Permutations by swapping: Difference between revisions

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=={{header|REXX}}==
=={{header|REXX}}==
<lang rexx>/*REXX program generates all permutations of N different objects by swapping. */
<lang rexx>/*REXX program generates all permutations of N different objects by swapping. */
parse arg things bunch . /*get optional arguments from the C.L. */
parse arg things bunch . /*obtain optional arguments from the CL*/
things = p(things 4) /*should use the default for THINGS ? */
if things=='' | things=="," then things=4 /*Not specified? Then use the default.*/
bunch = p(bunch things) /* " " " " " BUNCH ? */
if bunch =='' | bunch =="," then bunch =things /* " " " " " " */
call permSets things, bunch /*invoke permutations by swapping sub. */
call permSets things, bunch /*invoke permutations by swapping sub. */
exit /*stick a fork in it, we're all done. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
!: procedure; !=1; do j=2 to arg(1); !=!*j; end /*j*/; return !
!: procedure; !=1; do j=2 to arg(1); !=!*j; end; return !
c: return substr(arg(1), arg(2), 1) /*pick a single character from a string*/
p: return word(arg(1), 1) /*pick 1st word (or number) from a list*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
permSets: procedure; parse arg x,y /*take X things Y at a time. */
permSets: procedure; parse arg x,y /*take X things Y at a time. */
!.=0; pad=left('',x*y) /*Note: X can't be > length(@0abcs). */
!.=0; pad=left('', x*y) /*X can't be > length of below str (62)*/
z=left('123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ', x); q=z
@abc = 'abcdefghijklmnopqrstuvwxyz'; @abcU=@abc; upper @abcU /*build symbols*/
@abcS= @abcU || @abc; @0abcS=123456789 || @abcS /* ··· and more*/
z= /*define Z to be a null value for start*/
do i=1 for x /*build list of (permutation) symbols. */
z=z || c(@0abcS, i) /*append the char to the symbol list. */
⚫
end /*i*/
#=1 /*the number of permutations (so far).*/
#=1 /*the number of permutations (so far).*/
!.z=1; q=z; s=1; times=!(x)% !(x-y) /*calculate (#) TIMES using factorial.*/
!.z=1; s=1; times=!(x) % !(x-y) /*calculate (#) TIMES using factorial.*/
w=max(length(z), length('permute')) /*maximum width of Z and also PERMUTE.*/
w=max(length(z), length('permute') ) /*maximum width of Z and also PERMUTE.*/
say center('permutations for ' x ' things taken ' y " at a time",60,'═')
say center('permutations for ' x ' things taken ' y " at a time",60,'═')
say
say
say pad 'permutation' center("permute", w, '─') "sign"
say pad 'permutation' center("permute", w, '─') "sign"
say pad '───────────' center("───────", w, '─') "────"
say pad '───────────' center("───────", w, '─') "────"
say pad center(#, 11) center(z , w) right(s, 4-1)
say pad center(#, 11) center(z , w) right(s, 4-1)


do $=1 until #==times /*perform permutation until # of times.*/
do $=1 until #==times /*perform permutation until # of times.*/
do k=1 for x-1 /*step thru things for things-1 times.*/
do k=1 for x-1 /*step thru things for things-1 times.*/
do m=k+1 to x; ?= /*this method doesn't use adjacency. */
do m=k+1 to x; ?= /*this method doesn't use adjacency. */
do n=1 for x /*build the new permutation by swapping*/
do n=1 for x /*build the new permutation by swapping*/
if n\==k & n\==m then ? = ? || c(z, n)
if n\==k & n\==m then ? = ? || substr(z, n, 1)
else if n==k then ? = ? || c(z, m)
else if n==k then ? = ? || substr(z, m, 1)
else ? = ? || c(z, k)
else ? = ? || substr(z, k, 1)
end /*n*/
end /*n*/
z=? /*save this permutation for next swap. */
z=? /*save this permutation for next swap. */
if !.? then iterate m /*if defined before, then try next one.*/
if !.? then iterate m /*if defined before, then try next one.*/
_=0 /* [↓] count number of swapped symbols*/
_=0 /* [↓] count number of swapped symbols*/
do d=1 for x while $\==1; _=_+(c(?,d)\==c(prev,d)); end /*d*/
do d=1 for x while $\==1; _= _ + (substr(?,d,1)\==substr(prev,d,1))
if _>2 then do; _=z
end /*d*/
a=$//x+1; q=q+_ /* [← ↓] this swapping tries adjacency*/
if _>2 then do; _=z
b=q//x+1; if b==a then b=a+1; if b>x then b=a-1
a=$//x+1; q=q + _ /* [← ↓] this swapping tries adjacency*/
z=overlay(c(z, b), overlay(c(z, a), _, b), a)
b=q//x+1; if b==a then b=a + 1; if b>x then b=a - 1
iterate $ /*now, try this particular permutation.*/
z=overlay( substr(z,b,1), overlay( substr(z,a,1), _, b), a)
end
iterate $ /*now, try this particular permutation.*/
#=#+1; s=-s; say pad center(#,11) center(?,w) right(s,4-1)
end
!.?=1; prev=?; iterate $ /*now, try another swapped permutation.*/
#=#+1; s= -s; say pad center(#, 11) center(?, w) right(s, 4-1)
end /*m*/
!.?=1; prev=?; iterate $ /*now, try another swapped permutation.*/
end /*k*/
end /*m*/
end /*$*/
end /*k*/
⚫
end /*$*/
return /*we're all finished with permutating. */</lang>
return /*we're all finished with permutating. */</lang>
'''output''' &nbsp; when using the default inputs:
{{out|output|text=&nbsp; when using the default input:}}
<pre>
<pre>
══════permutations for 4 things taken 4 at a time═══════
══════permutations for 4 things taken 4 at a time═══════
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