Generating combinations from multiple sets


#1

Dear all,

I have a requirement as below.

There are ‘n’ containers of lengths {l_i}, i = 1,…,n. All these
containers are collected into an array. Picking one element at a time
from each container, an array has to be constructed and either yielded
or accumulated.

I have written the following code that seems to work reasonably. Are
there simpler or more efficient ways of doing this?

Thanks in advance,

JS


def generate_combinations(cont_ary, &blk)

cont_count = cont_ary.length

return if cont_count < 1

if cont_count == 1
if block_given?
cont_ary[0].each { | el | yield [el] }
return
else
return cont_ary[0].collect { | el | [el] }
end
end

cur_indices = Array.new(cont_count, 0)
combinations = []

generate_combinations_iterator(cont_ary, 0, cur_indices,
:working_set => Array.new(cont_count),
:accumulator => combinations,
&blk)

return combinations unless block_given?

end

def generate_combinations_iterator(cont_ary, cur_cont, cur_indices, opts
= {}, &blk)

cont_ary[cur_cont].each_with_index do | el, i |

 opts[:working_set][cur_cont] = el

 case cur_cont
 when 0
   cur_indices[cur_cont] = i
   (1...cur_indices.length).each { | j | cur_indices[j] = 0 }
   generate_combinations_iterator(cont_ary, cur_cont + 1,

cur_indices, opts, &blk)

 when cont_ary.length-1
   if block_given?
     yield opts[:working_set]
   else
     opts[:accumulator] << Array.new(opts[:working_set])
   end

 else
   cur_indices[cur_cont] = i
   generate_combinations_iterator(cont_ary, cur_cont + 1,

cur_indices, opts, &blk)
end

end

end

Output

irb(main):011:0> load ‘combination-generator.rb’
=> true

irb(main):012:0> ary1 = []
=> []

irb(main):013:0> generate_combinations(ary1)
=> nil

irb(main):014:0> ary2 = [[1, 2, 3, 4]]
=> [[1, 2, 3, 4]]

irb(main):015:0> pp generate_combinations(ary2)
[[1], [2], [3], [4]]
=> nil

irb(main):016:0> ary3 = [[1, 2, 3, 4], [‘a’, ‘b’, ‘c’]]
=> [[1, 2, 3, 4], [“a”, “b”, “c”]]

irb(main):017:0> pp generate_combinations(ary3)
[[1, “a”],
[1, “b”],
[1, “c”],
[2, “a”],
[2, “b”],
[2, “c”],
[3, “a”],
[3, “b”],
[3, “c”],
[4, “a”],
[4, “b”],
[4, “c”]]
=> nil


#2

In case the gateway is broken again:

I have a shorter alternative; it may be more efficient but you’ll have
to
test that for yourself:

def all_combinations(enum,&bl)
pre = “”
post = “”
middle = []
enum.each_with_index do |en,idx|
item = “e#{idx}”
pre << “enum[” << idx.to_s << “].each {|” << item << “| "
middle << item
post << “}”
end
eval(pre << “bl[” << middle.join(”,") << “]” << post)
end

irb(main):053:0> all_combinations([[1,2,3],%w{a b c d}]) {|*a| p a}
[1, “a”]
[1, “b”]
[1, “c”]
[1, “d”]
[2, “a”]
[2, “b”]
[2, “c”]
[2, “d”]
[3, “a”]
[3, “b”]
[3, “c”]
[3, “d”]
=> [1, 2, 3]

You can even change this to work with arbitrary Enumerables - this
version
depens on “enum” being an Array.

Kind regards

robert

#3

Thank you!

Preliminary testing seems to show that it indeed is faster. I think it
is understandable since it is doing inline expansion, rather than
recursion.

Nice use of code generation.

Best regards,

JS