A-M baby
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65
Task/Knapsack-problem-Unbounded/0DESCRIPTION
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65
Task/Knapsack-problem-Unbounded/0DESCRIPTION
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See also: [[Knapsack problem/Bounded]], [[Knapsack problem/0-1]]
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A traveller gets diverted and has to make an unscheduled stop in what turns out to be Shangri La. Opting to leave, he is allowed to take as much as he likes of the following items, so long as it will fit in his knapsack, and he can carry it.
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He knows that he can carry no more than 25 'weights' in total; and that the capacity of his knapsack is 0.25 'cubic lengths'.
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Looking just above the bar codes on the items he finds their weights and volumes. He digs out his recent copy of a financial paper and gets the value of each item.
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<table
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style="text-align: left; width: 80%;" border="4"
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cellpadding="2" cellspacing="2"><tr><td
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style="font-weight: bold;" align="left" nowrap="nowrap"
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valign="middle">Item</td><td
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style="font-weight: bold;" align="left" nowrap="nowrap"
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valign="middle">Explanation</td><td
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style="font-weight: bold;" align="left" nowrap="nowrap"
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valign="middle">Value (each)</td><td
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style="font-weight: bold;" align="left" nowrap="nowrap"
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valign="middle">weight</td><td
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style="font-weight: bold;" align="left" nowrap="nowrap"
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valign="middle">Volume (each)</td></tr><tr><td
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align="left" nowrap="nowrap" valign="middle">panacea
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(vials of)</td><td align="left" nowrap="nowrap"
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valign="middle">Incredible healing properties</td><td
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align="left" nowrap="nowrap" valign="middle">3000</td><td
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align="left" nowrap="nowrap" valign="middle">0.3</td><td
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align="left" nowrap="nowrap" valign="middle">0.025</td></tr><tr><td
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align="left" nowrap="nowrap" valign="middle">ichor
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(ampules of)</td><td align="left" nowrap="nowrap"
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valign="middle">Vampires blood</td><td align="left"
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nowrap="nowrap" valign="middle">1800</td><td
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align="left" nowrap="nowrap" valign="middle">0.2</td><td
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align="left" nowrap="nowrap" valign="middle">0.015</td></tr><tr><td
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align="left" nowrap="nowrap" valign="middle">gold
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(bars)</td><td align="left" nowrap="nowrap"
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valign="middle">Shiney shiney</td><td align="left"
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nowrap="nowrap" valign="middle">2500</td><td
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align="left" nowrap="nowrap" valign="middle">2.0</td><td
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align="left" nowrap="nowrap" valign="middle">0.002</td></tr><tr><td
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style="background-color: rgb(255, 204, 255);" align="left"
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nowrap="nowrap" valign="middle">Knapsack</td><td
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style="background-color: rgb(255, 204, 255);" align="left"
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nowrap="nowrap" valign="middle">For the carrying of</td><td
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style="background-color: rgb(255, 204, 255);" align="left"
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nowrap="nowrap" valign="middle">-</td><td
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style="background-color: rgb(255, 204, 255);" align="left"
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nowrap="nowrap" valign="middle"><=25</td><td
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style="background-color: rgb(255, 204, 255);" align="left"
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nowrap="nowrap" valign="middle"><=0.25 </td></tr></table>
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He can only take whole units of any item, but there is much more of any item than he could ever carry
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'''How many of each item does he take to maximise the value of items he is carrying away with him?'''
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Note:
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# There are four solutions that maximise the value taken. Only one ''need'' be given.
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<!-- All solutions
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# ((value, -weight, -volume), (#panacea, #ichor, #gold)
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[((54500, -25.0, -0.24699999999999997), (0, 15, 11)),
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((54500, -24.899999999999999, -0.247), (3, 10, 11)),
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((54500, -24.800000000000001, -0.24700000000000003), (6, 5, 11)),
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((54500, -24.699999999999999, -0.247), (9, 0, 11))]
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# (9, 0, 11) also minimizes weight and volume within the limits of calculation
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-->
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2
Task/Knapsack-problem-Unbounded/1META.yaml
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Task/Knapsack-problem-Unbounded/1META.yaml
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---
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note: Classic CS problems and programs
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MODE BOUNTY = STRUCT(STRING name, INT value, weight, volume);
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[]BOUNTY items = (
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("panacea", 3000, 3, 25),
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("ichor", 1800, 2, 15),
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("gold", 2500, 20, 2)
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);
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BOUNTY sack := ("sack", 0, 250, 250);
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OP * = ([]INT a,b)INT: ( # dot product operator #
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INT sum := 0;
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FOR i TO UPB a DO sum +:= a[i]*b[i] OD;
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sum
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);
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OP INIT = (REF[]INT vector)VOID:
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FOR index FROM LWB vector TO UPB vector DO
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vector[index]:=0
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OD;
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OP INIT = (REF[,]INT matrix)VOID:
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FOR row index FROM LWB matrix TO UPB matrix DO
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INIT matrix[row index,]
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OD;
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PROC total value = ([]INT items count, []BOUNTY items, BOUNTY sack) STRUCT(INT value, weight, volume):(
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###
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Given the count of each item in the sack return -1 if they can"t be carried or their total value.
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(also return the negative of the weight and the volume so taking the max of a series of return
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values will minimise the weight if values tie, and minimise the volume if values and weights tie).
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###
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INT weight = items count * weight OF items;
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INT volume = items count * volume OF items;
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IF weight > weight OF sack OR volume > volume OF sack THEN
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(-1, 0, 0)
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ELSE
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( items count * value OF items, -weight, -volume)
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FI
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);
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PRIO WRAP = 5; # wrap negative array indices as per python's indexing regime #
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OP WRAP = (INT index, upb)INT:
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IF index>=0 THEN index ELSE upb + index + 1 FI;
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PROC knapsack dp = ([]BOUNTY items, BOUNTY sack)[]INT:(
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###
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Solves the Knapsack problem, with two sets of weights,
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using a dynamic programming approach
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###
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# (weight+1) x (volume+1) table #
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# table[w,v] is the maximum value that can be achieved #
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# with a sack of weight w and volume v. #
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# They all start out as 0 (empty sack) #
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[0:weight OF sack, 0:volume OF sack]INT table; INIT table;
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FOR w TO 1 UPB table DO
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FOR v TO 2 UPB table DO
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### Consider the optimal solution, and consider the "last item" added
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to the sack. Removing this item must produce an optimal solution
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to the subproblem with the sack"s weight and volume reduced by that
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of the item. So we search through all possible "last items": ###
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FOR item index TO UPB items DO
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BOUNTY item := items[item index];
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# Only consider items that would fit: #
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IF w >= weight OF item AND v >= volume OF item THEN
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# Optimal solution to subproblem + value of item: #
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INT candidate := table[w-weight OF item,v-volume OF item] + value OF item;
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IF candidate > table[w,v] THEN
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table[w,v] := candidate
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FI
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FI
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OD
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OD
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OD;
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[UPB items]INT result; INIT result;
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INT w := weight OF sack, v := volume OF sack;
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WHILE table[w,v] /= 0 DO
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# Find the last item that was added: #
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INT needle = table[w,v];
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INT item index;
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FOR i TO UPB items WHILE
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item index := i;
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BOUNTY item = items[item index];
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INT candidate = table[w-weight OF item WRAP UPB table, v-volume OF item WRAP 2 UPB table] + value OF item;
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# WHILE # candidate NE needle DO
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SKIP
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OD;
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# Record it in the result, and remove it: #
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result[item index] +:= 1;
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w -:= weight OF items[item index];
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v -:= volume OF items[item index]
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OD;
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result
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);
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[]INT max items = knapsack dp(items, sack);
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STRUCT (INT value, weight, volume) max := total value(max items, items, sack);
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max := (value OF max, -weight OF max, -volume OF max);
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FORMAT d = $zz-d$;
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printf(($"The maximum value achievable (by dynamic programming) is "gl$, value OF max));
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printf(($" The number of ("n(UPB items-1)(g", ")g") items to achieve this is: ("n(UPB items-1)(f(d)",")f(d)") respectively"l$,
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name OF items, max items));
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printf(($" The weight to carry is "f(d)", and the volume used is "f(d)l$,
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weight OF max, volume OF max))
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@ -0,0 +1,65 @@
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with Ada.Text_IO;
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procedure Knapsack_Unbounded is
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type Bounty is record
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Value : Natural;
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Weight : Float;
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Volume : Float;
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end record;
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function Min (A, B : Float) return Float is
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begin
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if A < B then
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return A;
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else
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return B;
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end if;
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end Min;
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Panacea : Bounty := (3000, 0.3, 0.025);
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Ichor : Bounty := (1800, 0.2, 0.015);
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Gold : Bounty := (2500, 2.0, 0.002);
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Limits : Bounty := ( 0, 25.0, 0.250);
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Best : Bounty := ( 0, 0.0, 0.000);
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Current : Bounty := ( 0, 0.0, 0.000);
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Best_Amounts : array (1 .. 3) of Natural := (0, 0, 0);
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Max_Panacea : Natural := Natural (Float'Floor (Min
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(Limits.Weight / Panacea.Weight,
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Limits.Volume / Panacea.Volume)));
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Max_Ichor : Natural := Natural (Float'Floor (Min
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(Limits.Weight / Ichor.Weight,
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Limits.Volume / Ichor.Volume)));
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Max_Gold : Natural := Natural (Float'Floor (Min
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(Limits.Weight / Gold.Weight,
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Limits.Volume / Gold.Volume)));
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begin
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for Panacea_Count in 0 .. Max_Panacea loop
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for Ichor_Count in 0 .. Max_Ichor loop
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for Gold_Count in 0 .. Max_Gold loop
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Current.Value := Panacea_Count * Panacea.Value +
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Ichor_Count * Ichor.Value +
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Gold_Count * Gold.Value;
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Current.Weight := Float (Panacea_Count) * Panacea.Weight +
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Float (Ichor_Count) * Ichor.Weight +
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Float (Gold_Count) * Gold.Weight;
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Current.Volume := Float (Panacea_Count) * Panacea.Volume +
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Float (Ichor_Count) * Ichor.Volume +
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Float (Gold_Count) * Gold.Volume;
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if Current.Value > Best.Value and
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Current.Weight <= Limits.Weight and
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Current.Volume <= Limits.Volume then
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Best := Current;
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Best_Amounts := (Panacea_Count, Ichor_Count, Gold_Count);
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end if;
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end loop;
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end loop;
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end loop;
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Ada.Text_IO.Put_Line ("Maximum value:" & Natural'Image (Best.Value));
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Ada.Text_IO.Put_Line ("Panacea:" & Natural'Image (Best_Amounts (1)));
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Ada.Text_IO.Put_Line ("Ichor: " & Natural'Image (Best_Amounts (2)));
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Ada.Text_IO.Put_Line ("Gold: " & Natural'Image (Best_Amounts (3)));
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end Knapsack_Unbounded;
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@ -0,0 +1,25 @@
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Item = Panacea,Ichor,Gold
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Value = 3000,1800,2500
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Weight= 3,2,20 ; *10
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Volume= 25,15,2 ; *1000
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StringSplit I, Item, `, ; Put input in arrays
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StringSplit W, Weight,`,
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StringSplit $, Value, `,
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StringSplit V, Volume,`,
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SetFormat Float, 0.3
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W := 250, V := 250, sW:=.1, sV:=.001 ; limits for the total, scale factors
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p := -1, Wp := -W1, Vp := -V1 ; initial values
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While (Wp+=W1) <= W && (Vp+=V1) <= V {
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p++, Wi := Wp-W2, Vi := Vp-V2, i := -1
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While (Wi+=W2) <= W && (Vi+=V2) <= V {
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i++, Wg := Wi-W3, Vg := Vi-V3, g := -1
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While (Wg+=W3) <= W && (Vg+=V3) <= V
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If ($ <= Val := p*$1 + i*$2 + ++g*$3)
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t := ($=Val ? t "`n " : " ")
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. p "`t " i "`t " g "`t " Wg*sW "`t " Vg*sV
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, $ := Val
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}
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}
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MsgBox Value = %$%`n`nPanacea`tIchor`tGold`tWeight`tVolume`n%t%
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@ -0,0 +1,70 @@
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(knapsack=
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( things
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= (panacea.3000.3/10.25/1000)
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(ichor.1800.2/10.15/1000)
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(gold.2500.2.2/1000)
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)
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& 0:?maxvalue
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& :?sack
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& ( add
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= cumwght
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cumvol
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cumvalue
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cumsack
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name
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wght
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val
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vol
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tings
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n
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ncumwght
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ncumvalue
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ncumvol
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. !arg
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: ( ?cumwght
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. ?cumvol
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. ?cumvalue
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. ?cumsack
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. (?name.?val.?wght.?vol) ?tings
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)
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& -1:?n
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& whl
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' ( 1+!n:?n
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& !cumwght+!n*!wght:~>25:?ncumwght
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& !cumvol+!n*!vol:~>250/1000:?ncumvol
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& !cumvalue+!n*!val:?ncumvalue
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& ( !tings:
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& ( !ncumvalue:>!maxvalue:?maxvalue
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& !cumsack
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( !n:0&
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| ( !cumsack:&Take
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| Finally
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)
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" take "
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!n
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" items of "
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!name
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".\n"
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)
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: ?sack
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)
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| add
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$ ( !ncumwght
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. !ncumvol
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. !ncumvalue
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. !cumsack
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( !n:0&
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| "Take " !n " items of " !name ".\n"
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)
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. !tings
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)
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)
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)
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)
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& add$(0.0.0..!things)
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& out$(str$(!sack "The value in the knapsack is " !maxvalue "."))
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&
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);
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!knapsack;
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@ -0,0 +1,52 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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struct {
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double val, wgt, vol;
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const char * name;
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} items[] = { // value in hundreds, volume in thousandths
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{30, .3, 25, "panacea"},
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{18, .2, 15, "ichor"},
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{25, 2., 2, "gold"},
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{0,0,0,0}
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};
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/* silly setup for silly task */
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int best_cnt[16] = {0}, cnt[16] = {0};
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double best_v = 0;
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void grab_em(int idx, double cap_v, double cap_w, double v)
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{
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double val;
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int t = cap_w / items[idx].wgt;
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cnt[idx] = cap_v / items[idx].vol;
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if (cnt[idx] > t) cnt[idx] = t;
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while (cnt[idx] >= 0) {
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val = v + cnt[idx] * items[idx].val;
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if (!items[idx + 1].name) {
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if (val > best_v) {
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best_v = val;
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memcpy(best_cnt, cnt, sizeof(int) * (1 + idx));
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}
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return;
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}
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grab_em(idx + 1, cap_v - cnt[idx] * items[idx].vol,
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cap_w - cnt[idx] * items[idx].wgt, val);
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cnt[idx]--;
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}
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}
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int main(void)
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{
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int i;
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grab_em(0, 250, 25, 0);
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printf("value: %g hundreds\n", best_v);
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for (i = 0; items[i].name; i++)
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printf("%d %s\n", best_cnt[i], items[i].name);
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return 0;
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}
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@ -0,0 +1,9 @@
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(defstruct item :value :weight :volume)
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(defn total [key items quantities]
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(reduce + (map * quantities (map key items))))
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(defn max-count [item max-weight max-volume]
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(let [mcw (/ max-weight (:weight item))
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mcv (/ max-volume (:volume item))]
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(min mcw mcv)))
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(defn knapsacks []
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(let [pan (struct item 3000 0.3 0.025)
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ich (struct item 1800 0.2 0.015)
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gol (struct item 2500 2.0 0.002)
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types [pan ich gol]
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max-w 25.0
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max-v 0.25
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iters #(range (inc (max-count % max-w max-v)))]
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(filter (complement nil?)
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(pmap
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#(let [[p i g] %
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w (total :weight types %)
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v (total :volume types %)]
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(if (and (<= w max-w) (<= v max-v))
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(with-meta (struct item (total :value types %) w v) {:p p :i i :g g})))
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(for [p (iters pan)
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i (iters ich)
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g (iters gol)]
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[p i g])))))
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@ -0,0 +1,10 @@
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(defn best-by-value [ks]
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(reduce #(if (> (:value %1) (:value %2)) %1 %2) ks))
|
||||
|
||||
(defn print-knapsack[k]
|
||||
(let [ {val :value w :weight v :volume} k
|
||||
{p :p i :i g :g} ^k]
|
||||
(println "Maximum value:" (float val))
|
||||
(println "Total weight: " (float w))
|
||||
(println "Total volume: " (float v))
|
||||
(println "Containing: " p "Panacea," i "Ichor," g "Gold")))
|
||||
|
|
@ -0,0 +1,8 @@
|
|||
(defn all-best-by-value [ks]
|
||||
(let [b (best-by-value ks)]
|
||||
(filter #(= (:value b) (:value %)) ks)))
|
||||
|
||||
(defn print-knapsacks [ks]
|
||||
(doseq [k ks]
|
||||
(print-knapsack k)
|
||||
(println)))
|
||||
|
|
@ -0,0 +1,44 @@
|
|||
(defun fill-knapsack (items max-volume max-weight)
|
||||
"Items is a list of lists of the form (name value weight volume) where weight
|
||||
and value are integers. max-volume and max-weight, also integers, are the
|
||||
maximum volume and weight of the knapsack. fill-knapsack returns a list of the
|
||||
form (total-value inventory total-volume total-weight) where total-value is the
|
||||
total-value of a knapsack packed with inventory (a list whose elements are
|
||||
elements of items), and total-weight and total-volume are the total weights and
|
||||
volumes of the inventory."
|
||||
;; maxes is a table indexed by volume and weight, where maxes[volume,weight]
|
||||
;; is a list of the form (value inventory used-volume used-weight) where
|
||||
;; inventory is a list of items of maximum value fitting within volume and
|
||||
;; weight, value is the maximum value, and used-volume/used-weight are the
|
||||
;; actual volume/weight of the inventory.
|
||||
(let* ((VV (1+ max-volume))
|
||||
(WW (1+ max-weight))
|
||||
(maxes (make-array (list VV WW))))
|
||||
;; fill in the base cases where volume or weight is 0
|
||||
(dotimes (v VV) (setf (aref maxes v 0) (list 0 '() 0 0)))
|
||||
(dotimes (w WW) (setf (aref maxes 0 w) (list 0 '() 0 0)))
|
||||
;; populate the rest of the table. The best value for a volume/weight
|
||||
;; combination is the best way of adding an item to any of the inventories
|
||||
;; from [volume-1,weight], [volume,weight-1], or [volume-1,weight-1], or the
|
||||
;; best of these, if no items can be added.
|
||||
(do ((v 1 (1+ v))) ((= v VV) (aref maxes max-volume max-weight))
|
||||
(do ((w 1 (1+ w))) ((= w WW))
|
||||
(let ((options (sort (list (aref maxes v (1- w))
|
||||
(aref maxes (1- v) w)
|
||||
(aref maxes (1- v) (1- w)))
|
||||
'> :key 'first)))
|
||||
(destructuring-bind (b-value b-items b-volume b-weight) (first options)
|
||||
(dolist (option options)
|
||||
(destructuring-bind (o-value o-items o-volume o-weight) option
|
||||
(dolist (item items)
|
||||
(destructuring-bind (_ i-value i-volume i-weight) item
|
||||
(declare (ignore _))
|
||||
(when (and (<= (+ o-volume i-volume) v)
|
||||
(<= (+ o-weight i-weight) w)
|
||||
(> (+ o-value i-value) b-value))
|
||||
(setf b-value (+ o-value i-value)
|
||||
b-volume (+ o-volume i-volume)
|
||||
b-weight (+ o-weight i-weight)
|
||||
b-items (list* item o-items)))))))
|
||||
(setf (aref maxes v w)
|
||||
(list b-value b-items b-volume b-weight))))))))
|
||||
|
|
@ -0,0 +1,53 @@
|
|||
import std.stdio, std.algorithm, std.typecons;
|
||||
|
||||
struct Bounty {
|
||||
int value;
|
||||
double weight, volume;
|
||||
}
|
||||
|
||||
void main() {
|
||||
immutable Bounty panacea = {3000, 0.3, 0.025};
|
||||
immutable Bounty ichor = {1800, 0.2, 0.015};
|
||||
immutable Bounty gold = {2500, 2.0, 0.002};
|
||||
immutable Bounty sack = { 0, 25.0, 0.25};
|
||||
|
||||
Bounty best = {0, 0.0, 0.0};
|
||||
Bounty current = {0, 0.0, 0.0};
|
||||
Tuple!(int, int, int) bestAmounts;
|
||||
|
||||
immutable maxPanacea = cast(int)(min(sack.weight / panacea.weight,
|
||||
sack.volume / panacea.volume));
|
||||
immutable maxIchor = cast(int)(min(sack.weight / ichor.weight,
|
||||
sack.volume / ichor.volume));
|
||||
immutable maxGold = cast(int)(min(sack.weight / gold.weight,
|
||||
sack.volume / gold.volume));
|
||||
|
||||
foreach (nPanacea; 0 .. maxPanacea)
|
||||
foreach (nIchor; 0 .. maxIchor)
|
||||
foreach (nGold; 0 .. maxGold) {
|
||||
current.value = nPanacea * panacea.value +
|
||||
nIchor * ichor.value +
|
||||
nGold * gold.value;
|
||||
current.weight = nPanacea * panacea.weight +
|
||||
nIchor * ichor.weight +
|
||||
nGold * gold.weight;
|
||||
current.volume = nPanacea * panacea.volume +
|
||||
nIchor * ichor.volume +
|
||||
nGold * gold.volume;
|
||||
|
||||
if (current.value > best.value &&
|
||||
current.weight <= sack.weight &&
|
||||
current.volume <= sack.volume) {
|
||||
best = Bounty(current.value,
|
||||
current.weight,
|
||||
current.volume);
|
||||
bestAmounts = tuple(nPanacea, nIchor, nGold);
|
||||
}
|
||||
}
|
||||
|
||||
writeln("Maximum value achievable is ", best.value);
|
||||
writefln("This is achieved by carrying (one solution) %d" ~
|
||||
" panacea, %d ichor and %d gold", bestAmounts.tupleof);
|
||||
writefln("The weight to carry is %4.1f and the volume used is %5.3f",
|
||||
best.weight, best.volume);
|
||||
}
|
||||
|
|
@ -0,0 +1,80 @@
|
|||
pragma.enable("accumulator")
|
||||
|
||||
/** A data type representing a bunch of stuff (or empty space). */
|
||||
def makeQuantity(value, weight, volume, counts) {
|
||||
def quantity {
|
||||
to __printOn(out) {
|
||||
for name => n in counts { out.print(`$n $name `) }
|
||||
out.print(`(val=$value wt=$weight vol=$volume)`)
|
||||
}
|
||||
to value () { return value }
|
||||
to weight() { return weight }
|
||||
to volume() { return volume }
|
||||
to counts() { return counts }
|
||||
to subtract(other) { return quantity + other * -1 }
|
||||
to add(other) {
|
||||
return makeQuantity(value + other.value (),
|
||||
weight + other.weight(),
|
||||
volume + other.volume(),
|
||||
accum counts for name => n in other.counts() { _.with(name, n+counts.fetch(name, fn {0})) })
|
||||
}
|
||||
to multiply(scalar) {
|
||||
return makeQuantity(value * scalar,
|
||||
weight * scalar,
|
||||
volume * scalar,
|
||||
accum [].asMap() for name => n in counts { _.with(name, n*scalar) })
|
||||
}
|
||||
/** a.fit(b) the greatest integer k such that a - b * k does not have negative weight or volume. */
|
||||
to fit(item) {
|
||||
return (weight // item.weight()) \
|
||||
.min(volume // item.volume())
|
||||
}
|
||||
}
|
||||
return quantity
|
||||
}
|
||||
|
||||
/** Fill the space with the treasures, returning candidate results as spaceAvailable - the items. */
|
||||
def fill(spaceAvailable, treasures) {
|
||||
if (treasures.size().isZero()) { # nothing to pick
|
||||
return [spaceAvailable]
|
||||
}
|
||||
|
||||
# Pick one treasure type
|
||||
def [unit] + otherTreasures := treasures
|
||||
|
||||
var results := []
|
||||
for count in (0..spaceAvailable.fit(unit)).descending() {
|
||||
results += fill(spaceAvailable - unit * count, otherTreasures)
|
||||
if (otherTreasures.size().isZero()) {
|
||||
break # If there are no further kinds, there is no point in taking less than the most
|
||||
}
|
||||
}
|
||||
return results
|
||||
}
|
||||
|
||||
def chooseBest(emptyKnapsack, treasures) {
|
||||
var maxValue := 0
|
||||
var best := []
|
||||
for result in fill(emptyKnapsack, treasures) {
|
||||
def taken := emptyKnapsack - result # invert the backwards result fill() returns
|
||||
if (taken.value() > maxValue) {
|
||||
best := [taken]
|
||||
maxValue := taken.value()
|
||||
} else if (taken.value() <=> maxValue) {
|
||||
best with= taken
|
||||
}
|
||||
}
|
||||
return best
|
||||
}
|
||||
|
||||
def printBest(emptyKnapsack, treasures) {
|
||||
for taken in chooseBest(emptyKnapsack, treasures) { println(` $taken`) }
|
||||
}
|
||||
|
||||
def panacea := makeQuantity(3000, 0.3, 0.025, ["panacea" => 1])
|
||||
def ichor := makeQuantity(1800, 0.2, 0.015, ["ichor" => 1])
|
||||
def gold := makeQuantity(2500, 2.0, 0.002, ["gold" => 1])
|
||||
def emptyKnapsack \
|
||||
:= makeQuantity( 0, 25, 0.250, [].asMap())
|
||||
|
||||
printBest(emptyKnapsack, [panacea, ichor, gold])
|
||||
|
|
@ -0,0 +1,41 @@
|
|||
USING: accessors combinators kernel locals math math.order
|
||||
math.vectors sequences sequences.product combinators.short-circuit ;
|
||||
IN: knapsack
|
||||
|
||||
CONSTANT: values { 3000 1800 2500 }
|
||||
CONSTANT: weights { 0.3 0.2 2.0 }
|
||||
CONSTANT: volumes { 0.025 0.015 0.002 }
|
||||
|
||||
CONSTANT: max-weight 25.0
|
||||
CONSTANT: max-volume 0.25
|
||||
|
||||
TUPLE: bounty amounts value weight volume ;
|
||||
|
||||
: <bounty> ( items -- bounty )
|
||||
[ bounty new ] dip {
|
||||
[ >>amounts ]
|
||||
[ values v. >>value ]
|
||||
[ weights v. >>weight ]
|
||||
[ volumes v. >>volume ]
|
||||
} cleave ;
|
||||
|
||||
: valid-bounty? ( bounty -- ? )
|
||||
{ [ weight>> max-weight <= ]
|
||||
[ volume>> max-volume <= ] } 1&& ;
|
||||
|
||||
M:: bounty <=> ( a b -- <=> )
|
||||
a valid-bounty? [
|
||||
b valid-bounty? [
|
||||
a b [ value>> ] compare
|
||||
] [ +gt+ ] if
|
||||
] [ b valid-bounty? +lt+ +eq+ ? ] if ;
|
||||
|
||||
: find-max-amounts ( -- amounts )
|
||||
weights volumes [
|
||||
[ max-weight swap / ]
|
||||
[ max-volume swap / ] bi* min >integer
|
||||
] 2map ;
|
||||
|
||||
: best-bounty ( -- bounty )
|
||||
find-max-amounts [ 1 + iota ] map <product-sequence>
|
||||
[ <bounty> ] [ max ] map-reduce ;
|
||||
|
|
@ -0,0 +1,60 @@
|
|||
\ : value ; immediate
|
||||
: weight cell+ ;
|
||||
: volume 2 cells + ;
|
||||
: number 3 cells + ;
|
||||
|
||||
\ item value weight volume number
|
||||
create panacea 30 , 3 , 25 , 0 ,
|
||||
create ichor 18 , 2 , 15 , 0 ,
|
||||
create gold 25 , 20 , 2 , 0 ,
|
||||
create sack 0 , 250 , 250 ,
|
||||
|
||||
: fits? ( item -- ? )
|
||||
dup weight @ sack weight @ > if drop false exit then
|
||||
volume @ sack volume @ > 0= ;
|
||||
|
||||
: add ( item -- )
|
||||
dup @ sack +!
|
||||
dup weight @ negate sack weight +!
|
||||
dup volume @ negate sack volume +!
|
||||
1 swap number +! ;
|
||||
|
||||
: take ( item -- )
|
||||
dup @ negate sack +!
|
||||
dup weight @ sack weight +!
|
||||
dup volume @ sack volume +!
|
||||
-1 swap number +! ;
|
||||
|
||||
variable max-value
|
||||
variable max-pan
|
||||
variable max-ich
|
||||
variable max-au
|
||||
|
||||
: .solution
|
||||
cr
|
||||
max-pan @ . ." Panaceas, "
|
||||
max-ich @ . ." Ichors, and "
|
||||
max-au @ . ." Gold for a total value of "
|
||||
max-value @ 100 * . ;
|
||||
|
||||
: check
|
||||
sack @ max-value @ <= if exit then
|
||||
sack @ max-value !
|
||||
panacea number @ max-pan !
|
||||
ichor number @ max-ich !
|
||||
gold number @ max-au !
|
||||
( .solution ) ; \ and change <= to < to see all solutions
|
||||
|
||||
: solve-gold
|
||||
gold fits? if gold add recurse gold take
|
||||
else check then ;
|
||||
|
||||
: solve-ichor
|
||||
ichor fits? if ichor add recurse ichor take then
|
||||
solve-gold ;
|
||||
|
||||
: solve-panacea
|
||||
panacea fits? if panacea add recurse panacea take then
|
||||
solve-ichor ;
|
||||
|
||||
solve-panacea .solution
|
||||
|
|
@ -0,0 +1,34 @@
|
|||
0 VALUE vials
|
||||
0 VALUE ampules
|
||||
0 VALUE bars
|
||||
0 VALUE bag
|
||||
|
||||
#250 3 / #250 #25 / MIN 1+ CONSTANT maxvials
|
||||
#250 2/ #250 #15 / MIN 1+ CONSTANT maxampules
|
||||
#250 #20 / #250 2/ MIN 1+ CONSTANT maxbars
|
||||
|
||||
: RESULTS ( v a b -- k )
|
||||
3DUP #20 * SWAP 2* + SWAP 3 * + #250 > IF 3DROP -1 EXIT ENDIF
|
||||
3DUP 2* SWAP #15 * + SWAP #25 * + #250 > IF 3DROP -1 EXIT ENDIF
|
||||
#2500 * SWAP #1800 * + SWAP #3000 * + ;
|
||||
|
||||
: .SOLUTION ( -- )
|
||||
CR ." The traveller's knapsack contains "
|
||||
vials DEC. ." vials of panacea, "
|
||||
ampules DEC. ." ampules of ichor, "
|
||||
CR bars DEC. ." bars of gold, a total value of "
|
||||
vials ampules bars RESULTS 0DEC.R ." ." ;
|
||||
|
||||
: KNAPSACK ( -- )
|
||||
-1 TO bag
|
||||
maxvials 0 ?DO
|
||||
maxampules 0 ?DO
|
||||
maxbars 0 ?DO
|
||||
K J I RESULTS DUP
|
||||
bag > IF TO bag K TO vials J TO ampules I TO bars
|
||||
ELSE DROP
|
||||
ENDIF
|
||||
LOOP
|
||||
LOOP
|
||||
LOOP
|
||||
.SOLUTION ;
|
||||
|
|
@ -0,0 +1,48 @@
|
|||
PROGRAM KNAPSACK
|
||||
|
||||
IMPLICIT NONE
|
||||
|
||||
REAL :: totalWeight, totalVolume
|
||||
INTEGER :: maxPanacea, maxIchor, maxGold, maxValue = 0
|
||||
INTEGER :: i, j, k
|
||||
INTEGER :: n(3)
|
||||
|
||||
TYPE Bounty
|
||||
INTEGER :: value
|
||||
REAL :: weight
|
||||
REAL :: volume
|
||||
END TYPE Bounty
|
||||
|
||||
TYPE(Bounty) :: panacea, ichor, gold, sack, current
|
||||
|
||||
panacea = Bounty(3000, 0.3, 0.025)
|
||||
ichor = Bounty(1800, 0.2, 0.015)
|
||||
gold = Bounty(2500, 2.0, 0.002)
|
||||
sack = Bounty(0, 25.0, 0.25)
|
||||
|
||||
maxPanacea = MIN(sack%weight / panacea%weight, sack%volume / panacea%volume)
|
||||
maxIchor = MIN(sack%weight / ichor%weight, sack%volume / ichor%volume)
|
||||
maxGold = MIN(sack%weight / gold%weight, sack%volume / gold%volume)
|
||||
|
||||
DO i = 0, maxPanacea
|
||||
DO j = 0, maxIchor
|
||||
Do k = 0, maxGold
|
||||
current%value = k * gold%value + j * ichor%value + i * panacea%value
|
||||
current%weight = k * gold%weight + j * ichor%weight + i * panacea%weight
|
||||
current%volume = k * gold%volume + j * ichor%volume + i * panacea%volume
|
||||
IF (current%weight > sack%weight .OR. current%volume > sack%volume) CYCLE
|
||||
IF (current%value > maxValue) THEN
|
||||
maxValue = current%value
|
||||
totalWeight = current%weight
|
||||
totalVolume = current%volume
|
||||
n(1) = i ; n(2) = j ; n(3) = k
|
||||
END IF
|
||||
END DO
|
||||
END DO
|
||||
END DO
|
||||
|
||||
WRITE(*, "(A,I0)") "Maximum value achievable is ", maxValue
|
||||
WRITE(*, "(3(A,I0),A)") "This is achieved by carrying ", n(1), " panacea, ", n(2), " ichor and ", n(3), " gold items"
|
||||
WRITE(*, "(A,F4.1,A,F5.3)") "The weight to carry is ", totalWeight, " and the volume used is ", totalVolume
|
||||
|
||||
END PROGRAM KNAPSACK
|
||||
|
|
@ -0,0 +1,70 @@
|
|||
package main
|
||||
|
||||
import "fmt"
|
||||
|
||||
type Item struct {
|
||||
Name string
|
||||
Value int
|
||||
Weight, Volume float64
|
||||
}
|
||||
|
||||
type Result struct {
|
||||
Counts []int
|
||||
Sum int
|
||||
}
|
||||
|
||||
func min(a, b int) int {
|
||||
if a < b {
|
||||
return a
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
func Knapsack(items []Item, index int, weight, volume float64) (best *Result) {
|
||||
if index == len(items) {
|
||||
return &Result{make([]int, len(items)), 0}
|
||||
}
|
||||
itemValue := items[index].Value
|
||||
itemWeight := items[index].Weight
|
||||
itemVolume := items[index].Volume
|
||||
maxCount := min(int(weight/itemWeight), int(volume/itemVolume))
|
||||
for count := 0; count <= maxCount; count++ {
|
||||
sol := Knapsack(items, index+1,
|
||||
weight-float64(count)*itemWeight,
|
||||
volume-float64(count)*itemVolume)
|
||||
if sol != nil {
|
||||
sol.Counts[index] = count
|
||||
sol.Sum += itemValue * count
|
||||
if best == nil || sol.Sum > best.Sum {
|
||||
best = sol
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
func main() {
|
||||
items := []Item{
|
||||
Item{"Panacea", 3000, 0.3, 0.025},
|
||||
Item{"Ichor", 1800, 0.2, 0.015},
|
||||
Item{"Gold", 2500, 2.0, 0.002},
|
||||
}
|
||||
var sumCount, sumValue int
|
||||
var sumWeight, sumVolume float64
|
||||
|
||||
result := Knapsack(items, 0, 25, 0.25)
|
||||
|
||||
for i := range result.Counts {
|
||||
fmt.Printf("%-8s x%3d -> Weight: %4.1f Volume: %5.3f Value: %6d\n",
|
||||
items[i].Name, result.Counts[i], items[i].Weight*float64(result.Counts[i]),
|
||||
items[i].Volume*float64(result.Counts[i]), items[i].Value*result.Counts[i])
|
||||
|
||||
sumCount += result.Counts[i]
|
||||
sumValue += items[i].Value * result.Counts[i]
|
||||
sumWeight += items[i].Weight * float64(result.Counts[i])
|
||||
sumVolume += items[i].Volume * float64(result.Counts[i])
|
||||
}
|
||||
|
||||
fmt.Printf("TOTAL (%3d items) Weight: %4.1f Volume: %5.3f Value: %6d\n",
|
||||
sumCount, sumWeight, sumVolume, sumValue)
|
||||
}
|
||||
|
|
@ -0,0 +1,24 @@
|
|||
def totalWeight = { list -> list.collect{ it.item.weight * it.count }.sum() }
|
||||
def totalVolume = { list -> list.collect{ it.item.volume * it.count }.sum() }
|
||||
def totalValue = { list -> list.collect{ it.item.value * it.count }.sum() }
|
||||
|
||||
def knapsackUnbounded = { possibleItems, BigDecimal weightMax, BigDecimal volumeMax ->
|
||||
def n = possibleItems.size()
|
||||
def wm = weightMax.unscaledValue()
|
||||
def vm = volumeMax.unscaledValue()
|
||||
def m = (0..n).collect{ i -> (0..wm).collect{ w -> (0..vm).collect{ v -> [] } } }
|
||||
(1..wm).each { w ->
|
||||
(1..vm).each { v ->
|
||||
(1..n).each { i ->
|
||||
def item = possibleItems[i-1]
|
||||
def wi = item.weight.unscaledValue()
|
||||
def vi = item.volume.unscaledValue()
|
||||
def bi = [w.intdiv(wi),v.intdiv(vi)].min()
|
||||
m[i][w][v] = (0..bi).collect{ count ->
|
||||
m[i-1][w - wi * count][v - vi * count] + [[item:item, count:count]]
|
||||
}.max(totalValue).findAll{ it.count }
|
||||
}
|
||||
}
|
||||
}
|
||||
m[n][wm][vm]
|
||||
}
|
||||
|
|
@ -0,0 +1,21 @@
|
|||
Set solutions = []
|
||||
items.eachPermutation { itemList ->
|
||||
def start = System.currentTimeMillis()
|
||||
def packingList = knapsackUnbounded(itemList, 25.0, 0.250)
|
||||
def elapsed = System.currentTimeMillis() - start
|
||||
|
||||
println "\n Item Order: ${itemList.collect{ it.name.split()[0] }}"
|
||||
println "Elapsed Time: ${elapsed/1000.0} s"
|
||||
|
||||
solutions << (packingList as Set)
|
||||
}
|
||||
|
||||
solutions.each { packingList ->
|
||||
println "\nTotal Weight: ${totalWeight(packingList)}"
|
||||
println "Total Volume: ${totalVolume(packingList)}"
|
||||
println " Total Value: ${totalValue(packingList)}"
|
||||
packingList.each {
|
||||
printf (' item: %-22s count:%2d weight:%4.1f Volume:%5.3f\n',
|
||||
it.item.name, it.count, it.item.weight * it.count, it.item.volume * it.count)
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,38 @@
|
|||
import Data.List (maximumBy)
|
||||
import Data.Ord (comparing)
|
||||
|
||||
(maxWgt, maxVol) = (25, 0.25)
|
||||
items =
|
||||
[Bounty "panacea" 3000 0.3 0.025,
|
||||
Bounty "ichor" 1800 0.2 0.015,
|
||||
Bounty "gold" 2500 2.0 0.002]
|
||||
|
||||
data Bounty = Bounty
|
||||
{itemName :: String,
|
||||
itemVal :: Int,
|
||||
itemWgt, itemVol :: Double}
|
||||
|
||||
names = map itemName items
|
||||
vals = map itemVal items
|
||||
wgts = map itemWgt items
|
||||
vols = map itemVol items
|
||||
|
||||
dotProduct :: (Num a, Integral b) => [a] -> [b] -> a
|
||||
dotProduct factors = sum . zipWith (*) factors . map fromIntegral
|
||||
|
||||
options :: [[Int]]
|
||||
options = filter fits $ mapM f items
|
||||
where f (Bounty _ _ w v) = [0 .. m]
|
||||
where m = floor $ min (maxWgt / w) (maxVol / v)
|
||||
fits opt = dotProduct wgts opt <= maxWgt &&
|
||||
dotProduct vols opt <= maxVol
|
||||
|
||||
showOpt :: [Int] -> String
|
||||
showOpt opt = concat (zipWith showItem names opt) ++
|
||||
"total weight: " ++ show (dotProduct wgts opt) ++
|
||||
"\ntotal volume: " ++ show (dotProduct vols opt) ++
|
||||
"\ntotal value: " ++ show (dotProduct vals opt) ++ "\n"
|
||||
where showItem name num = name ++ ": " ++ show num ++ "\n"
|
||||
|
||||
main = putStr $ showOpt $ best options
|
||||
where best = maximumBy $ comparing $ dotProduct vals
|
||||
|
|
@ -0,0 +1,28 @@
|
|||
CHARACTER list*1000
|
||||
|
||||
NN = ALIAS($Panacea, $Ichor, $Gold, wSack, wPanacea, wIchor, wGold, vSack, vPanacea, vIchor, vGold)
|
||||
NN = (3000, 1800, 2500, 25, 0.3, 0.2, 2.0, 0.25, 0.025, 0.015, 0.002)
|
||||
maxItems = ALIAS(maxPanacea, maxIchor, maxGold)
|
||||
maxItems = ( MIN( wSack/wPanacea, vSack/vPanacea), MIN( wSack/wIchor, vSack/vIchor), MIN( wSack/wGold, vSack/vGold) )
|
||||
|
||||
maxValue = 0
|
||||
DO Panaceas = 0, maxPanacea
|
||||
DO Ichors = 0, maxIchor
|
||||
DO Golds = 0, maxGold
|
||||
weight = Panaceas*wPanacea + Ichors*wIchor + Golds*wGold
|
||||
IF( weight <= wSack ) THEN
|
||||
volume = Panaceas*vPanacea + Ichors*vIchor + Golds*vGold
|
||||
IF( volume <= vSack ) THEN
|
||||
value = Panaceas*$Panacea + Ichors*$Ichor + Golds*$Gold
|
||||
IF( value > maxValue ) THEN
|
||||
maxValue = value
|
||||
! this restarts the list, removing all previous entries:
|
||||
WRITE(Text=list, Name) value, Panaceas, Ichors, Golds, weight, volume, $CR//$LF
|
||||
ELSEIF( value == maxValue ) THEN
|
||||
WRITE(Text=list, Name, APPend) value, Panaceas, Ichors, Golds, weight, volume, $CR//$LF
|
||||
ENDIF
|
||||
ENDIF
|
||||
ENDIF
|
||||
ENDDO
|
||||
ENDDO
|
||||
ENDDO
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
value=54500; Panaceas=0; Ichors=15; Golds=11; weight=25; volume=0.247;
|
||||
value=54500; Panaceas=3; Ichors=10; Golds=11; weight=24.9; volume=0.247;
|
||||
value=54500; Panaceas=6; Ichors=5; Golds=11; weight=24.8; volume=0.247;
|
||||
value=54500; Panaceas=9; Ichors=0; Golds=11; weight=24.7; volume=0.247;
|
||||
|
|
@ -0,0 +1,18 @@
|
|||
mwv=: 25 0.25
|
||||
prods=: <;. _1 ' panacea: ichor: gold:'
|
||||
hdrs=: <;. _1 ' weight: volume: value:'
|
||||
vls=: 3000 1800 2500
|
||||
ws=: 0.3 0.2 2.0
|
||||
vs=: 0.025 0.015 0.002
|
||||
|
||||
ip=: +/ .*
|
||||
prtscr=: (1!:2)&2
|
||||
|
||||
KS=: 3 : 0
|
||||
os=. (#:i.@(*/)) mwv >:@<.@<./@:% ws,:vs
|
||||
bo=.os#~(ws,:vs) mwv&(*./@:>)@ip"_ 1 os
|
||||
mo=.bo{~{.\: vls ip"1 bo
|
||||
prtscr &.> prods ([,' ',":@])&.>mo
|
||||
prtscr &.> hdrs ('total '&,@[,' ',":@])&.> mo ip"1 ws,vs,:vls
|
||||
LF
|
||||
)
|
||||
|
|
@ -0,0 +1,84 @@
|
|||
package hu.pj.alg;
|
||||
|
||||
import hu.pj.obj.Item;
|
||||
import java.text.*;
|
||||
|
||||
public class UnboundedKnapsack {
|
||||
|
||||
protected Item [] items = {
|
||||
new Item("panacea", 3000, 0.3, 0.025),
|
||||
new Item("ichor" , 1800, 0.2, 0.015),
|
||||
new Item("gold" , 2500, 2.0, 0.002)
|
||||
};
|
||||
protected final int n = items.length; // the number of items
|
||||
protected Item sack = new Item("sack" , 0, 25.0, 0.250);
|
||||
protected Item best = new Item("best" , 0, 0.0, 0.000);
|
||||
protected int [] maxIt = new int [n]; // maximum number of items
|
||||
protected int [] iIt = new int [n]; // current indexes of items
|
||||
protected int [] bestAm = new int [n]; // best amounts
|
||||
|
||||
public UnboundedKnapsack() {
|
||||
// initializing:
|
||||
for (int i = 0; i < n; i++) {
|
||||
maxIt [i] = Math.min(
|
||||
(int)(sack.getWeight() / items[i].getWeight()),
|
||||
(int)(sack.getVolume() / items[i].getVolume())
|
||||
);
|
||||
} // for (i)
|
||||
|
||||
// calc the solution:
|
||||
calcWithRecursion(0);
|
||||
|
||||
// Print out the solution:
|
||||
NumberFormat nf = NumberFormat.getInstance();
|
||||
System.out.println("Maximum value achievable is: " + best.getValue());
|
||||
System.out.print("This is achieved by carrying (one solution): ");
|
||||
for (int i = 0; i < n; i++) {
|
||||
System.out.print(bestAm[i] + " " + items[i].getName() + ", ");
|
||||
}
|
||||
System.out.println();
|
||||
System.out.println("The weight to carry is: " + nf.format(best.getWeight()) +
|
||||
" and the volume used is: " + nf.format(best.getVolume())
|
||||
);
|
||||
|
||||
}
|
||||
|
||||
// calculation the solution with recursion method
|
||||
// item : the number of item in the "items" array
|
||||
public void calcWithRecursion(int item) {
|
||||
for (int i = 0; i <= maxIt[item]; i++) {
|
||||
iIt[item] = i;
|
||||
if (item < n-1) {
|
||||
calcWithRecursion(item+1);
|
||||
} else {
|
||||
int currVal = 0; // current value
|
||||
double currWei = 0.0; // current weight
|
||||
double currVol = 0.0; // current Volume
|
||||
for (int j = 0; j < n; j++) {
|
||||
currVal += iIt[j] * items[j].getValue();
|
||||
currWei += iIt[j] * items[j].getWeight();
|
||||
currVol += iIt[j] * items[j].getVolume();
|
||||
}
|
||||
|
||||
if (currVal > best.getValue()
|
||||
&&
|
||||
currWei <= sack.getWeight()
|
||||
&&
|
||||
currVol <= sack.getVolume()
|
||||
)
|
||||
{
|
||||
best.setValue (currVal);
|
||||
best.setWeight(currWei);
|
||||
best.setVolume(currVol);
|
||||
for (int j = 0; j < n; j++) bestAm[j] = iIt[j];
|
||||
} // if (...)
|
||||
} // else
|
||||
} // for (i)
|
||||
} // calcWithRecursion()
|
||||
|
||||
// the main() function:
|
||||
public static void main(String[] args) {
|
||||
new UnboundedKnapsack();
|
||||
} // main()
|
||||
|
||||
} // class
|
||||
|
|
@ -0,0 +1,51 @@
|
|||
package hu.pj.obj;
|
||||
|
||||
public class Item {
|
||||
protected String name = "";
|
||||
protected int value = 0;
|
||||
protected double weight = 0;
|
||||
protected double volume = 0;
|
||||
|
||||
public Item() {
|
||||
}
|
||||
|
||||
public Item(String name, int value, double weight, double volume) {
|
||||
setName(name);
|
||||
setValue(value);
|
||||
setWeight(weight);
|
||||
setVolume(volume);
|
||||
}
|
||||
|
||||
public int getValue() {
|
||||
return value;
|
||||
}
|
||||
|
||||
public void setValue(int value) {
|
||||
this.value = Math.max(value, 0);
|
||||
}
|
||||
|
||||
public double getWeight() {
|
||||
return weight;
|
||||
}
|
||||
|
||||
public void setWeight(double weight) {
|
||||
this.weight = Math.max(weight, 0);
|
||||
}
|
||||
|
||||
public double getVolume() {
|
||||
return volume;
|
||||
}
|
||||
|
||||
public void setVolume(double volume) {
|
||||
this.volume = Math.max(volume, 0);
|
||||
}
|
||||
|
||||
public String getName() {
|
||||
return name;
|
||||
}
|
||||
|
||||
public void setName(String name) {
|
||||
this.name = name;
|
||||
}
|
||||
|
||||
} // class
|
||||
|
|
@ -0,0 +1,51 @@
|
|||
var gold = { 'value': 2500, 'weight': 2.0, 'volume': 0.002 },
|
||||
panacea = { 'value': 3000, 'weight': 0.3, 'volume': 0.025 },
|
||||
ichor = { 'value': 1800, 'weight': 0.2, 'volume': 0.015 },
|
||||
|
||||
items = [gold, panacea, ichor],
|
||||
knapsack = {'weight': 25, 'volume': 0.25},
|
||||
max_val = 0,
|
||||
solutions = [],
|
||||
g, p, i, item, val;
|
||||
|
||||
for (i = 0; i < items.length; i += 1) {
|
||||
item = items[i];
|
||||
item.max = Math.min(
|
||||
Math.floor(knapsack.weight / item.weight),
|
||||
Math.floor(knapsack.volume / item.volume)
|
||||
);
|
||||
}
|
||||
|
||||
for (g = 0; g <= gold.max; g += 1) {
|
||||
for (p = 0; p <= panacea.max; p += 1) {
|
||||
for (i = 0; i <= ichor.max; i += 1) {
|
||||
if (i * ichor.weight + g * gold.weight + p * panacea.weight > knapsack.weight) {
|
||||
continue;
|
||||
}
|
||||
if (i * ichor.volume + g * gold.volume + p * panacea.volume > knapsack.volume) {
|
||||
continue;
|
||||
}
|
||||
val = i * ichor.value + g * gold.value + p * panacea.value;
|
||||
if (val > max_val) {
|
||||
solutions = [];
|
||||
max_val = val;
|
||||
}
|
||||
if (val === max_val) {
|
||||
solutions.push([g, p, i]);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
document.write("maximum value: " + max_val + '<br>');
|
||||
for (i = 0; i < solutions.length; i += 1) {
|
||||
item = solutions[i];
|
||||
document.write("(gold: " + item[0] + ", panacea: " + item[1] + ", ichor: " + item[2] + ")<br>");
|
||||
}
|
||||
|
||||
output:
|
||||
<pre>maximum value: 54500
|
||||
(gold: 11, panacea: 0, ichor: 15)
|
||||
(gold: 11, panacea: 3, ichor: 10)
|
||||
(gold: 11, panacea: 6, ichor: 5)
|
||||
(gold: 11, panacea: 9, ichor: 0)</pre>
|
||||
|
|
@ -0,0 +1,36 @@
|
|||
items = { ["panaea"] = { ["value"] = 3000, ["weight"] = 0.3, ["volume"] = 0.025 },
|
||||
["ichor"] = { ["value"] = 1800, ["weight"] = 0.2, ["volume"] = 0.015 },
|
||||
["gold"] = { ["value"] = 2500, ["weight"] = 2.0, ["volume"] = 0.002 }
|
||||
}
|
||||
|
||||
max_weight = 25
|
||||
max_volume = 0.25
|
||||
|
||||
max_num_items = {}
|
||||
for i in pairs( items ) do
|
||||
max_num_items[i] = math.floor( math.min( max_weight / items[i].weight, max_volume / items[i].volume ) )
|
||||
end
|
||||
|
||||
best = { ["value"] = 0.0, ["weight"] = 0.0, ["volume"] = 0.0 }
|
||||
best_amounts = {}
|
||||
|
||||
for i = 1, max_num_items["panaea"] do
|
||||
for j = 1, max_num_items["ichor"] do
|
||||
for k = 1, max_num_items["gold"] do
|
||||
current = { ["value"] = i*items["panaea"]["value"] + j*items["ichor"]["value"] + k*items["gold"]["value"],
|
||||
["weight"] = i*items["panaea"]["weight"] + j*items["ichor"]["weight"] + k*items["gold"]["weight"],
|
||||
["volume"] = i*items["panaea"]["volume"] + j*items["ichor"]["volume"] + k*items["gold"]["volume"]
|
||||
}
|
||||
|
||||
if current.value > best.value and current.weight <= max_weight and current.volume <= max_volume then
|
||||
best = { ["value"] = current.value, ["weight"] = current.weight, ["volume"] = current.volume }
|
||||
best_amounts = { ["panaea"] = i, ["ichor"] = j, ["gold"] = k }
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
print( "Maximum value:", best.value )
|
||||
for k, v in pairs( best_amounts ) do
|
||||
print( k, v )
|
||||
end
|
||||
|
|
@ -0,0 +1,34 @@
|
|||
divert(-1)
|
||||
define(`set2d',`define(`$1[$2][$3]',`$4')')
|
||||
define(`get2d',`defn(`$1[$2][$3]')')
|
||||
define(`for',
|
||||
`ifelse($#,0,``$0'',
|
||||
`ifelse(eval($2<=$3),1,
|
||||
`pushdef(`$1',$2)$4`'popdef(`$1')$0(`$1',incr($2),$3,`$4')')')')
|
||||
|
||||
define(`min',
|
||||
`define(`ma',eval($1))`'define(`mb',eval($2))`'ifelse(eval(ma<mb),1,ma,mb)')
|
||||
|
||||
define(`setv',
|
||||
`set2d($1,$2,1,$3)`'set2d($1,$2,2,$4)`'set2d($1,$2,3,$5)`'set2d($1,$2,4,$6)')
|
||||
|
||||
dnl name,value (each),weight,volume
|
||||
setv(a,0,`knapsack',0,250,250)
|
||||
setv(a,1,`panacea',3000,3,25)
|
||||
setv(a,2,`ichor',1800,2,15)
|
||||
setv(a,3,`gold',2500,20,2)
|
||||
|
||||
define(`mv',0)
|
||||
for(`x',0,min(get2d(a,0,3)/get2d(a,1,3),get2d(a,0,4)/get2d(a,1,4)),
|
||||
`for(`y',0,min((get2d(a,0,3)-x*get2d(a,1,3))/get2d(a,2,3),
|
||||
(get2d(a,0,4)-x*get2d(a,1,4))/get2d(a,2,4)),
|
||||
`
|
||||
define(`z',min((get2d(a,0,3)-x*get2d(a,1,3)-y*get2d(a,2,3))/get2d(a,3,3),
|
||||
(get2d(a,0,4)-x*get2d(a,1,4)-y*get2d(a,2,4))/get2d(a,3,4)))
|
||||
define(`cv',eval(x*get2d(a,1,2)+y*get2d(a,2,2)+z*get2d(a,3,2)))
|
||||
ifelse(eval(cv>mv),1,
|
||||
`define(`mv',cv)`'define(`best',(x,y,z))',
|
||||
`ifelse(cv,mv,`define(`best',best (x,y,z))')')
|
||||
')')
|
||||
divert
|
||||
mv best
|
||||
|
|
@ -0,0 +1,10 @@
|
|||
{pva,pwe,pvo}={3000,3/10,1/40};
|
||||
{iva,iwe,ivo}={1800,2/10,3/200};
|
||||
{gva,gwe,gvo}={2500,2,2/1000};
|
||||
wemax=25;
|
||||
vomax=1/4;
|
||||
{pmax,imax,gmax}=Floor/@{Min[vomax/pvo,wemax/pwe],Min[vomax/ivo,wemax/iwe],Min[vomax/gvo,wemax/gwe]};
|
||||
|
||||
data=Flatten[Table[{{p,i,g}.{pva,iva,gva},{p,i,g}.{pwe,iwe,gwe},{p,i,g}.{pvo,ivo,gvo},{p,i,g}},{p,0,pmax},{i,0,imax},{g,0,gmax}],2];
|
||||
data=Select[data,#[[2]]<=25&&#[[3]]<=1/4&];
|
||||
First[SplitBy[Sort[data,First[#1]>First[#2]&],First]]
|
||||
|
|
@ -0,0 +1 @@
|
|||
{{54500,247/10,247/1000,{9,0,11}},{54500,124/5,247/1000,{6,5,11}},{54500,249/10,247/1000,{3,10,11}},{54500,25,247/1000,{0,15,11}}}
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
p:9 i:0 v:11
|
||||
p:6 i:5 v:11
|
||||
p:3 i:10 v:11
|
||||
p:0 i:15 v:11
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
/*Knapsack
|
||||
|
||||
This model finds the integer optimal packing of a knapsack
|
||||
|
||||
Nigel_Galloway
|
||||
January 9th., 2012
|
||||
*/
|
||||
|
||||
set Items;
|
||||
param weight{t in Items};
|
||||
param value{t in Items};
|
||||
param volume{t in Items};
|
||||
|
||||
var take{t in Items}, integer, >=0;
|
||||
|
||||
knap_weight : sum{t in Items} take[t] * weight[t] <= 25;
|
||||
knap_vol : sum{t in Items} take[t] * volume[t] <= 0.25;
|
||||
|
||||
maximize knap_value: sum{t in Items} take[t] * value[t];
|
||||
|
||||
data;
|
||||
|
||||
param : Items : weight value volume :=
|
||||
panacea 0.3 3000 0.025
|
||||
ichor 0.2 1800 0.015
|
||||
gold 2.0 2500 0.002
|
||||
;
|
||||
|
||||
end;
|
||||
|
|
@ -0,0 +1,47 @@
|
|||
MODULE Knapsack EXPORTS Main;
|
||||
|
||||
FROM IO IMPORT Put;
|
||||
FROM Fmt IMPORT Int, Real;
|
||||
|
||||
TYPE Bounty = RECORD
|
||||
value: INTEGER;
|
||||
weight, volume: REAL;
|
||||
END;
|
||||
|
||||
VAR totalWeight, totalVolume: REAL;
|
||||
maxPanacea, maxIchor, maxGold, maxValue: INTEGER := 0;
|
||||
n: ARRAY [1..3] OF INTEGER;
|
||||
panacea, ichor, gold, sack, current: Bounty;
|
||||
|
||||
BEGIN
|
||||
panacea := Bounty{3000, 0.3, 0.025};
|
||||
ichor := Bounty{1800, 0.2, 0.015};
|
||||
gold := Bounty{2500, 2.0, 0.002};
|
||||
sack := Bounty{0, 25.0, 0.25};
|
||||
|
||||
maxPanacea := FLOOR(MIN(sack.weight / panacea.weight, sack.volume / panacea.volume));
|
||||
maxIchor := FLOOR(MIN(sack.weight / ichor.weight, sack.volume / ichor.volume));
|
||||
maxGold := FLOOR(MIN(sack.weight / gold.weight, sack.volume / gold.volume));
|
||||
|
||||
FOR i := 0 TO maxPanacea DO
|
||||
FOR j := 0 TO maxIchor DO
|
||||
FOR k := 0 TO maxGold DO
|
||||
current.value := k * gold.value + j * ichor.value + i * panacea.value;
|
||||
current.weight := FLOAT(k) * gold.weight + FLOAT(j) * ichor.weight + FLOAT(i) * panacea.weight;
|
||||
current.volume := FLOAT(k) * gold.volume + FLOAT(j) * ichor.volume + FLOAT(i) * panacea.volume;
|
||||
IF current.weight > sack.weight OR current.volume > sack.volume THEN
|
||||
EXIT;
|
||||
END;
|
||||
IF current.value > maxValue THEN
|
||||
maxValue := current.value;
|
||||
totalWeight := current.weight;
|
||||
totalVolume := current.volume;
|
||||
n[1] := i; n[2] := j; n[3] := k;
|
||||
END;
|
||||
END;
|
||||
END;
|
||||
END;
|
||||
Put("Maximum value achievable is " & Int(maxValue) & "\n");
|
||||
Put("This is achieved by carrying " & Int(n[1]) & " panacea, " & Int(n[2]) & " ichor and " & Int(n[3]) & " gold items\n");
|
||||
Put("The weight of this carry is " & Real(totalWeight) & " and the volume used is " & Real(totalVolume) & "\n");
|
||||
END Knapsack.
|
||||
|
|
@ -0,0 +1,71 @@
|
|||
my (@names, @val, @weight, @vol, $max_vol, $max_weight, $vsc, $wsc);
|
||||
|
||||
if (1) { # change 1 to 0 for different data set
|
||||
@names = qw(panacea icor gold);
|
||||
@val = qw(3000 1800 2500);
|
||||
@weight = qw(3 2 20 );
|
||||
@vol = qw(25 15 2 );
|
||||
$max_weight = 250;
|
||||
$max_vol = 250;
|
||||
$vsc = 1000;
|
||||
$wsc = 10;
|
||||
} else { # with these numbers cache would have been useful
|
||||
@names = qw(panacea icor gold banana monkey );
|
||||
@val = qw(17 11 5 3 34 );
|
||||
@weight = qw(14 3 2 2 10 );
|
||||
@vol = qw(3 4 2 1 12 );
|
||||
$max_weight = 150;
|
||||
$max_vol = 100;
|
||||
$vsc = $wsc = 1;
|
||||
}
|
||||
|
||||
my @cache;
|
||||
my ($hits, $misses) = (0, 0);
|
||||
sub solu {
|
||||
my ($i, $w, $v) = @_;
|
||||
return [0, []] if $i < 0;
|
||||
|
||||
if ($cache[$i][$w][$v]) {
|
||||
$hits ++;
|
||||
return $cache[$i][$w][$v]
|
||||
}
|
||||
$misses ++;
|
||||
|
||||
my $x = solu($i - 1, $w, $v);
|
||||
|
||||
my ($w1, $v1);
|
||||
for (my $t = 1; ; $t++) {
|
||||
last if ($w1 = $w - $t * $weight[$i]) < 0;
|
||||
last if ($v1 = $v - $t * $vol[$i]) < 0;
|
||||
|
||||
my $y = solu($i - 1, $w1, $v1);
|
||||
|
||||
if ( (my $tmp = $y->[0] + $val[$i] * $t) > $x->[0] ) {
|
||||
$x = [ $tmp, [ @{$y->[1]}, [$i, $t] ] ];
|
||||
}
|
||||
}
|
||||
|
||||
$cache[$i][$w][$v] = $x
|
||||
}
|
||||
|
||||
my $x = solu($#names, $max_weight, $max_vol);
|
||||
print "Max value $x->[0], with:\n",
|
||||
" Item\tQty\tWeight Vol Value\n", '-'x 50, "\n";
|
||||
|
||||
my ($wtot, $vtot) = (0, 0);
|
||||
for (@{$x->[1]}) {
|
||||
my $i = $_->[0];
|
||||
printf " $names[$i]:\t% 3d % 8d% 8g% 8d\n",
|
||||
$_->[1],
|
||||
$weight[$i] * $_->[1] / $wsc,
|
||||
$vol[$i] * $_->[1] / $vsc,
|
||||
$val[$i] * $_->[1];
|
||||
|
||||
$wtot += $weight[$i] * $_->[1];
|
||||
$vtot += $vol[$i] * $_->[1];
|
||||
}
|
||||
print "-" x 50, "\n";
|
||||
printf " Total:\t % 8d% 8g% 8d\n",
|
||||
$wtot/$wsc, $vtot/$vsc, $x->[0];
|
||||
|
||||
print "\nCache hit: $hits\tmiss: $misses\n";
|
||||
|
|
@ -0,0 +1,24 @@
|
|||
(de *Items
|
||||
("panacea" 3 25 3000)
|
||||
("ichor" 2 15 1800)
|
||||
("gold" 20 2 2500) )
|
||||
|
||||
(de knapsack (Lst W V)
|
||||
(when Lst
|
||||
(let X (knapsack (cdr Lst) W V)
|
||||
(if (and (ge0 (dec 'W (cadar Lst))) (ge0 (dec 'V (caddar Lst))))
|
||||
(maxi
|
||||
'((L) (sum cadddr L))
|
||||
(list
|
||||
X
|
||||
(cons (car Lst) (knapsack (cdr Lst) W V))
|
||||
(cons (car Lst) (knapsack Lst W V)) ) )
|
||||
X ) ) ) )
|
||||
|
||||
(let K (knapsack *Items 250 250)
|
||||
(for (L K L)
|
||||
(let (N 1 X)
|
||||
(while (= (setq X (pop 'L)) (car L))
|
||||
(inc 'N) )
|
||||
(apply tab X (4 2 8 5 5 7) N "x") ) )
|
||||
(tab (14 5 5 7) NIL (sum cadr K) (sum caddr K) (sum cadddr K)) )
|
||||
|
|
@ -0,0 +1,86 @@
|
|||
:- use_module(library(simplex)).
|
||||
|
||||
% tuples (name, Explantion, Value, weights, volume).
|
||||
knapsack :-
|
||||
L =[( panacea, 'Incredible healing properties', 3000, 0.3, 0.025),
|
||||
( ichor, 'Vampires blood', 1800, 0.2, 0.015),
|
||||
( gold , 'Shiney shiney', 2500, 2.0, 0.002)],
|
||||
|
||||
gen_state(S0),
|
||||
length(L, N),
|
||||
numlist(1, N, LN),
|
||||
|
||||
% to get statistics
|
||||
time((create_constraint_N(LN, L, S0, S1, [], LVa, [], LW, [], LVo),
|
||||
constraint(LW =< 25.0, S1, S2),
|
||||
constraint(LVo =< 0.25, S2, S3),
|
||||
maximize(LVa, S3, S4)
|
||||
)),
|
||||
|
||||
% we display the results
|
||||
compute_lenword(L, 0, Len),
|
||||
sformat(A0, '~~w~~t~~~w|', [3]),
|
||||
sformat(A1, '~~w~~t~~~w|', [Len]),
|
||||
sformat(A2, '~~t~~w~~~w|', [10]),
|
||||
sformat(A3, '~~t~~2f~~~w|', [10]),
|
||||
sformat(A4, '~~t~~3f~~~w|', [10]),
|
||||
sformat(A33, '~~t~~w~~~w|', [10]),
|
||||
sformat(A44, '~~t~~w~~~w|', [10]),
|
||||
|
||||
sformat(W0, A0, ['Nb']),
|
||||
sformat(W1, A1, ['Items']),
|
||||
sformat(W2, A2, ['Value']),
|
||||
sformat(W3, A33, ['Weigth']),
|
||||
sformat(W4, A44, ['Volume']),
|
||||
format('~w~w~w~w~w~n', [W0, W1,W2,W3,W4]),
|
||||
|
||||
print_results(S4, A0, A1, A2, A3, A4, L, LN, 0, 0, 0).
|
||||
|
||||
|
||||
create_constraint_N([], [], S, S, LVa, LVa, LW, LW, LVo, LVo).
|
||||
|
||||
create_constraint_N([HN|TN], [(_, _,Va, W, Vo) | TL], S1, SF, LVa, LVaF, LW, LWF, LVo, LVoF) :-
|
||||
constraint(integral(x(HN)), S1, S2),
|
||||
constraint([x(HN)] >= 0, S2, S3),
|
||||
create_constraint_N(TN, TL, S3, SF,
|
||||
[Va * x(HN) | LVa], LVaF,
|
||||
[W * x(HN) | LW], LWF,
|
||||
[Vo * x(HN) | LVo], LVoF).
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%
|
||||
compute_lenword([], N, N).
|
||||
compute_lenword([(Name, _, _, _, _)|T], N, NF):-
|
||||
atom_length(Name, L),
|
||||
( L > N -> N1 = L; N1 = N),
|
||||
compute_lenword(T, N1, NF).
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%
|
||||
print_results(_S, A0, A1, A2, A3, A4, [], [], VaM, WM, VoM) :-
|
||||
sformat(W0, A0, [' ']),
|
||||
sformat(W1, A1, [' ']),
|
||||
sformat(W2, A2, [VaM]),
|
||||
sformat(W3, A3, [WM]),
|
||||
sformat(W4, A4, [VoM]),
|
||||
format('~w~w~w~w~w~n', [W0, W1,W2,W3,W4]).
|
||||
|
||||
|
||||
print_results(S, A0, A1, A2, A3, A4, [(Name, _, Va, W, Vo)|T], [N|TN], Va1, W1, Vo1) :-
|
||||
variable_value(S, x(N), X),
|
||||
( X = 0 -> Va1 = Va2, W1 = W2, Vo1 = Vo2
|
||||
;
|
||||
sformat(S0, A0, [X]),
|
||||
sformat(S1, A1, [Name]),
|
||||
Vatemp is X * Va,
|
||||
Wtemp is X * W,
|
||||
Votemp is X * Vo,
|
||||
sformat(S2, A2, [Vatemp]),
|
||||
sformat(S3, A3, [Wtemp]),
|
||||
sformat(S4, A4, [Votemp]),
|
||||
format('~w~w~w~w~w~n', [S0,S1,S2,S3,S4]),
|
||||
Va2 is Va1 + Vatemp,
|
||||
W2 is W1 + Wtemp,
|
||||
Vo2 is Vo1 + Votemp ),
|
||||
print_results(S, A0, A1, A2, A3, A4, T, TN, Va2, W2, Vo2).
|
||||
|
|
@ -0,0 +1,22 @@
|
|||
# Define consts
|
||||
weights <- c(panacea=0.3, ichor=0.2, gold=2.0)
|
||||
volumes <- c(panacea=0.025, ichor=0.015, gold=0.002)
|
||||
values <- c(panacea=3000, ichor=1800, gold=2500)
|
||||
sack.weight <- 25
|
||||
sack.volume <- 0.25
|
||||
max.items <- floor(pmin(sack.weight/weights, sack.volume/volumes))
|
||||
|
||||
# Some utility functions
|
||||
getTotalValue <- function(n) sum(n*values)
|
||||
getTotalWeight <- function(n) sum(n*weights)
|
||||
getTotalVolume <- function(n) sum(n*volumes)
|
||||
willFitInSack <- function(n) getTotalWeight(n) <= sack.weight && getTotalVolume(n) <= sack.volume
|
||||
|
||||
# Find all possible combination, then eliminate those that won't fit in the sack
|
||||
knapsack <- expand.grid(lapply(max.items, function(n) seq.int(0, n)))
|
||||
ok <- apply(knapsack, 1, willFitInSack)
|
||||
knapok <- knapsack[ok,]
|
||||
|
||||
# Find the solutions with the highest value
|
||||
vals <- apply(knapok, 1, getTotalValue)
|
||||
knapok[vals == max(vals),]
|
||||
|
|
@ -0,0 +1,46 @@
|
|||
/*REXX program solves a knapsack/unbounded problem. */
|
||||
maxPanacea=0
|
||||
maxIchor =0
|
||||
maxGold =0
|
||||
max$ =0
|
||||
current. =0
|
||||
|
||||
/* value weight volume */
|
||||
/* ═══════ ═══════ ══════ */
|
||||
panacea.$= 3000 ; panacea.w= 0.3 ; panacea.v= 0.025
|
||||
ichor.$= 1800 ; ichor.w= 0.2 ; ichor.v= 0.015
|
||||
gold.$= 2500 ; gold.w= 2 ; gold.v= 0.002
|
||||
sack.$= 0 ; sack.w= 25 ; sack.v= 0.25
|
||||
|
||||
maxPanacea = min(sack.w/panacea.w, sack.v/panacea.v)
|
||||
maxIchor = min(sack.w/ ichor.w, sack.v/ ichor.v)
|
||||
maxGold = min(sack.w/ gold.w, sack.v/ gold.v)
|
||||
|
||||
do p=0 to maxpanacea
|
||||
do i=0 to maxichor
|
||||
do g=0 to maxgold
|
||||
current.$=g*gold.$ + i*ichor.$ + p*panacea.$
|
||||
current.w=g*gold.w + i*ichor.w + p*panacea.w
|
||||
current.v=g*gold.v + i*ichor.v + p*panacea.v
|
||||
if current.w>sack.w | current.v>sack.v then iterate
|
||||
if current.$>max$ then do
|
||||
max$ = current.$
|
||||
totalW = current.w
|
||||
totalV = current.v
|
||||
maxP=p; maxI=i; maxG=g
|
||||
end
|
||||
end /*g (gold) */
|
||||
end /*i (ichor) */
|
||||
end /*p (panacea)*/
|
||||
|
||||
cTot=maxP+maxI+maxG
|
||||
L=length(cTot)+1
|
||||
say ' panacea in sack:' right(maxP,L)
|
||||
say ' ichors in sack:' right(maxI,L)
|
||||
say ' gold items in sack:' right(maxG,L)
|
||||
say '════════════════════' copies('═',L)
|
||||
say 'carrying a total of:' right(cTot,L)
|
||||
say left('',40) 'total value: ' max$/1
|
||||
say left('',40) 'total weight: ' totalW/1
|
||||
say left('',40) 'total volume: ' totalV/1
|
||||
/*stick a fork in it, we're done.*/
|
||||
|
|
@ -0,0 +1,37 @@
|
|||
KnapsackItem = Struct.new(:volume, :weight, :value)
|
||||
panacea = KnapsackItem.new(0.025, 0.3, 3000)
|
||||
ichor = KnapsackItem.new(0.015, 0.2, 1800)
|
||||
gold = KnapsackItem.new(0.002, 2.0, 2500)
|
||||
maximum = KnapsackItem.new(0.25, 25, 0)
|
||||
|
||||
max_items = {}
|
||||
for item in [panacea, ichor, gold]
|
||||
max_items[item] = [(maximum.volume/item.volume).to_i, (maximum.weight/item.weight).to_i].min
|
||||
end
|
||||
|
||||
maxval = 0
|
||||
solutions = []
|
||||
|
||||
0.upto(max_items[ichor]) do |i|
|
||||
0.upto(max_items[panacea]) do |p|
|
||||
0.upto(max_items[gold]) do |g|
|
||||
next if i*ichor.weight + p*panacea.weight + g*gold.weight > maximum.weight
|
||||
next if i*ichor.volume + p*panacea.volume + g*gold.volume > maximum.volume
|
||||
val = i*ichor.value + p*panacea.value + g*gold.value
|
||||
if val > maxval
|
||||
maxval = val
|
||||
solutions = [[i, p, g]]
|
||||
elsif val == maxval
|
||||
solutions << [i, p, g]
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
puts "The maximal solution has value #{maxval}"
|
||||
solutions.each do |i, p, g|
|
||||
printf " ichor=%2d, panacea=%2d, gold=%2d -- weight:%.1f, volume=%.3f\n",
|
||||
i, p, g,
|
||||
i*ichor.weight + p*panacea.weight + g*gold.weight,
|
||||
i*ichor.volume + p*panacea.volume + g*gold.volume
|
||||
end
|
||||
|
|
@ -0,0 +1,31 @@
|
|||
#!/usr/bin/env tclsh
|
||||
proc main argv {
|
||||
array set value {panacea 3000 ichor 1800 gold 2500}
|
||||
array set weight {panacea 0.3 ichor 0.2 gold 2.0 max 25}
|
||||
array set volume {panacea 0.025 ichor 0.015 gold 0.002 max 0.25}
|
||||
|
||||
foreach i {panacea ichor gold} {
|
||||
set max($i) [expr {min(int($volume(max)/$volume($i)),
|
||||
int($weight(max)/$weight($i)))}]
|
||||
}
|
||||
set maxval 0
|
||||
for {set i 0} {$i < $max(ichor)} {incr i} {
|
||||
for {set p 0} {$p < $max(panacea)} {incr p} {
|
||||
for {set g 0} {$g < $max(gold)} {incr g} {
|
||||
if {$i*$weight(ichor) + $p*$weight(panacea) + $g*$weight(gold)
|
||||
> $weight(max)} continue
|
||||
if {$i*$volume(ichor) + $p*$volume(panacea) + $g*$volume(gold)
|
||||
> $volume(max)} continue
|
||||
set val [expr {$i*$value(ichor)+$p*$value(panacea)+$g*$value(gold)}]
|
||||
if {$val == $maxval} {
|
||||
lappend best [list i $i p $p g $g]
|
||||
} elseif {$val > $maxval} {
|
||||
set maxval $val
|
||||
set best [list [list i $i p $p g $g]]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
puts "maxval: $maxval, best: $best"
|
||||
}
|
||||
main $argv
|
||||
Loading…
Add table
Add a link
Reference in a new issue