A-M baby
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Ingy döt Net
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Task/Knapsack-problem-0-1/REXX/knapsack-problem-0-1.rexx
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Task/Knapsack-problem-0-1/REXX/knapsack-problem-0-1.rexx
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/*REXX pgm solves a knapsack problem (22 items with weight restriction).*/
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@.=
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@.1 = 'map 9 150'
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@.2 = 'compass 13 35'
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@.3 = 'water 153 200'
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@.4 = 'sandwich 50 160'
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@.5 = 'glucose 15 60'
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@.6 = 'tin 68 45'
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@.7 = 'banana 27 60'
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@.8 = 'apple 39 40'
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@.9 = 'cheese 23 30'
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@.10 = 'beer 52 10'
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@.11 = 'suntan_cream 11 70'
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@.12 = 'camera 32 30'
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@.13 = 'T-shirt 24 15'
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@.14 = 'trousers 48 10'
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@.15 = 'umbrella 73 40'
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@.16 = 'waterproof_trousers 42 70'
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@.17 = 'waterproof_overclothes 43 75'
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@.18 = 'note-case 22 80'
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@.19 = 'sunglasses 7 20'
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@.20 = 'towel 18 12'
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@.21 = 'socks 4 50'
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@.22 = 'book 30 10'
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maxWeight=400 /*the maximum weight for knapsack*/
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say; say 'maximum weight allowed for a knapsack:' comma(maxWeight); say
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maxL=length('item') /*maximum width for table names. */
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maxL=length('knapsack items') /*maximum width for table names. */
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maxW=length('weight') /* " " " " weights*/
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maxV=length('value') /* " " " " values.*/
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maxQ=length('pieces') /* " " " " quant. */
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highQ=0 /*max quantity specified (if any)*/
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items=0; i.=; w.=0; v.=0; q.=0; Tw=0; Tv=0; Tq=0 /*initialize stuff.*/
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/*────────────────────────────────sort the choices by decreasing weight.*/
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/*this minimizes # combinations. */
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do j=1 while @.j\=='' /*process each choice and sort. */
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_=@.j; _wt=word(_,2) /*choose first item (arbitrary). */
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_wt=word(_,2)
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do k=j+1 while @.k\=='' /*find a possible heavier item. */
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?wt=word(@.k,2)
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if ?wt>_wt then do; _=@.k; @.k=@.j; @.j=_; _wt=?wt; end
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end /*k*/
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end /*j*/
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obj=j-1 /*adjust for the DO loop index. */
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/*────────────────────────────────build list of choices.────────────────*/
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do j=1 for obj /*build a list of choices. */
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_=space(@.j) /*remove superfluous blanks. */
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parse var _ item w v q . /*parse original choice for table*/
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if w>maxWeight then iterate /*if the weight > maximum, ignore*/
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Tw=Tw+w; Tv=Tv+v; Tq=Tq+1 /*add totals up (for alignment). */
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maxL=max(maxL,length(item)) /*find maximum width for item. */
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if q=='' then q=1
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highQ=max(highQ,q)
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items=items+1 /*bump the item counter. */
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i.items=item; w.items=w; v.items=v; q.items=q
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do k=2 to q; items=items+1 /*bump the item counter. */
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i.items=item; w.items=w; v.items=v; q.items=q
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Tw=Tw+w; Tv=Tv+v; Tq=Tq+1
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end /*k*/
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end /*j*/
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maxW=max(maxW,length(comma(Tw))) /*find maximum width for weight. */
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maxV=max(maxV,length(comma(Tv))) /* " " " " value. */
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maxQ=max(maxQ,length(comma(Tq))) /* " " " " quantity*/
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maxL=maxL+maxL%4+4 /*extend width of name for table.*/
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/*────────────────────────────────show the list of choices.─────────────*/
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call hdr 'item'; do j=1 for obj /*show all choices, nice format. */
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parse var @.j item weight value q .
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if highq==1 then q=
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else if q=='' then q=1
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call show item,weight,value,q
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end /*j*/
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say; say 'number of items:' items; say
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/*─────────────────────────────────────examine the possible choices. */
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h=items; ho=h+1; m=maxWeight; $=0; call sim22
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/*─────────────────────────────────────show the best choice (weight,val)*/
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do h-1; ?=strip(strip(?),"L",0); end
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bestC=?; bestW=0; bestV=$; highQ=0; totP=words(bestC)
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call hdr 'best choice'
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do j=1 to totP /*J is modified within DO loop. */
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_=word(bestC,j); _w=w._; _v=v._; q=1
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if _==0 then iterate
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do k=j+1 to totP
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__=word(bestC,k); if i._\==i.__ then leave
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j=j+1; w._=w._+_w; v._=v._+_v; q=q+1
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end /*k*/
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call show i._,w._,v._,q; bestW=bestw+w._
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end /*j*/
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call hdr2; say
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call show 'best weight' ,bestW /*show a nicely formatted winnerW*/
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call show 'best value' ,,bestV /*show a nicely formatted winnerV*/
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call show 'knapsack items',,,totP /*show a nicely formatted pieces.*/
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exit /*stick a fork in it, we're done.*/
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/*────────────────────────────────COMMA subroutine──────────────────────*/
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comma: procedure; parse arg _,c,p,t;arg ,cu;c=word(c ",",1)
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if cu=='BLANK' then c=' ';o=word(p 3,1);p=abs(o);t=word(t 999999999,1)
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if \datatype(p,'W')|\datatype(t,'W')|p==0|arg()>4 then return _;n=_'.9'
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#=123456789;k=0;if o<0 then do;b=verify(_,' ');if b==0 then return _
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e=length(_)-verify(reverse(_),' ')+1;end;else do;b=verify(n,#,"M")
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e=verify(n,#'0',,verify(n,#"0.",'M'))-p-1;end
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do j=e to b by -p while k<t;_=insert(c,_,j);k=k+1;end;return _
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/*────────────────────────────────HDR subroutine────────────────────────*/
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hdr: parse arg _item_,_; if highq\==1 then _=center('pieces',maxq)
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call show center( _item_ ,maxL),,
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center('weight',maxW),,
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center('value' ,maxV),,
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center(_ ,maxQ)
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call hdr2
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return
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/*────────────────────────────────HDR2 subroutine───────────────────────*/
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hdr2: _=maxQ; if highq==1 then _=0; call show copies('=' ,maxL),,
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copies('=' ,maxW),,
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copies('=' ,maxV),,
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copies('=' ,_ )
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return
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/*────────────────────────────────J? subroutine─────────────────────────*/
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j?: parse arg _,?; $=value('V'_); do j=1 for _; ?=? value('J'j); end; return
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/*────────────────────────────────SHOW subroutine───────────────────────*/
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show: parse arg _item,_weight,_value,_quant
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say translate(left(_item,maxL,'─'),,'_'),
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right(comma(_weight),maxW),
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right(comma(_value ),maxV),
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right(comma(_quant ),maxQ)
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return
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/*────────────────────────────────SIM22 subroutine──────────────────────*/
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sim22: do j1=0 for h+1; w1=w.j1;v1=v.j1;if v1>$ then call j? 1
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do j2=j1+(j1\==0) to h
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if w.j2+w1>m then iterate j1;w2=w1+w.j2;v2=v1+v.j2;if v2>$ then call j? 2
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do j3=j2+(j2\==0) to h
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if w.j3+w2>m then iterate j2;w3=w2+w.j3;v3=v2+v.j3;if v3>$ then call j? 3
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do j4=j3+(j3\==0) to h
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if w.j4+w3>m then iterate j3;w4=w3+w.j4;v4=v3+v.j4;if v4>$ then call j? 4
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do j5=j4+(j4\==0) to h
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if w.j5+w4>m then iterate j4;w5=w4+w.j5;v5=v4+v.j5;if v5>$ then call j? 5
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do j6=j5+(j5\==0) to h
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if w.j6+w5>m then iterate j5;w6=w5+w.j6;v6=v5+v.j6;if v6>$ then call j? 6
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do j7=j6+(j6\==0) to h
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if w.j7+w6>m then iterate j6;w7=w6+w.j7;v7=v6+v.j7;if v7>$ then call j? 7
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do j8=j7+(j7\==0) to h
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if w.j8+w7>m then iterate j7;w8=w7+w.j8;v8=v7+v.j8;if v8>$ then call j? 8
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do j9=j8+(j8\==0) to h
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if w.j9+w8>m then iterate j8;w9=w8+w.j9;v9=v8+v.j9;if v9>$ then call j? 9
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do j10=j9+(j9\==0) to h
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if w.j10+w9>m then iterate j9;w10=w9+w.j10;v10=v9+v.j10;if v10>$ then call j? 10
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do j11=j10+(j10\==0) to h
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if w.j11+w10>m then iterate j10;w11=w10+w.j11;v11=v10+v.j11;if v11>$ then call j? 11
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do j12=j11+(j11\==0) to h
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if w.j12+w11>m then iterate j11;w12=w11+w.j12;v12=v11+v.j12;if v12>$ then call j? 12
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do j13=j12+(j12\==0) to h
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if w.j13+w12>m then iterate j12;w13=w12+w.j13;v13=v12+v.j13;if v13>$ then call j? 13
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do j14=j13+(j13\==0) to h
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if w.j14+w13>m then iterate j13;w14=w13+w.j14;v14=v13+v.j14;if v14>$ then call j? 14
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do j15=j14+(j14\==0) to h
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if w.j15+w14>m then iterate j14;w15=w14+w.j15;v15=v14+v.j15;if v15>$ then call j? 15
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do j16=j15+(j15\==0) to h
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if w.j16+w15>m then iterate j15;w16=w15+w.j16;v16=v15+v.j16;if v16>$ then call j? 16
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do j17=j16+(j16\==0) to h
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if w.j17+w16>m then iterate j16;w17=w16+w.j17;v17=v16+v.j17;if v17>$ then call j? 17
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do j18=j17+(j17\==0) to h
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if w.j18+w17>m then iterate j17;w18=w17+w.j18;v18=v17+v.j18;if v18>$ then call j? 18
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do j19=j18+(j18\==0) to h
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if w.j19+w18>m then iterate j18;w19=w18+w.j19;v19=v18+v.j19;if v19>$ then call j? 19
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do j20=j19+(j19\==0) to h
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if w.j20+w19>m then iterate j19;w20=w19+w.j20;v20=v19+v.j20;if v20>$ then call j? 20
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do j21=j20+(j20\==0) to h
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if w.j21+w20>m then iterate j20;w21=w20+w.j21;v21=v20+v.j21;if v21>$ then call j? 21
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do j22=j21+(j21\==0) to h
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if w.j22+w21>m then iterate j21;w22=w21+w.j22;v22=v21+v.j22;if v22>$ then call j? 22
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end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end
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return
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