44 lines
3.7 KiB
Rexx
44 lines
3.7 KiB
Rexx
//*REXX program displays the ordered partitions as: orderedPartitions(i, j, k, ···). */
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call orderedPartitions 2,0,2 /*Note: 2,,2 will also work. */
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call orderedPartitions 1,1,1
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call orderedPartitions 1,2,0,1 /*Note: 1,2,,1 will also work. */
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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orderedPartitions: procedure; #=arg(); bot.=; top.=; low=; high=; d=123456789
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t=0 /*T: is the sum of all the arguments.*/
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do i=1 for #; t=t + arg(i) /*sum all the highest numbers in parts.*/
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end /*i*/ /* [↑] may have an omitted argument. */
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hdr= ' partitions for: ' /*define the start of the header text. */
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do j=1 for #; _= arg(j) /* _: is the Jth argument. */
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len.j=max(1, _) /*LEN: length of args. «0 is special»*/
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bot.j=left(d, _); if _==0 then bot.j=0 /*define the bottom number for range.*/
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top.j=right(left(d,t),_); if _==0 then top.j=0 /* " " top " " " */
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@.j=left(d, t); if _==0 then @.j=0 /*define the digits used for VERIFY. */
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hdr=hdr _ /*build (by appending) display header.*/
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low=low || bot.j; high=high || top.j /*the low and high numbers for DO below*/
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end /*j*/
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/* [↓] same as: okD=left('0'd, t+1) */
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/*define the legal digits to be used. */
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okD=left(0 || d, t + 1) /*define the legal digits to be used. */
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say; hdr=center(hdr" ", 60, '═'); say hdr /*display centered title for the output*/
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say /*show a blank line (as a separator). */
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do g=low to high /* [↑] generate the ordered partitions*/
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if verify(g, okD) \==0 then iterate /*filter out unwanted partitions (digs)*/
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p=1 /*P: is the position of a decimal dig.*/
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$= /*$: will be the transformed numbers. */
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do k=1 for #; _=substr(g, p, len.k) /*verify the partitions numbers. */
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if verify(_, @.k) \==0 then iterate g /*is the decimal digit not valid ? */
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!= /* [↓] validate the decimal number. */
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if @.k\==0 then do j=1 for length(_); z=substr(_, j, 1) /*get a dig.*/
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if pos(z, $)\==0 then iterate g /*previous ?*/
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!=!','z /*add comma.*/
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if j==1 then iterate /*is firstt?*/
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if z<=substr(_, j-1, 1) then iterate g /*ordered ?*/
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if pos(z, _, 1 +pos(z, _))\==0 then iterate g /*duplicate?*/
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end /*j*/
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p=p + len.k /*point to the next decimal digit (num)*/
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$=$ ' {'strip(translate(!, ,0), ,",")'}' /*dress number up by suppessing LZ ··· */
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end /*k*/
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say center($, length(hdr) ) /*display numbers in ordered partition.*/
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end /*g*/
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return
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