# Iterate over a cartesian product

I have an array of N arrays A_i: [A_1,A_2,…,A_N].

I want to iterate over the cartesian product A_1xA_2…xA_N.

Is there a simple way of doing this without specifying N?

This thread seems to be a pretty thorough treatment of the idea:
Cartesian product of arrays - Ruby - Ruby-Forum . It was the first result of a
search on “ruby cross_product”.

Handy G. wrote:

I have an array of N arrays A_i: [A_1,A_2,…,A_N].

I want to iterate over the cartesian product A_1xA_2…xA_N.

Is there a simple way of doing this without specifying N?

``````ary = [[1, 2], [3, 4, 5], [6, 7, 8, 9]]
ary.first.product(*ary.drop(1))
# => [
# =>   [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9],
# =>   [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 4, 9],
# =>   [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 5, 9],
# =>   [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 3, 9],
# =>   [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 4, 9],
# =>   [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 5, 9]
# => ]
``````

jwm

On Tue, 14 Sep 20 10 17:13:11 +0200, JÃ¶rg W Mittag wrote:

``````# =>   [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9], # =>   [1, 4, 6],
[1, 4, 7], [1, 4, 8], [1, 4, 9], # =>   [1, 5, 6], [1, 5, 7], [1, 5,
8], [1, 5, 9], # =>   [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 3, 9], #
=>   [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 4, 9], # =>   [2, 5, 6],
[2, 5, 7], [2, 5, 8], [2, 5, 9] # => ]
``````

jwm

That looks so cool I wish I knew what it does.

ary.first is the first element of ary.
ary.product(one, two, …) is the cartesian product of ary with its
arguments.
ary.drop(1) is ary[1…-1], all the elements of ary but the first.
ary.product(*ary.drop(1)) passes each element of ary[1…-1] to
product() as an argument, making it equivalent to

ary.product(ary[1], ary[2], …, ary[-1])

Whoops, that should be ary.first.product, of course.

2010/9/14 Jörg W Mittag [email protected]:

# => ]

This looks nice. How did you do the formatting?

If destruction is allowed, we can do:

irb(main):013:0> ary = [[1, 2], [3, 4, 5], [6, 7, 8, 9]]
=> [[1, 2], [3, 4, 5], [6, 7, 8, 9]]
irb(main):014:0> pp ary.shift.product(*ary)
[[1, 3, 6],
[1, 3, 7],
[1, 3, 8],
[1, 3, 9],
[1, 4, 6],
[1, 4, 7],
[1, 4, 8],
[1, 4, 9],
[1, 5, 6],
[1, 5, 7],
[1, 5, 8],
[1, 5, 9],
[2, 3, 6],
[2, 3, 7],
[2, 3, 8],
[2, 3, 9],
[2, 4, 6],
[2, 4, 7],
[2, 4, 8],
[2, 4, 9],
[2, 5, 6],
[2, 5, 7],
[2, 5, 8],
[2, 5, 9]]
=> nil

Kind regards

robert

Robert K. wrote:

Â Â # => Â [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9],
Â Â # => Â [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 4, 9],
Â Â # => Â [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 5, 9],
Â Â # => Â [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 3, 9],
Â Â # => Â [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 4, 9],
Â Â # => Â [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 5, 9]
Â Â # => ]
This looks nice. How did you do the formatting?

By hand

Though I assume Hirb or awesome_print could probably do it
automatically.

If destruction is allowed, we can do:

irb(main):013:0> ary = [[1, 2], [3, 4, 5], [6, 7, 8, 9]]
=> [[1, 2], [3, 4, 5], [6, 7, 8, 9]]
irb(main):014:0> pp ary.shift.product(*ary)
[[1, 3, 6],

=> nil

That’s nice. Having toyed with Scala and Haskell, mutation just feels
so dirty to me. I guess I need some re-education to get back into
the idiomatic Ruby mindset.

jwm

2010/9/15 Jörg W Mittag [email protected]:

# => ]

This looks nice. How did you do the formatting?

By hand

14:09:29 ~\$ gem19 install ‘By hand’
ERROR: could not find gem By hand locally or in a repository
14:09:58 ~\$

Hm…

=> nil

That’s nice. Having toyed with Scala and Haskell, mutation just feels
so dirty to me. I guess I need some re-education to get back into
the idiomatic Ruby mindset.

Unfortunately there is no #slice which has two return values. If
there was we could do

a,b = arr.slice 0,1

But we can do this to achieve the same (i.e. non destructively
partitioning):

irb(main):016:0> a=(1…5).to_a
=> [1, 2, 3, 4, 5]
irb(main):017:0> y=(x=a.dup).slice! 0,1
=> [1]
irb(main):018:0> x
=> [2, 3, 4, 5]
irb(main):019:0> a
=> [1, 2, 3, 4, 5]

Well, I guess the simplest approach is still

irb(main):001:0> a=(1…5).to_a
=> [1, 2, 3, 4, 5]
irb(main):002:0> x,*y = a
=> [1, 2, 3, 4, 5]
irb(main):003:0> x
=> 1
irb(main):004:0> y
=> [2, 3, 4, 5]

So we can do

irb(main):026:0> ary = [[1, 2], [3, 4, 5], [6, 7, 8, 9]]
=> [[1, 2], [3, 4, 5], [6, 7, 8, 9]]
irb(main):027:0> x, *y = ary
=> [[1, 2], [3, 4, 5], [6, 7, 8, 9]]
irb(main):028:0> pp x.product(*y)
[[1, 3, 6],
[1, 3, 7],
[1, 3, 8],
[1, 3, 9],
[1, 4, 6],
[1, 4, 7],
[1, 4, 8],
[1, 4, 9],
[1, 5, 6],
[1, 5, 7],
[1, 5, 8],
[1, 5, 9],
[2, 3, 6],
[2, 3, 7],
[2, 3, 8],
[2, 3, 9],
[2, 4, 6],
[2, 4, 7],
[2, 4, 8],
[2, 4, 9],
[2, 5, 6],
[2, 5, 7],
[2, 5, 8],
[2, 5, 9]]
=> nil

Kind regards

robert