Here's the Quora problem I wanted to solve with the partition question:
*A hotel has 4 rooms. In one of them, there are 4 beds and in the rest 2
beds. How many different ways can you put 10 passengers in these rooms?*
Using the J programming language, brute force approach:
p=.1 0 0 0 1 0 1 0 1 0 NB. Partition vector
Generate all the permutations on 10 unique items. Partition each
permutation into 4 partitions, (4, 2, 2, 2). Sort each partition, then
remove all duplicate sets of 4 partition sets. Store the reduced partition
sets in nn, and report the final size.
$nn=.~.;"1/:~"1 ea p<;.1"1 perm 10
18900 10
So the answer is 18,900 unique ways to partition 10 guests in 4 rooms (4,
2, 2, 2).
Show the first and last few partition options:
10{. pnn=.p<;.1"1 nn
│0 1 2 3│4 5│6 7│8 9│
│0 1 2 3│4 5│6 8│7 9│
│0 1 2 3│4 5│6 9│7 8│
│0 1 2 3│4 5│7 8│6 9│
│0 1 2 3│4 5│7 9│6 8│
│0 1 2 3│4 5│8 9│6 7│
│0 1 2 3│4 6│5 7│8 9│
│0 1 2 3│4 6│5 8│7 9│
│0 1 2 3│4 6│5 9│7 8│
│0 1 2 3│4 6│7 8│5 9│ …..
….│6 7 8 9│3 5│0 4│1 2│
│6 7 8 9│3 5│1 2│0 4│
│6 7 8 9│3 5│1 4│0 2│
│6 7 8 9│3 5│2 4│0 1│
│6 7 8 9│4 5│0 1│2 3│
│6 7 8 9│4 5│0 2│1 3│
│6 7 8 9│4 5│0 3│1 2│
│6 7 8 9│4 5│1 2│0 3│
│6 7 8 9│4 5│1 3│0 2│
│6 7 8 9│4 5│2 3│0 1│
Skip Cave
Cave Consulting LLC
On Tue, Apr 7, 2020 at 4:13 PM Hauke Rehr <[email protected]> wrote:
> sorry, I mistook the full stop for an inflection
>
> Am 07.04.20 um 23:10 schrieb Skip Cave:
> > L: https://code.jsoftware.com/wiki/Vocabulary/lcapco
> > Skip Cave
> > Cave Consulting LLC
> >
> >
> > On Tue, Apr 7, 2020 at 4:03 PM Skip Cave <[email protected]>
> wrote:
> >
> >> It is just L:
> >>
> >> Skip Cave
> >> Cave Consulting LLC
> >>
> >>
> >> On Tue, Apr 7, 2020 at 4:02 PM Hauke Rehr <[email protected]>
> wrote:
> >>
> >>> Where is L:. documented? I can’t find it in the Vocabulary.
> >>>
> >>> Am 07.04.20 um 22:59 schrieb Skip Cave:
> >>>> That's it!
> >>>> I wanted a combination of partitioning and indexing, and L: does the
> >>> job. I'll
> >>>> have to do some studying to understand L:.
> >>>>
> >>>> r
> >>>>
> >>>> 9 8 6 1 2 2 2 6 8 7
> >>>>
> >>>> 5 4 8 4 2 7 9 1 4 1
> >>>>
> >>>> 4 3 3 7 7 0 6 7 6 6
> >>>>
> >>>> m1
> >>>>
> >>>> ┌───────┬─────┬───┬─┐
> >>>>
> >>>> │0 1 5 3│4 2 8│7 6│9│
> >>>>
> >>>> └───────┴─────┴───┴─┘
> >>>>
> >>>> m1 {L:0"1 r
> >>>>
> >>>> ┌───────┬─────┬───┬─┐
> >>>>
> >>>> │9 8 2 1│2 6 8│6 2│7│
> >>>>
> >>>> ├───────┼─────┼───┼─┤
> >>>>
> >>>> │5 4 7 4│2 8 4│1 9│1│
> >>>>
> >>>> ├───────┼─────┼───┼─┤
> >>>>
> >>>> │4 3 0 7│7 3 6│7 6│6│
> >>>>
> >>>> └───────┴─────┴───┴─┘
> >>>>
> >>>>
> >>>> On the other hand, if all I want to do is partition arrays, Michael
> >>> Day's
> >>>> solution is a handy technique that I will try to remember:
> >>>>
> >>>>
> >>>> 1 0 0 0 1 0 0 1 0 1 <;.1"1 r
> >>>>
> >>>> ┌───────┬─────┬───┬─┐
> >>>>
> >>>> │9 8 6 1│2 2 2│6 8│7│
> >>>>
> >>>> ├───────┼─────┼───┼─┤
> >>>>
> >>>> │5 4 8 4│2 7 9│1 4│1│
> >>>>
> >>>> ├───────┼─────┼───┼─┤
> >>>>
> >>>> │4 3 3 7│7 0 6│7 6│6│
> >>>>
> >>>> └───────┴─────┴───┴─┘
> >>>> Skip Cave
> >>>> ----------------------------------------------------------------------
> >>>> For information about J forums see
> http://www.jsoftware.com/forums.htm
> >>>>
> >>>
> >>> --
> >>> ----------------------
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> >>>
> >>
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> >
>
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