September 2017 Update
This commit is contained in:
Ingy döt Net
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14570 changed files with 153136 additions and 63871 deletions
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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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@.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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@.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*/
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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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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; ?=; $=v22; do j=1 for _; ?=? value("J"j); end /*j*/; end
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end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end
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bestC=?; bestW=0; bestV=$; totP=words(bestC); say
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call hdr 'best choice'
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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: 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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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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/*REXX program solves a knapsack problem (22 {+1} items with a weight restriction). */
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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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call gen@ /*generate the @ array of choices. */
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call sortD /* sort " " " " " */
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call build /*build some associative arrays from @.*/
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call findBest /*go ye forth and find the best choises*/
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call results /*display the best choices for knapsack*/
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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build: do j=1 for obj; parse var @.j x w v . /*construct a list of knapsack choices.*/
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if w>maxWeight then iterate /*Is weight greater than max? Ignore.*/
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totW=totW + w; totV=totV + v /*add the totals (for output alignment)*/
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maxL=max(maxL, length(x) ) /*determine maximum width for an item. */
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#=#+1; i.#=x; w.#=w; v.#=v /*bump the number of items (choices). */
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end /*j*/ /* [↑] build indexable arrays of items*/
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maxL= maxL + maxL%4 + 4 /*extend width of name for shown table.*/
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maxW= max(maxW, length( commas(totW) ) ) /*find the maximum width for weight. */
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maxV= max(maxV, length( commas(totV) ) ) /* " " " " " value. */
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call hdr 'potential knapsack items' /*display a header for list of choices.*/
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do j=1 for obj; parse var @.j i w v . /*show all the choices in a nice format*/
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if w<=maxWeight then call show i,w,v /*Is weight within limits? Then show. */
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end /*j*/ /* [↑] display the list of choices. */
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$=0
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say; say 'number of allowable items: ' #
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return
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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; comma=','
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do j=e to b by -3; _=insert(comma, _, j); end /*j*/; return _
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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findBest: m=maxWeight /*items are in decreasing weight.*/
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do j1 =0 for #+1; w1 = w.j1 ; z1 = v.j1
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do j2 =j1 +(j1 >0) to #; if w.j2 +w1 >m then iterate j1 ; w2 =w1 +w.j2 ; z2 =z1 +v.j2
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do j3 =j2 +(j2 >0) to #; if w.j3 +w2 >m then iterate j2 ; w3 =w2 +w.j3 ; z3 =z2 +v.j3
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do j4 =j3 +(j3 >0) to #; if w.j4 +w3 >m then iterate j3 ; w4 =w3 +w.j4 ; z4 =z3 +v.j4
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do j5 =j4 +(j4 >0) to #; if w.j5 +w4 >m then iterate j4 ; w5 =w4 +w.j5 ; z5 =z4 +v.j5
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do j6 =j5 +(j5 >0) to #; if w.j6 +w5 >m then iterate j5 ; w6 =w5 +w.j6 ; z6 =z5 +v.j6
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do j7 =j6 +(j6 >0) to #; if w.j7 +w6 >m then iterate j6 ; w7 =w6 +w.j7 ; z7 =z6 +v.j7
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do j8 =j7 +(j7 >0) to #; if w.j8 +w7 >m then iterate j7 ; w8 =w7 +w.j8 ; z8 =z7 +v.j8
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do j9 =j8 +(j8 >0) to #; if w.j9 +w8 >m then iterate j8 ; w9 =w8 +w.j9 ; z9 =z8 +v.j9
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do j10=j9 +(j9 >0) to #; if w.j10+w9 >m then iterate j9 ; w10=w9 +w.j10; z10=z9 +v.j10
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do j11=j10+(j10>0) to #; if w.j11+w10>m then iterate j10; w11=w10+w.j11; z11=z10+v.j11
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do j12=j11+(j11>0) to #; if w.j12+w11>m then iterate j11; w12=w11+w.j12; z12=z11+v.j12
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do j13=j12+(j12>0) to #; if w.j13+w12>m then iterate j12; w13=w12+w.j13; z13=z12+v.j13
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do j14=j13+(j13>0) to #; if w.j14+w13>m then iterate j13; w14=w13+w.j14; z14=z13+v.j14
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do j15=j14+(j14>0) to #; if w.j15+w14>m then iterate j14; w15=w14+w.j15; z15=z14+v.j15
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do j16=j15+(j15>0) to #; if w.j16+w15>m then iterate j15; w16=w15+w.j16; z16=z15+v.j16
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do j17=j16+(j16>0) to #; if w.j17+w16>m then iterate j16; w17=w16+w.j17; z17=z16+v.j17
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do j18=j17+(j17>0) to #; if w.j18+w17>m then iterate j17; w18=w17+w.j18; z18=z17+v.j18
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do j19=j18+(j18>0) to #; if w.j19+w18>m then iterate j18; w19=w18+w.j19; z19=z18+v.j19
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do j20=j19+(j19>0) to #; if w.j20+w19>m then iterate j19; w20=w19+w.j20; z20=z19+v.j20
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do j21=j20+(j20>0) to #; if w.j21+w20>m then iterate j20; w21=w20+w.j21; z21=z20+v.j21
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do j22=j21+(j21>0) to #; if w.j22+w21>m then iterate j21; w22=w21+w.j22; z22=z21+v.j22
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if z22>$ then do; ?=; $=z22; do j=1 for 22; ?=? 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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return
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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gen@: @. = ; @.12= 'camera 32 30'
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@.1 = 'map 9 150' ; @.13= 'T-shirt 24 15'
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@.2 = 'compass 13 35' ; @.14= 'trousers 48 10'
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@.3 = 'water 153 200' ; @.15= 'umbrella 73 40'
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@.4 = 'sandwich 50 160' ; @.16= 'waterproof_trousers 42 70'
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@.5 = 'glucose 15 60' ; @.17= 'waterproof_overclothes 43 75'
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@.6 = 'tin 68 45' ; @.18= 'note-case 22 80'
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@.7 = 'banana 27 60' ; @.19= 'sunglasses 7 20'
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@.8 = 'apple 39 40' ; @.20= 'towel 18 12'
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@.9 = 'cheese 23 30' ; @.21= 'socks 4 50'
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@.10= 'beer 52 10' ; @.22= 'book 30 10'
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@.11= 'suntan_cream 11 70' ; @.23= 'anvil 100000 1'
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maxL = length('potential knapsack items') /*maximum width for the table items. */
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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; totW=0; totV=0 /*initialize some REX variables stuff. */
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return
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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hdr: say; call show center(arg(1),maxL),center('weight',maxW),center("value",maxV)
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hdr2: call show copies('═',maxL),copies('═',maxW),copies('═',maxV); return
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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results: do #; ?=strip( space(?), "L", 0); end /*h*/ /*elide leading zeroes*/
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bestC=?; bestW=0; totP=words(bestC); say; call hdr 'best choice'
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do j=1 for totP; _=word(bestC, j); _w=w._; _v=v._
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do k=j+1 to totP; __=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; @bestTK= 'best total knapsack'
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call show @bestTK 'weight' , bestW /*display a nicely formatted winner wt.*/
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call show @bestTK 'value' ,, $ /* " " " " winner val*/
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call show @bestTK 'items' ,,, totP /* " " " " pieces. */
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return
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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show: parse arg _i,_w,_v,_p; say translate( left(_i,maxL,'─'), , "_") ,
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right(commas(_w),maxW) right(commas(_v),maxV) _p; return
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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sortD: do j=1 while @.j\==''; y=word(@.j,2) /*process each of the knapsack choices.*/
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do k=j+1 while @.k\=='' /*find a possible heavier knapsack item*/
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?=word(@.k,2); if ?>y then do; _=@.k; @.k=@.j; @.j=_; y=?; end /*swap*/
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end /*k*/
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end /*j*/ /* [↑] sort choices by decreasing wt. */
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obj=j-1; return /*decrement J for the DO loop index*/
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