Ordered partitions: Difference between revisions

<lang rexx>/*REXX program displays ordered partitions: orderedPartitions(i, j, k, ···). */

call orderedPartitions 2,0,2 /*Note: 2,,2 will also work. */

call orderedPartitions 1,1,1

call orderedPartitions 1,2,0,1 /*Note: 1,2,1 will also work. */

exit /*stick a fork in it, we're all done. */

orderedPartitions: procedure; #=arg(); hdr=; bot.=; top.=; low=; high=; d=123456789

dt=1234567890 /*handy-dandyT: is the sum of literalall forthe digitsarguments.*/

t=0 do i=1 for #; t=t + arg(i) /*T:sum isall the sumhighest ofnumbers allin argumentsparts.*/

doend /*i=1*/ for #; t=t+('0'arg(i)) /*sum all[↑] may have thean highestomitted #sargument. in parts*/

do j=1 for #; _=arg(j) /* _: is the /* [↓]Jth argument. process each of arguments*/

do len.j=max(1, _) for #; _=arg(j) /* _: is the Jth argument /*LEN: length of args, 0=special. */

lenbot.j=maxleft(1d, _); if _==0 then bot.j=0 /*define the bottom number. /*LEN: length of args, 0=special*/

bottop.j=right(left(d,t),_); if _==0 then bottop.j=0 /*define the bottom" " top " num*/

top@.j=right(left(d, t),_); if _==0 then top @.j=0 /*define the "digits used for VERIFY. " top " */

@.jhdr=left(d,t);hdr _ if _==0 then @.j=0 /*definebuild (by appending) VERIFYdisplay digitsheader.*/

hdrlow=hdrlow _|| bot.j; high=high || top.j /*the low and high numbers for DO /*build display header.below*/

okD=left(0 || d, t+1) /*define the legal digits to be used. */

say center(' partitions for: ' hdr" ",50 60, '─'); say/*display centered title for the output*/

do g=low to high /* [↑] generate orderedthe parts.ordered partitions*/

if verify(g, okD)\==0 then iterate /*filter out the unwanted decimal digits. */

p=1 /*P: is the position of a digitdecimal dig.*/

$= /*$: will be the transformed #snumbers. */

do k=1 for # /*verify the partitions numbers. */

/*validate# number: dups/ordered/repeats*/

_=substr(g,p,len.k) /*ordered partpartition num.number to be tested.*/

if verify(_, @.k)\==0 then iterate g /*is the decimal digit ¬not valid ? */

!= /* [↓] validate numthe decimal number. */

if @.k\==0 then do j=1 for length(_); z=substr(_, j, 1)

if pos(z, $)\==0 then iterate g /*prevprevious. */

if j==1 then iterate /*is firstt?*/

if z<=substr(_, j-1, 1) then iterate g /*ordordered. */

if pos(z, _, 1+pos(z,_))\==0 then iterate g /*dupduplicate.*/

p=p + len.k /*point to the next #decimal number. */

$=$ ' {'strip( translate(!, ,0), ,'",'")"'}" ' /*dress thenumber #up up.by suppressing LZ ···*/

'''{{out|output'''|text=&nbsp; when using the default inputs:}}

{1,2} {} {3,4}

{1,3} {} {2,4}

{1,4} {} {2,3}

{2,3} {} {1,4}

{2,4} {} {1,3}

{3,4} {} {1,2}

{1} {2} {3}

{1} {3} {2}

{2} {1} {3}

{2} {3} {1}

{3} {1} {2}

{3} {2} {1}

─────────────────────────── partitions for: 1 2 0 1 ─────────────────────────────

{1} {2,3} {} {4}

{1} {2,4} {} {3}

{1} {3,4} {} {2}

{2} {1,3} {} {4}

{2} {1,4} {} {3}

{2} {3,4} {} {1}

{3} {1,2} {} {4}

{3} {1,4} {} {2}

{3} {2,4} {} {1}

{4} {1,2} {} {3}

{4} {1,3} {} {2}

{4} {2,3} {} {1}