a", "k", "f", "i", "l", "g",
"b"}, {"h", "c", "e", "j"}}, {{"e", "f", "i", "c", "a", "j",
"b"}, {"d", "g", "k", "h", "l"}}, {{"e", "l", "c", "d", "f",
"a"}, {"h", "g", "k", "b", "i", "j"}}}
