2016 Update
This commit is contained in:
Tina Müller
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7965 changed files with 139854 additions and 31002 deletions
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@ -1,4 +1,4 @@
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/*REXX program solves a knapsack problem (22 items with a weight restriction).*/
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/*REXX program solves a knapsack problem (23 items with a weight restriction).*/
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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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@ -21,124 +21,92 @@
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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 /*maximum weight for the knapsack*/
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say; say 'maximum weight allowed for a knapsack:' commas(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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do j=1 while @.j\=='' /*process each choice and sort. */
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_=space(@.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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@.23 = 'anvil 1000 1250'
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maxWeight=400 /*the maximum weight for the knapsack. */
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say 'maximum weight allowed for a knapsack:' commas(maxWeight); say
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pot_item= 'potential knapsack items' /*the full name for the header title. */
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maxL=length(pot_item) /*maximum width for the table names. */
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maxW=length('weight') /* " " " " " weights. */
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maxV=length('value') /* " " " " " values. */
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#=0; i.=; w.=0; v.=0; q.=0; Tw=0; Tv=0 /*initialize some stuff.*/
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/*══════════════════════════════════════sort the choices by decreasing weight.*/
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do j=1 while @.j\=='' /*process each of the knapsack choices.*/
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_=space(@.j); _wt=word(_, 2) /*choose the first item (arbitrary). */
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do k=j+1 while @.k\=='' /*find a possible heavier knapsack 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*/ /*adjust for the DO loop index.*/
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obj=j-1
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/*════════════════════════════════build list of choices.════════════════*/
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end /*j*/
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obj=j-1 /*decrement J for the DO loop index*/
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/*══════════════════════════════════════build list of choices.════════════════*/
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do j=1 for obj /*construct a list of knapsack choices.*/
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parse var @.j item w v . /*parse the original choice for table. */
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if w>maxWeight then iterate /*Is weight greater than max? Ignore.*/
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Tw=Tw+w; Tv=Tv+v /*add the totals (for output alignment)*/
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maxL=max(maxL, length(item)) /*determine the maximum width for item.*/
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#=#+1; i.#=item; w.#=w; v.#=v /*bump the number of items (choices). */
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end /*j*/
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do j=1 for obj /*build a list of choices. */
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parse var @.j 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 # items.*/
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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 # items.*/
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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(commas(Tw))) /*find maximum width for weight. */
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maxV=max(maxV,length(commas(Tv))) /* " " " " value. */
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maxQ=max(maxQ,length(commas(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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maxW=max(maxW,length(commas(Tw))) /*find the maximum width for weight. */
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maxV=max(maxV,length(commas(Tv))) /* " " " " " value. */
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maxL=maxL + maxL%4 + 4 /*extend the width of name for table. */
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/*══════════════════════════════════════show the list of choices.═════════════*/
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call hdr pot_item; do j=1 for obj /*show all choices in a nice format. */
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parse var @.j item weight value .
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call show item, weight, value
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end /*j*/
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say
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say 'number of allowable items: ' # /* [↓] examine all possible choices. */
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$=0; m=maxWeight
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do j1 =0 for #+1; w1 = w.j1; v1 = v.j1
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do j2 =j1 +(j1 \==0) to #; if w.j2 +w1 >m then iterate j1 ; w2 =w1 +w.j2; v2 =v1 +v.j2
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do j3 =j2 +(j2 \==0) to #; if w.j3 +w2 >m then iterate j2 ; w3 =w2 +w.j3; v3 =v2 +v.j3
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do j4 =j3 +(j3 \==0) to #; if w.j4 +w3 >m then iterate j3 ; w4 =w3 +w.j4; v4 =v3 +v.j4
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do j5 =j4 +(j4 \==0) to #; if w.j5 +w4 >m then iterate j4 ; w5 =w4 +w.j5; v5 =v4 +v.j5
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do j6 =j5 +(j5 \==0) to #; if w.j6 +w5 >m then iterate j5 ; w6 =w5 +w.j6; v6 =v5 +v.j6
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do j7 =j6 +(j6 \==0) to #; if w.j7 +w6 >m then iterate j6 ; w7 =w6 +w.j7; v7 =v6 +v.j7
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do j8 =j7 +(j7 \==0) to #; if w.j8 +w7 >m then iterate j7 ; w8 =w7 +w.j8; v8 =v7 +v.j8
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do j9 =j8 +(j8 \==0) to #; if w.j9 +w8 >m then iterate j8 ; w9 =w8 +w.j9; v9 =v8 +v.j9
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do j10=j9 +(j9 \==0) to #; if w.j10+w9 >m then iterate j9 ; w10=w9 +w.j10;v10=v9 +v.j10
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do j11=j10+(j10\==0) to #; if w.j11+w10>m then iterate j10; w11=w10+w.j11;v11=v10+v.j11
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do j12=j11+(j11\==0) to #; if w.j12+w11>m then iterate j11; w12=w11+w.j12;v12=v11+v.j12
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do j13=j12+(j12\==0) to #; if w.j13+w12>m then iterate j12; w13=w12+w.j13;v13=v12+v.j13
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do j14=j13+(j13\==0) to #; if w.j14+w13>m then iterate j13; w14=w13+w.j14;v14=v13+v.j14
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do j15=j14+(j14\==0) to #; if w.j15+w14>m then iterate j14; w15=w14+w.j15;v15=v14+v.j15
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do j16=j15+(j15\==0) to #; if w.j16+w15>m then iterate j15; w16=w15+w.j16;v16=v15+v.j16
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do j17=j16+(j16\==0) to #; if w.j17+w16>m then iterate j16; w17=w16+w.j17;v17=v16+v.j17
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do j18=j17+(j17\==0) to #; if w.j18+w17>m then iterate j17; w18=w17+w.j18;v18=v17+v.j18
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do j19=j18+(j18\==0) to #; if w.j19+w18>m then iterate j18; w19=w18+w.j19;v19=v18+v.j19
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do j20=j19+(j19\==0) to #; if w.j20+w19>m then iterate j19; w20=w19+w.j20;v20=v19+v.j20
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do j21=j20+(j20\==0) to #; if w.j21+w20>m then iterate j20; w21=w20+w.j21;v21=v20+v.j21
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do j22=j21+(j21\==0) to #; if w.j22+w21>m then iterate j21; w22=w21+w.j22;v22=v21+v.j22
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if v22>$ then do; _=22; ?=; $=v22; do j=1 for _; ?=? value("J"j); end /*j*/; end
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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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say; say 'number of items:' items; say
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/*═════════════════════════════════════examine all 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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bestC=?; bestW=0; bestV=$; totP=words(bestC); say
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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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do j=1 for totP; _=word(bestC, j); _w=w._; _v=v._
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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
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end /*k*/
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call show i._,w._,v._; bestW=bestw+w._
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end /*j*/
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call hdr2; say; @btk= 'best total knapsack'
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call show @btk 'weight' , bestW /*display a nicely formatted winnerW. */
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call show @btk 'value' ,, bestV /* " " " " winnerV. */
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call show @btk 'items' ,,, totP /* " " " " pieces. */
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exit /*stick a fork in it, we're all done. */
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/*────────────────────────────────────────────────────────────────────────────*/
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commas: procedure; parse arg _; n=_'.9'; #=123456789; b=verify(n,#,"M")
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e=verify(n,#'0',,verify(n,#"0.",'M'))-4
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do j=e to b by -3; _=insert(',',_,j); end /*j*/; return _
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/*────────────────────────────────────────────────────────────────────────────────────────*/
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hdr: parse arg _item_,_; if highq\==1 then _=center('pieces',maxq)
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call show center(_item_,maxL),center('weight',maxW),center('value',maxV),center(_,maxQ)
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call hdr2; return
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commas: procedure; parse arg _; n=_'.9'; #=123456789; b=verify(n, #, "M")
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e=verify(n, #'0', , verify(n, #"0.", 'M')) - 4
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do j=e to b by -3; _=insert(',', _, j); end /*j*/; return _
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/*────────────────────────────────────────────────────────────────────────────*/
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hdr2: _=maxQ; if highq==1 then _=0
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call show copies('═',maxL),copies('═',maxW),copies('═',maxV),copies('═',_)
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return
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/*─────────────────────────────────────────────────────────────────────────────────────*/
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j?: parse arg _,?; $=value('V'_); do j=1 for _; ?=? value('J'j); end; return
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hdr: call show center(arg(1),maxL),center('weight',maxW),center("value",maxV)
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call hdr2; return
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/*────────────────────────────────────────────────────────────────────────────*/
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show: parse arg _item,_weight,_value,_quant
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say translate(left(_item,maxL,'─'),,'_') right(commas(_weight),maxW),
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right(commas(_value ),maxV),
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right(commas(_quant ),maxQ)
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return
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/*───────────────────────────────────────────────────────────────────────────────────────────────────────────*/
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sim22:
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do j1 =0 for h+1; w1 = w.j1; v1 = v.j1; if v1>$ then call j? 1
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do j2 =j1 +(j1 \==0) to h;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;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;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;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;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;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;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;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;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;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;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;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;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;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;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;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;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;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;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;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;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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hdr2: call show copies('═',maxL),copies('═',maxW),copies('═',maxV); return
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/*────────────────────────────────────────────────────────────────────────────*/
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show: parse arg _it,_wt,_val,_p; say translate( left(_it, maxL, '─'),,"_"),
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right(commas(_wt),maxW) right(commas(_val),maxV) ' ' _p; return
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