Found a bug when the top left atom of the matrix is 1
rectgrps -.tst1
0 0 0 3 3 3
0 0 0 9 9 9
3 3 3 15 15 15
18 18 18 3 3 3
18 18 18 3 3 3
3 3 3 33 33 33
3 3 3 33 33 33
3 3 3 3 3 3
3 3 3 3 3 3
3 3 3 3 3 3
60 60 60 3 3 3
60 60 60 3 3 3
The following change seems to fix it.
rectgrps=: ([EMAIL PROTECTED] ([EMAIL PROTECTED] $ ])
}.@(i.~@(0&,@(,.&,/))))@:rplhv
rectgrps -.tst1
1 1 1 0 0 0
1 1 1 10 10 10
0 0 0 16 16 16
19 19 19 0 0 0
19 19 19 0 0 0
0 0 0 34 34 34
0 0 0 34 34 34
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
61 61 61 0 0 0
61 61 61 0 0 0
---Sherlock, Ric wrote:
> I've "tidied up" your algorithm below. Thanks again!
>
> NB. running sum of starts of connected 1s in each row
> incgrp=: [:($$ [:+/\ ,) (1, }:~: }.)"1
> rpl=: ] - (-/ , 0:)@[ {~ [EMAIL PROTECTED] i. ] NB. numeric replace
> (RMiller)
>
> hv=: *"_ _1 incgrp,: incgrp&.|: NB. hor. & vert. connected 1s.
> rplhv=: (([:(,:|.) ,"_1) rpl"_1 ]) @: hv
> rectgrps=: ([EMAIL PROTECTED]([EMAIL PROTECTED] $ ]) i.~@,.&,/) @: rplhv NB.
> rectangular groups of 1s
>
> NB. topleft and bottomright corners of each group
> tlbr=: ($#: (](i.}.@,. i:) 0~.@,])@,) @: rectgrps
> blocks2=: ([,: (-~>:))/"_1 @: tlbr NB. Topleft and shape of
> each group
>
> blocks2 tst1
> 0 3
> 1 3
>
> 2 0
> 1 3
>
> 3 3
> 2 3
>
> 5 0
> 5 3
>
> 7 3
> 3 3
>
> 10 3
> 2 3
>
>
> ---R.E. Boss wrote:
> > T2=: [:($$ [:+/\ ,) (1, }:~: }.)"1
> >
> > [;/'H V'=: (*"_ _1 T2,: T2&.|:) tst1
> > NB. hor. & vert. connected 1's
> > +-----------------+---------------+
> > | 0 0 0 2 2 2|0 0 0 16 21 26|
> > | 0 0 0 0 0 0|0 0 0 0 0 0|
> > | 4 4 4 0 0 0|2 7 12 0 0 0|
> > | 0 0 0 7 7 7|0 0 0 18 23 28|
> > | 0 0 0 9 9 9|0 0 0 18 23 28|
> > |10 10 10 0 0 0|4 9 14 0 0 0|
> > |12 12 12 0 0 0|4 9 14 0 0 0|
> > |14 14 14 14 14 14|4 9 14 20 25 30|
> > |15 15 15 15 15 15|4 9 14 20 25 30|
> > |16 16 16 16 16 16|4 9 14 20 25 30|
> > | 0 0 0 18 18 18|0 0 0 20 25 30|
> > | 0 0 0 20 20 20|0 0 0 20 25 30|
> > +-----------------+---------------+
> >
> > rpl=:] - (-/ , 0:)@[ {~ [EMAIL PROTECTED] i. ]
> > NB. Millers solution in
> > NB.
> > http://www.jsoftware.com/pipermail/programming/2007-July/007303.html
> >
> > V ( [EMAIL PROTECTED] $]) i.~@,.&,/ (([:(,:|.) ,"_1) rpl"_1 ])H,:~V
> > NB. indicating blocks of 1's
> > 0 0 0 3 3 3
> > 0 0 0 0 0 0
> > 12 12 12 0 0 0
> > 0 0 0 21 21 21
> > 0 0 0 21 21 21
> > 30 30 30 0 0 0
> > 30 30 30 0 0 0
> > 30 30 30 45 45 45
> > 30 30 30 45 45 45
> > 30 30 30 45 45 45
> > 0 0 0 63 63 63
> > 0 0 0 63 63 63
> >
> > [R=: V ([ (,:&, rpl [) [EMAIL PROTECTED] $]) i.~@,.&,/ (([:(,:|.) ,"_1)
> > rpl"_1 ])H,:~V
> > NB. less blocks, but if H is used as LHS, answer is
> wrong ...
> > 0 0 0 3 3 3
> > 0 0 0 0 0 0
> > 12 12 12 0 0 0
> > 0 0 0 21 21 21
> > 0 0 0 21 21 21
> > 30 30 30 0 0 0
> > 30 30 30 0 0 0
> > 30 30 30 45 45 45
> > 30 30 30 45 45 45
> > 30 30 30 45 45 45
> > 0 0 0 45 45 45
> > 0 0 0 45 45 45
> >
> > ([:([,: (-~>:))/"_1 $#: (](i.}.@,. i:) 0~.@,])@,) R
> > 0 3
> > 1 3
> >
> > 2 0
> > 1 3
> >
> > 3 3
> > 2 3
> >
> > 5 0
> > 5 3
> >
> > 7 3
> > 5 3
> >
> >
> > R.E. Boss
> >
> >
> > > -----Oorspronkelijk bericht-----
> > > Van: [EMAIL PROTECTED] [mailto:programming-
> > > [EMAIL PROTECTED] Namens Sherlock, Ric
> > > Verzonden: woensdag 11 juni 2008 14:45
> > > Aan: Programming forum
> > > Onderwerp: [Jprogramming] Finding blocks in a table/matrix
> > >
> > > Below is a problem that I have enjoyed working on that
> stems from an
> > > attempt to generalise the writing of a boxed table of mixed
> > type to an
> > > Excel worksheet.
> > >
> > > My attempt at a solution in the script at the bottom gives
> > a non-optimal
> > > answer (it only finds blocks within rows) that I'd like to
> > improve if
> > > possible/practical.
> > >
> > > tsta is a boxed table(matrix) of mixed numeric and literal type
> > >
> > > ischar=: 3!:0 e. 2 131072"_
> > > tst1=: ischar &> tsta NB. Mask of boxed literals in tsta
> > >
> > > NB. Below is an example tst1 for copying into a session.
> > > tst1=: _99&".;._2 (0 : 0)
> > > 0 0 0 1 1 1
> > > 0 0 0 0 0 0
> > > 1 1 1 0 0 0
> > > 0 0 0 1 1 1
> > > 0 0 0 1 1 1
> > > 1 1 1 0 0 0
> > > 1 1 1 0 0 0
> > > 1 1 1 1 1 1
> > > 1 1 1 1 1 1
> > > 1 1 1 1 1 1
> > > 0 0 0 1 1 1
> > > 0 0 0 1 1 1
> > > )
> > >
> > > The problem is to specify the blocks of ones in the table.
> > > A block is specified by the position of its top left member
> > and its shape.
> > >
> > > Below is an example desired output of a verb "blocks" for tst1:
> > > blocks tst1
> > > 0 3 NB. topleft of block
> > > 1 3 NB. shape of block
> > >
> > > 2 0
> > > 1 3
> > >
> > > 3 3
> > > 2 3
> > >
> > > 5 0
> > > 5 3
> > >
> > > 7 3
> > > 5 3
> > >
> > > $blocks tst1
> > > 5 2 2
> > >
> > > Obviously there are other ways to organise the blocks of
> > ones in tst1. A
> > > solution is correct as long as all ones in tst1 are
> > included in one and
> > > only one block. Solutions that produce fewer blocks are
> > better provided
> > > they don't take much longer to find the minimum number of blocks.
> > >
> > > tst2=: 5 [EMAIL PROTECTED] NB. Another example table of 0s & 1s that
> > blocks should
> > > work with
> > >
> > >
> > >
> > > NB.========Start of Script======================================
> > > ischar =: 3!:0 e. 2 131072"_
> > > firstones=: > 0: , }: NB. Mask of first ones
> > >
> > > tlcols=: <@[EMAIL PROTECTED]"1 NB. leftmost columns of
> > blocks of 1s
> > > toplefts=: i.@:# ,.&.> tlcols NB. topleft index of blocks of 1s
> > >
> > > bytype=: 1 : 'u;.1~ (1, 2~:/\ ])'
> > > lens=: <@({.bytype # #bytype)"1 NB. lengths of blocks of 1s
> > > shapes=: 1: ,. &.> lens NB. shapes of blocks of 1s
> > >
> > > blocks=: ;@toplefts ,:"1 ;@shapes NB. blocks of 1s
> > >
> > > Note 'testing'
> > > ;toplefts tst1 NB. list of topleft of blocks of 1s
> > > ;toplefts -.tst1 NB. list of topleft of blocks of 0s
> > > (;@toplefts ,:"1 ;@shapes) tst1 NB. List of blocks
> > > ;(toplefts ,:"1 &.> shapes) tst1 NB. Also list of blocks
> > >
> > > (blocks ischar &> tsta) <;.0 tsta NB. blocks of char
> > (you will need to
> > > create a tsta to run this)
> > > (blocks -.ischar &> tsta) <;.0 tsta NB. blocks of non-char
> > > )
> > > NB.=======End of Script==========================================
> > >
> >
> ----------------------------------------------------------------------
> > > For information about J forums see
> > http://www.jsoftware.com/forums.htm
> >
> >
> ----------------------------------------------------------------------
> > For information about J forums see
> http://www.jsoftware.com/forums.htm
> >
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
