Knapsack problem/Continuous: Difference between revisions

<lang rexx>/*REXX programpgm solves the (continuous) burglar's knapsack problem.; items with weight and value*/

@.= /*═══════ name weight value ══════*/

@.1 = 'flitch 4 30 '

@.2 = 'beef 3.8 36 '

@.3 = 'pork 5.4 43 '

@.4 = 'greaves 2.4 45 '

@.5 = 'brawn 2.5 56 '

@.6 = 'welt 3.7 67 '

@.7 = 'ham 3.6 90 '

@.8 = 'salami 3 95 '

@.9 = 'sausage 5.9 98 '

parse arg maxW d . /*get possible arguments from the C.L. */

if maxW=='' | maxW=='",'" then maxW=15 /*the burglar's knapsack maximum weight*/

if d=='' | d=='",'" then d= 3 /*number of decimal digits in FORMAT. */

wL=d+length('weight'); nL=d+length('"total weight'"); vL=d+length('value')

do #=1 while @.#\==''; parse var @.# n.# w.# v.# .

end /*#*/ /* [↑] assign item to separate lists. */

#=#-1 /*#: is the number of items in @ list.*/

call show 'unsorted item list' /*display the header and the @ list.*/

call sortD /*invoke sort (which sorts descending).*/

do j=1 for # while totW<maxW; f=1 /*process the items. */

if totW+w.j>=maxW then f=(maxW-totW)/w.j /*calculate fractfraction. */

totW=totW+w.j*f; totV=totV+v.j*f /*add it ───► totals. */

call syf left(word('{all}',1+(f\==1)),5) n.j, w.j*f, v.j*f

end /*j*/ /* [↑] showdisplay item. */

call sep; say; t='t' /* [↓] $ suppresses trailing zeroes.*/

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

sortD: do s=2 to #; a=n.s; !=w.s; u=v.s /* [↓] this is a descending sort. */

do k=s-1 by -1 to 1 while v.k/w.k<u/!; ?=k+1; n.?=n.k; w.?=w.k;v.?=v.k;end

?=k+1; n.?=a; w.?=!; v.?=u

end /*s*/

return /* ↑↑↑ /* ↑↑↑ sort algorithm is OK for small arrays.*/

hdr: say; say; say center(arg(1),50,'─'); say; call title; call sep; return

sep: call sy copies('═', nL), copies("═", wL), copies('═', vL); return

show: call hdr arg(1); do j=1 for #; call syf n.j, w.j, v.j; end; return

sy: say left('',9) left(arg(1),nL) right(arg(2),wL) right(arg(3),vL); return

syf: call sy arg(1), $(format(arg(2), , d)), $(format(arg(3), , d)); return

title: call sy center('item',nL), center("weight", wL), center('value', vL); return

$: parse arg x; if pos(.,x)>1 then x=left(strip(strip(x,'T',0),,.),length(x)); return x</lang>