# Knapsack problem/Continuous

Knapsack problem/Continuous
You are encouraged to solve this task according to the task description, using any language you may know.

A thief burgles a butcher's shop, where he can select from some items.

The thief knows the weights and prices of each items.   Because he has a knapsack with 15 kg maximal capacity, he wants to select the items such that he would have his profit maximized.   He may cut the items;   the item has a reduced price after cutting that is proportional to the original price by the ratio of masses.   That means:   half of an item has half the price of the original.

This is the item list in the butcher's shop:

Table of potential knapsack items
Item Weight (kg) Price (Value)
beef 3.8 36
pork 5.4 43
ham 3.6 90
greaves 2.4 45
flitch 4.0 30
brawn 2.5 56
welt 3.7 67
salami 3.0 95
sausage 5.9 98
Knapsack <=15 kg  ?

Show which items the thief carries in his knapsack so that their total weight does not exceed 15 kg, and their total value is maximized.

with Ada.Text_IO;with Ada.Float_Text_IO;with Ada.Strings.Unbounded; procedure Knapsack_Continuous is   package US renames Ada.Strings.Unbounded;    type Item is record      Name   : US.Unbounded_String;      Weight : Float;      Value  : Positive;      Taken  : Float;   end record;    function "<" (Left, Right : Item) return Boolean is   begin      return Float (Left.Value) / Left.Weight <             Float (Right.Value) / Right.Weight;   end "<";    type Item_Array is array (Positive range <>) of Item;    function Total_Weight (Items : Item_Array) return Float is      Sum : Float := 0.0;   begin      for I in Items'Range loop         Sum := Sum + Items (I).Taken;      end loop;      return Sum;   end Total_Weight;    function Total_Value (Items : Item_Array) return Float is      Sum : Float := 0.0;   begin      for I in Items'Range loop         Sum := Sum + Float (Items (I).Value) / Items(I).Weight * Items (I).Taken;      end loop;      return Sum;   end Total_Value;    procedure Solve_Knapsack_Continuous     (Items        : in out Item_Array;      Weight_Limit : Float)   is   begin      -- order items by value per weight unit      Sorting : declare         An_Item : Item;         J       : Natural;      begin         for I in Items'First + 1 .. Items'Last loop            An_Item := Items (I);            J       := I - 1;            while J in Items'Range and then Items (J) < An_Item loop               Items (J + 1) := Items (J);               J             := J - 1;            end loop;            Items (J + 1) := An_Item;         end loop;      end Sorting;      declare         Rest : Float := Weight_Limit;      begin         for I in Items'Range loop            if Items (I).Weight <= Rest then               Items (I).Taken := Items (I).Weight;            else               Items (I).Taken := Rest;            end if;            Rest := Rest - Items (I).Taken;            exit when Rest <= 0.0;         end loop;      end;   end Solve_Knapsack_Continuous;    All_Items : Item_Array :=     ((US.To_Unbounded_String ("beef"), 3.8, 36, 0.0),      (US.To_Unbounded_String ("pork"), 5.4, 43, 0.0),      (US.To_Unbounded_String ("ham"), 3.6, 90, 0.0),      (US.To_Unbounded_String ("greaves"), 2.4, 45, 0.0),      (US.To_Unbounded_String ("flitch"), 4.0, 30, 0.0),      (US.To_Unbounded_String ("brawn"), 2.5, 56, 0.0),      (US.To_Unbounded_String ("welt"), 3.7, 67, 0.0),      (US.To_Unbounded_String ("salami"), 3.0, 95, 0.0),      (US.To_Unbounded_String ("sausage"), 5.9, 98, 0.0)); begin   Solve_Knapsack_Continuous (All_Items, 15.0);   Ada.Text_IO.Put ("Total Weight: ");   Ada.Float_Text_IO.Put (Total_Weight (All_Items), 0, 2, 0);   Ada.Text_IO.New_Line;   Ada.Text_IO.Put ("Total Value:  ");   Ada.Float_Text_IO.Put (Total_Value (All_Items), 0, 2, 0);   Ada.Text_IO.New_Line;   Ada.Text_IO.Put_Line ("Items:");   for I in All_Items'Range loop      if All_Items (I).Taken > 0.0 then         Ada.Text_IO.Put ("   ");         Ada.Float_Text_IO.Put (All_Items (I).Taken, 0, 2, 0);         Ada.Text_IO.Put_Line (" of " & US.To_String (All_Items (I).Name));      end if;   end loop;end Knapsack_Continuous;
Output:
Total Weight: 15.00
Total Value:  349.38
Items:
3.00 of salami
3.60 of ham
2.50 of brawn
2.40 of greaves
3.50 of welt


## GNU APL

⍝ DataItems←'beef' 'pork' 'ham' 'greaves' 'flitch' 'brawn' 'welt' 'salami' 'sausage'Weights←3.8 5.4 3.6 2.4 4 2.5 3.7 3 5.9Prices←36 43 90 45 30 56 67 95 98 ⍝ SolutionOrder←⍒Worth←Prices÷Weights                    ⍝ 'Worth' is each item value for 1 kg.diff←{¯1↓(⍵,0)-0,⍵}                             ⍝ 'diff' between each item and the prev item (the inverse of '+\').Filter←×Selected←diff 15⌊+\Weights[Order]      ⍝ 'Selected' weights totaling 15kg, others 0.Table←⊃{⍺,⍪⍵}/Items Weights Selected[⍋Order]Take←Filter[⍋Order]/[1]TableTotalCost←+/Prices×Selected[⍋Order]÷Weights ⍝ Output⎕←'ITEM' 'WEIGHT AVAILABLE' 'WEIGHT SELECTED' ⍪ Take⎕←''⎕←'total cost:' TotalCost
Output:
 ITEM      WEIGHT AVAILABLE   WEIGHT SELECTED
ham                    3.6               3.6
greaves                2.4               2.4
brawn                  2.5               2.5
welt                   3.7               3.5
salami                 3                 3

total cost: 349.3783784


## AWK

# syntax: GAWK -f KNAPSACK_PROBLEM_CONTINUOUS.AWKBEGIN {#   arr["item,weight,price"]    arr["beef,3.8,36"]    arr["pork,5.4,43"]    arr["ham,3.6,90"]    arr["greaves,2.4,45"]    arr["flitch,4.0,30"]    arr["brawn,2.5,56"]    arr["welt,3.7,67"]    arr["salami,3.0,95"]    arr["sausage,5.9,98"]    for (i in arr) {      split(i,tmp,",")      arr[i] = tmp[3] / tmp[2] # $/unit } sack_size = 15 # kg PROCINFO["sorted_in"] = "@val_num_desc" print("item weight price$/unit")    for (i in arr) {      if (total_weight >= sack_size) {        break      }      split(i,tmp,",")      weight = tmp[2]      if (total_weight + weight <= sack_size) {        price = tmp[3]        msg = "all"      }      else {        weight = sack_size - total_weight        price = weight * arr[i]        msg = weight " of " tmp[2]      }      printf("%-7s %6.2f %6.2f %6.2f take %s\n",tmp[1],weight,tmp[3],arr[i],msg)      total_items++      total_price += price      total_weight += weight    }    printf("%7d %6.2f %6.2f total\n",total_items,total_weight,total_price)    exit(0)}
Output:
item    weight  price $/unit salami 3.00 95.00 31.67 take all ham 3.60 90.00 25.00 take all brawn 2.50 56.00 22.40 take all greaves 2.40 45.00 18.75 take all welt 3.50 67.00 18.11 take 3.5 of 3.7 5 15.00 349.38 total  ## BBC BASIC  INSTALL @lib$+"SORTSALIB"      Sort% = FN_sortSAinit(1, 0) : REM Descending       nItems% = 9      maxWeight = 15.0       DIM items{(nItems%-1) name$, weight, price, worth} FOR item% = 0 TO nItems%-1 READ items{(item%)}.name$, items{(item%)}.weight, items{(item%)}.price        items{(item%)}.worth = items{(item%)}.price / items{(item%)}.weight      NEXT       DATA "beef", 3.8, 36, "pork", 5.4, 43, "ham", 3.6, 90      DATA "greaves", 2.4, 45, "flitch", 4.0, 30, "brawn", 2.5, 56      DATA "welt", 3.7, 67, "salami", 3.0, 95, "sausage", 5.9, 98       C% = nItems% : D% = 0      CALL Sort%, items{()}, items{(0)}.worth       TotalWeight = 0      TotalPrice = 0      FOR i% = 0 TO nItems%-1        IF TotalWeight + items{(i%)}.weight < maxWeight THEN          TotalWeight += items{(i%)}.weight          TotalPrice += items{(i%)}.price          PRINT "Take all the " items{(i%)}.name$ELSE weight = maxWeight - TotalWeight price = weight * items{(i%)}.worth TotalWeight += weight TotalPrice += price PRINT "Take "; weight " kg of " items{(i%)}.name$          EXIT FOR        ENDIF      NEXT       PRINT '"Total weight = " ; TotalWeight " kg"      PRINT "Total price  = " ; TotalPrice      END

Output:

Take all the salami
Take all the ham
Take all the brawn
Take all the greaves
Take 3.5 kg of welt

Total weight = 15 kg
Total price  = 349.378379


## Befunge

Translation of: XPL0

The table of weights and prices are stored as strings to make them easier to edit. Two characters for the weight (with the decimal point dropped), two characters for the price, and then the name of the item. The total numbers of items (9) is specified by the first value on the stack.

9:02p>:5+::::::0\g68*-55+*\1\g68*-+\0\pv>2gg!*::!2v>\!v|:-1p\3\0p\2\+-*86g\3\*+55-*86g\2<<1v*g21\*g2<[email protected]_>0022p6>12p:212gg48*:**012gg/\-:03^+>,,55+%6v#v0pg2231$$_^#+5g20:+1g21_+#!:#<0#<<p22<\v84,+*8<*>22gg+::55*6*\55*6*-*022gg\-:55+/68*+"."^>*"fo "v^6*55:,+55$$_,#!1#+#*:#82#42#:g<g22:4,,,,,,," kg"<3836beef5443pork3690ham2445greaves4030flitch2556brawn3767welt3095salami5998sausage
Output:
3.0 kg of salami
3.6 kg of ham
2.5 kg of brawn
2.4 kg of greaves
3.5 kg of welt

## Bracmat

( ( fixed    {function to convert a rational number to fixed point notation.                             The second argument is the number of decimals. }  =   value decimals powerOf10    .   !arg:(?value.?decimals)      & 10^!decimals:?powerOf10      &   str        $( div$(!value.1)            "."              mod            $(div$(!value+1/2*!powerOf10^-1.!powerOf10^-1).!powerOf10)          )  )&     (beef.38/10.36)      (pork.54/10.43)      (ham.36/10.90)      (greaves.24/10.45)      (flitch.40/10.30)      (brawn.25/10.56)      (welt.37/10.67)      (salami.30/10.95)      (sausage.59/10.98)  : ?items& 0:?sorteditems&   whl  ' ( !items:(?name.?mass.?price) ?items    & (!mass*!price^-1.!mass.!name)+!sorteditems:?sorteditems    )& 0:?totalMass& :?stolenItems&   whl  ' ( !sorteditems:(?massPerPriceunit.?mass.?name)+?sorteditems    &   (!mass.!massPerPriceunit.!name) !stolenItems      : ?stolenItems    & !mass+!totalMass:?totalMass:~>15    )& !stolenItems:(?mass.?massPerPriceunit.?name) ?stolenItems& 15+!mass+-1*!totalMass:?mass& (!mass.!massPerPriceunit.!name) !stolenItems:?stolenItems& 0:?totalPrice& (   !stolenItems    :   ?        ( (?mass.?massPerPriceunit.?name)        & out$(fixed$(!mass.1) "kg of" !name)        & !mass*!massPerPriceunit^-1+!totalPrice:?totalPrice        & ~        )        ?  | out$(fixed$(!totalPrice.2))  ));
Output:
3.5 kg of welt
2.4 kg of greaves
2.5 kg of brawn
3.6 kg of ham
3.0 kg of salami
349.38

## C

#include <stdio.h>#include <stdlib.h> struct item { double w, v; const char *name; } items[] = {	{ 3.8, 36, "beef" },	{ 5.4, 43, "pork" },	{ 3.6, 90, "ham" },	{ 2.4, 45, "greaves" },	{ 4.0, 30, "flitch" },	{ 2.5, 56, "brawn" },	{ 3.7, 67, "welt" },	{ 3.0, 95, "salami" },	{ 5.9, 98, "sausage" },}; int item_cmp(const void *aa, const void *bb){	const struct item *a = aa, *b = bb;	double ua = a->v / a->w, ub = b->v / b->w;	return ua < ub ? -1 : ua > ub;} int main(){	struct item *it;	double space = 15; 	qsort(items, 9, sizeof(struct item), item_cmp);	for (it = items + 9; it---items && space > 0; space -= it->w)		if (space >= it->w)			printf("take all %s\n", it->name);		else			printf("take %gkg of %g kg of %s\n",				space, it->w, it->name); 	return 0;}
output
take all salami
take all ham
take all brawn
take all greaves
take 3.5kg of 3.7 kg of welt



## Clojure

 ; Solve Continuous Knapsack Problem; Nicolas Modrzyk; January 2015 (def maxW 15.0)(def items  {:beef    [3.8 36]   :pork    [5.4 43]   :ham     [3.6 90]   :greaves [2.4 45]   :flitch  [4.0 30]   :brawn   [2.5 56]   :welt    [3.7 67]   :salami  [3.0 95]   :sausage [5.9 98]}) (defn rob [items maxW]  (let[     val-item        (fn[key]          (- (/ (second (items key)) (first (items key )))))    compare-items         (fn[key1 key2]            (compare (val-item key1) (val-item key2)))    sorted (into (sorted-map-by compare-items) items)]   (loop [current (first sorted)          array (rest sorted)          value 0          weight 0]    (let[new-weight (first (val current))          new-value (second (val current))]    (if (> (- maxW weight new-weight) 0)      (do         (println "Take all " (key current))        (recur          (first array)          (rest array)          (+ value new-value)         (+ weight new-weight)))      (let [t (- maxW weight)] ; else      (println        "Take " t " of "        (key current) "\n"       "Total Value is:"        (+ value (* t (/ new-value new-weight)))))))))) (rob items maxW) 
Output
Take all  :salami
Take all  :ham
Take all  :brawn
Take all  :greaves
Take  3.5  of  :welt
Total Value is: 349.3783783783784


### Alternate Version

 (def items  [{:name "beef" :weight 3.8 :price 36}   {:name "pork" :weight 5.4 :price 43}   {:name "ham" :weight 3.6 :price 90}   {:name "graves" :weight 2.4 :price 45}   {:name "flitch" :weight 4.0 :price 30}   {:name "brawn" :weight 2.5 :price 56}   {:name "welt" :weight 3.7 :price 67}   {:name "salami" :weight 3.0 :price 95}   {:name "sausage" :weight 5.9 :price 98}]) (defn per-kg [item] (/ (:price item) (:weight item))) (defn rob [items capacity]  (let [best-items (reverse (sort-by per-kg items))]    (loop [items best-items cap capacity total 0]      (let [item (first items)]        (if (< (:weight item) cap)          (do (println (str "Take all " (:name item)))              (recur (rest items) (- cap (:weight item)) (+ total (:price item))))          (println (format "Take %.1f kg of %s\nTotal: %.2f monies"                           cap (:name item) (+ total (* cap (per-kg item)))))))))) (rob items 15) 

## C++

#include<iostream>#include<algorithm>#include<string.h> using namespace std;double result;double capacity = 15;int NumberOfItems;int number; struct items{    char name[32];    double weight;    double price;    double m;} item[256]; bool cmp(items a,items b){    return a.price/a.weight > b.price/b.weight; // the compare function for the sorting algorithm} int main(){NumberOfItems=9;strcpy(item[1].name,"beef");item[1].weight=3.8;item[1].price=36; strcpy(item[2].name,"pork");item[2].weight=5.4;item[2].price=43; strcpy(item[3].name,"ham");item[3].weight=3.6;item[3].price=90; strcpy(item[4].name,"greaves");item[4].weight=2.4;item[4].price=45; strcpy(item[5].name,"flitch");item[5].weight=4.0;item[5].price=30; strcpy(item[6].name,"brawn");item[6].weight=2.5;item[6].price=56; strcpy(item[7].name,"welt");item[7].weight=3.7;item[7].price=67; strcpy(item[8].name,"salami");item[8].weight=3.0;item[8].price=95; strcpy(item[9].name,"sausage");item[9].weight=5.9;item[9].price=98;  sort(item+1,item+NumberOfItems+1,cmp); // We'll sort using Introsort from STL  number = 1; while(capacity>0&&number<=NumberOfItems) {  if(item[number].weight<=capacity)    {        result+=item[number].price;        capacity-=item[number].weight;        item[number].m=1;    }  else  {      result+=(item[number].price)*(capacity/item[number].weight);      item[number].m=(capacity/item[number].weight);      capacity=0;   }  ++number; } cout<<"Total Value = "<<result<<'\n';cout<<"Total Weight = "<<(double)15-capacity<<'\n';cout<<"Items Used:\n";for(int i=1;i<=NumberOfItems;++i)    if(item[i].m)    {       cout<<"We took "<<item[i].m*item[i].weight<<"kg of \""<<item[i].name<<"\" and the value it brought is "<<item[i].price*item[i].m<<"\n";    } return 0;}
Output:
Total Value = 349.378
Total Weight = 15
Items Used:
We took 3kg of "salami" and the value it brought is 95
We took 3.6kg of "ham" and the value it brought is 90
We took 2.5kg of "brawn" and the value it brought is 56
We took 2.4kg of "greaves" and the value it brought is 45
We took 3.5kg of "welt" and the value it brought is 63.3784


### Alternate Version

// C++11 version#include <iostream>#include <vector>#include <algorithm>#include <string> using namespace std; struct item_type{    double  weight, value;    string  name;}; vector< item_type > items ={    { 3.8, 36, "beef"    },    { 5.4, 43, "pork"    },    { 3.6, 90, "ham"     },    { 2.4, 45, "greaves" },    { 4.0, 30, "flitch"  },    { 2.5, 56, "brawn"   },    { 3.7, 67, "welt"    },    { 3.0, 95, "salami"  },    { 5.9, 98, "sausage" }}; int main(){    sort    (         begin( items ), end( items ),        [] (const item_type& a, const item_type& b)        {            return a.value / a.weight > b.value / b.weight;        }    );     double space = 15;     for ( const auto& item : items )    {        if ( space >= item.weight )            cout << "Take all " << item.name << endl;        else         {            cout << "Take " << space << "kg of " << item.name << endl;            break;        }         space -= item.weight;    }}
Output:
Take all salami
Take all ham
Take all brawn
Take all greaves
Take 3.5kg of welt


## Common Lisp

(defstruct item  (name nil :type string)  (weight nil :type real)  (price nil :type real)) (defun price-per-weight (item)  (/ (item-price item) (item-weight item))) (defun knapsack (items total-weight)  (loop with sorted = (sort items #'> :key #'price-per-weight)        while (plusp total-weight)        for item in sorted        for amount = (min (item-weight item) total-weight)        collect (list (item-name item) amount)        do (decf total-weight amount))) (defun main ()  (let ((items (list (make-item :name "beef"    :weight 3.8 :price 36)                     (make-item :name "pork"    :weight 5.4 :price 43)                     (make-item :name "ham"     :weight 3.6 :price 90)                     (make-item :name "greaves" :weight 2.4 :price 45)                     (make-item :name "flitch"  :weight 4.0 :price 30)                     (make-item :name "brawn"   :weight 2.5 :price 56)                     (make-item :name "welt"    :weight 3.7 :price 67)                     (make-item :name "salami"  :weight 3.0 :price 95)                     (make-item :name "sausage" :weight 5.9 :price 98))))    (loop for (name amount) in (knapsack items 15)          do (format t "~8A: ~,2F kg~%" name amount))))
Output:
salami  : 3.00 kg
ham     : 3.60 kg
brawn   : 2.50 kg
greaves : 2.40 kg
welt    : 3.50 kg

## D

import std.stdio, std.algorithm, std.string; struct Item {    string name;    real amount, value;     @property real valuePerKG() @safe const pure nothrow @nogc {        return value / amount;    }     string toString() const pure /*nothrow*/ @safe {        return format("%10s %7.2f %7.2f %7.2f",                      name, amount, value, valuePerKG);    }} real sumBy(string field)(in Item[] items) @safe pure nothrow @nogc {    return reduce!("a + b." ~ field)(0.0L, items);} void main() /*@safe*/ {    const items = [Item("beef",    3.8, 36.0),                   Item("pork",    5.4, 43.0),                   Item("ham",     3.6, 90.0),                   Item("greaves", 2.4, 45.0),                   Item("flitch",  4.0, 30.0),                   Item("brawn",   2.5, 56.0),                   Item("welt",    3.7, 67.0),                   Item("salami",  3.0, 95.0),                   Item("sausage", 5.9, 98.0)]                  .schwartzSort!(it => -it.valuePerKG)                  .release;     immutable(Item)[] chosen;    real space = 15.0;    foreach (const item; items)        if (item.amount < space) {            chosen ~= item;            space -= item.amount;        } else {            chosen ~= Item(item.name, space, item.valuePerKG * space);            break;        }     writefln("%10s %7s %7s %7s", "ITEM", "AMOUNT", "VALUE", "$/unit"); writefln("%(%s\n%)", chosen); Item("TOTAL", chosen.sumBy!"amount", chosen.sumBy!"value").writeln;} Output:  ITEM AMOUNT VALUE$/unit
salami    3.00   95.00   31.67
ham    3.60   90.00   25.00
brawn    2.50   56.00   22.40
greaves    2.40   45.00   18.75
welt    3.50   63.38   18.11
TOTAL   15.00  349.38   23.29

### Alternative Version

void main() {    import std.stdio, std.algorithm;     static struct T { string item; double weight, price; }     auto items = [T("beef",    3.8, 36.0),                  T("pork",    5.4, 43.0),                  T("ham",     3.6, 90.0),                  T("greaves", 2.4, 45.0),                  T("flitch",  4.0, 30.0),                  T("brawn",   2.5, 56.0),                  T("welt",    3.7, 67.0),                  T("salami",  3.0, 95.0),                  T("sausage", 5.9, 98.0)]                 .schwartzSort!q{ -a.price / a.weight };     auto left = 15.0;    foreach (it; items)        if (it.weight <= left) {            writeln("Take all the ", it.item);            if (it.weight == left)                return;            left -= it.weight;        } else            return writefln("Take %.1fkg %s", left, it.item);}
Output:
Take all the salami
Take all the ham
Take all the brawn
Take all the greaves
Take 3.5kg welt

## EchoLisp

 (lib 'struct)(lib 'sql) ;; for table (define T (make-table (struct meal (name poids price)))) (define meals  '((🐂-beef 	3.8 	36)    (🍖-pork 	5.4 	43)    (🍗-ham 	3.6 	90)    (🐪-greaves 	2.4 	45)    (flitch 	4.0 	30)    (brawn 	2.5 	56)    (welt 	3.7 	67)    (🐃--salami 	3.0 	95)    (🐖-sausage 	5.9 	98))) (list->table meals T);; sort table according to best price/poids ratio(define (price/poids a b  )	(-  (//  (* (meal-price b) (meal-poids a)) (meal-price a) (meal-poids b)) 1))(table-sort T price/poids) (define-syntax-rule (name i) (table-xref T i 0))(define-syntax-rule (poids i) (table-xref T i 1)) ;; shop : add items in basket, in order, until W exhausted(define (shop W )	(for/list ((i (table-count T)))	#:break (<= W 0)		(begin0		(cons (name i) (if  (<= (poids i) W) 'all W))		(set! W (- W (poids i)))))) ;; output(shop 15)   → ((🐃--salami . all) (🍗-ham . all) (brawn . all) (🐪-greaves . all) (welt . 3.5))   

## Eiffel

 class	CONTINUOUS_KNAPSACK create	make feature 	make		local			tup: TUPLE [name: STRING; weight: REAL_64; price: REAL_64]		do			create tup			create items.make_filled (tup, 1, 9)			create sorted.make			sorted.extend (-36.0 / 3.8)			sorted.extend (-43.0 / 5.4)			sorted.extend (-90.0 / 3.6)			sorted.extend (-45.0 / 2.4)			sorted.extend (-30.0 / 4.0)			sorted.extend (-56.0 / 2.5)			sorted.extend (-67.0 / 3.7)			sorted.extend (-95.0 / 3.0)			sorted.extend (-98.0 / 5.9)			tup := ["beef", 3.8, 36.0]			items [sorted.index_of (- tup.price / tup.weight, 1)] := tup			tup := ["pork", 5.4, 43.0]			items [sorted.index_of (- tup.price / tup.weight, 1)] := tup			tup := ["ham", 3.6, 90.0]			items [sorted.index_of (- tup.price / tup.weight, 1)] := tup			tup := ["greaves", 2.4, 45.0]			items [sorted.index_of (- tup.price / tup.weight, 1)] := tup			tup := ["flitch", 4.0, 30.0]			items [sorted.index_of (- tup.price / tup.weight, 1)] := tup			tup := ["brawn", 2.5, 56.0]			items [sorted.index_of (- tup.price / tup.weight, 1)] := tup			tup := ["welt", 3.7, 67.0]			items [sorted.index_of (- tup.price / tup.weight, 1)] := tup			tup := ["salami", 3.0, 95.0]			items [sorted.index_of (- tup.price / tup.weight, 1)] := tup			tup := ["sausage", 5.9, 98.0]			items [sorted.index_of (- tup.price / tup.weight, 1)] := tup			find_solution		end 	find_solution			-- Solution for the continuous Knapsack Problem.		local			maxW, value: REAL_64		do			maxW := 15			across				items as c			loop				if maxW - c.item.weight > 0 then					io.put_string ("Take all: " + c.item.name + ".%N")					value := value + c.item.price					maxW := maxW - c.item.weight				elseif maxW /= 0 then					io.put_string ("Take " + maxW.truncated_to_real.out + " kg off " + c.item.name + ".%N")					io.put_string ("The total value is " + (value + (c.item.price / c.item.weight) * maxW).truncated_to_real.out + ".")					maxW := 0				end			end		end 	items: ARRAY [TUPLE [name: STRING; weight: REAL_64; price: REAL_64]] 	sorted: SORTED_TWO_WAY_LIST [REAL_64] end 
Output:
Take all: salami.
Take all: ham.
Take all: brawn.
Take all: greaves.
Take 3.5kg off welt.
The total value is 349.378


## Elixir

Translation of: Erlang
defmodule KnapsackProblem do  def select( max_weight, items ) do    Enum.sort_by( items, fn {_name, weight, price} -> - price / weight end )    |> Enum.reduce( {max_weight, []}, &select_until/2 )    |> elem(1)    |> Enum.reverse  end   def task( items, max_weight ) do    IO.puts "The robber takes the following to maximize the value"    Enum.each( select( max_weight, items ), fn {name, weight} ->      :io.fwrite("~.2f of ~s~n", [weight, name])    end )  end   defp select_until( {name, weight, _price}, {remains, acc} ) when remains > 0 do    selected_weight = select_until_weight( weight, remains )    {remains - selected_weight, [{name, selected_weight} | acc]}  end  defp select_until( _item, acc ), do: acc   defp select_until_weight( weight, remains ) when weight < remains, do: weight  defp select_until_weight( _weight, remains ), do: remainsend items = [ {"beef",    3.8, 36},          {"pork",    5.4, 43},          {"ham",     3.6, 90},          {"greaves", 2.4, 45},          {"flitch",  4.0, 30},          {"brawn",   2.5, 56},          {"welt",    3.7, 67},          {"salami",  3.0, 95},          {"sausage", 5.9, 98} ] KnapsackProblem.task( items, 15 )
Output:
The robber takes the following to maximize the value
3.00 of salami
3.60 of ham
2.50 of brawn
2.40 of greaves
3.50 of welt


### Alternate Version

Translation of: Ruby
defmodule KnapsackProblem do  def continuous(items, max_weight) do    Enum.sort_by(items, fn {_item, {weight, price}} -> -price / weight end)    |> Enum.reduce_while({max_weight,0}, fn {item, {weight, price}}, {rest, value} ->         if rest > weight do           IO.puts "Take all #{item}"           {:cont, {rest - weight, value + price}}         else           :io.format "Take ~.3fkg of ~s~n~n", [rest, item]           :io.format "Total value of swag is ~.2f~n", [value + rest*price/weight]           {:halt, :ok}         end       end)    |> case do         {weight, value} ->             :io.format "Total:  weight ~.3fkg, value ~p~n", [max_weight-weight, value]         x -> x       end  endend items = [ beef:    {3.8, 36},          pork:    {5.4, 43},          ham:     {3.6, 90},          greaves: {2.4, 45},          flitch:  {4.0, 30},          brawn:   {2.5, 56},          welt:    {3.7, 67},          salami:  {3.0, 95},          sausage: {5.9, 98} ] KnapsackProblem.continuous( items, 15 )
Output:
Take all salami
Take all ham
Take all brawn
Take all greaves
Take 3.500kg of welt

Total value of swag is 349.38


## Erlang

Note use of lists:foldr/2, since sort is ascending.

 -module( knapsack_problem_continuous ). -export( [price_per_weight/1, select/2, task/0] ). price_per_weight( Items ) -> [{Name, Weight, Price / Weight} || {Name, Weight, Price} <-Items]. select( Max_weight, Items ) ->	{_Remains, Selected_items} = lists:foldr( fun select_until/2, {Max_weight, []}, lists:keysort(3, Items) ),	Selected_items. task() ->	Items = items(),	io:fwrite( "The robber takes the following to maximize the value~n" ),	[io:fwrite("~.2f of ~p~n", [Weight, Name]) || {Name, Weight} <- select( 15, price_per_weight(Items) )].   items() ->	[{"beef", 3.8, 36},	{"pork", 5.4, 43},	{"ham", 3.6, 90},	{"greaves", 2.4, 45},	{"flitch", 4.0, 30},	{"brawn", 2.5, 56},	{"welt", 3.7 , 67},	{"salami", 3.0, 95},	{"sausage",  5.9 , 98}	]. select_until( {Name, Weight, _Price}, {Remains, Acc} ) when Remains > 0 ->	Selected_weight = select_until_weight( Weight, Remains ),	{Remains - Selected_weight, [{Name, Selected_weight} | Acc]};select_until( _Item, Acc ) -> Acc. select_until_weight( Weight, Remains ) when Weight < Remains -> Weight;select_until_weight( _Weight, Remains ) -> Remains. 
Output:
11> knapsack_problem_continuous:task().
The robber takes the following to maximize the value
3.50 of "welt"
2.40 of "greaves"
2.50 of "brawn"
3.60 of "ham"
3.00 of "salami"


## F#

 //Fill a knapsack optimally - Nigel Galloway: February 1st., 2015let items = [("beef", 3.8, 36);("pork", 5.4, 43);("ham", 3.6, 90);("greaves", 2.4, 45);("flitch" , 4.0, 30);("brawn", 2.5, 56);("welt", 3.7, 67);("salami" , 3.0, 95);("sausage", 5.9, 98)]            |> List.sortBy(fun(_,weight,value) -> float(-value)/weight)   let knap items maxW=  let rec take(n,g,a) =     match g with      | i::e -> let name, weight, value = i                let total = n + weight                if total <= maxW then                   printfn "Take all %s" name                  take(total, e, a+float(value))                else                  printfn "Take %0.2f kg of %s\nTotal value of swag is %0.2f" (maxW - n) name (a + (float(value)/weight)*(maxW - n))      | []   -> printfn "Everything taken! Total value of swag is £%0.2f; Total weight of bag is %0.2fkg" a n  take(0.0, items, 0.0) 
Output:
> knap items 15.0;;
Take all salami
Take all ham
Take all brawn
Take all greaves
Take 3.50kg of welt
Total value of swag is £349.38


Should your burglar be greedy, he may bring a bigger bag.

> knap items 100.0;;
Take all salami
Take all ham
Take all brawn
Take all greaves
Take all welt
Take all sausage
Take all beef
Take all pork
Take all flitch
Everything taken! Total value of swag is £560.00; Total weight of bag is 34.30kg


## Forth

Translation of: D
Works with: 4tH version 3.62.0
include lib/selcsort.4th               \ use a tiny sorting algorithm 150 value left                         \ capacity in 1/10th kilo create items                           \ list of items  ," beef"     38 , 3600 ,             \ description, weight, price (cents)  ," pork"     54 , 4300 ,             \ weight in 1/10 kilo  ," ham"      36 , 9000 ,  ," greaves"  24 , 4500 ,  ," flitch"   40 , 3000 ,  ," brawn"    25 , 5600 ,  ," welt"     37 , 6700 ,  ," salami"   30 , 9500 ,  ," sausage"  59 , 9800 ,  here items - 3 / constant #items     \ total number of items :redo items swap 3 cells * + ;         \ calculate address of record #items array (items)                   \ array for sorting                                       ( a -- n): price/weight dup 2 cells + @c swap cell+ @c / ;: [email protected] @ cell+ @c ;                 ( a -- n): .item @ @c count type cr ;           ( a --)                                       \ how to sort: on price/weight:noname >r price/weight r> price/weight > ; is precedes : knapsack                             ( --)  (items) dup #items dup 0 ?do i items (items) i th ! loop sort  begin                                \ use the sorted array     dup [email protected] left <=               \ still room in the knapsack?  while      ." Take all of the " dup .item    \ take all of the item     left over [email protected] - to left cell+ \ adjust knapsack, increment item  repeat left 100 * dup                \ so how much is left?                                       \ if room, take as much as possible  if ." Take " . ." grams of the " .item else drop drop then; knapsack

## Fortran

Works with: Fortran version 90 and later
program KNAPSACK_CONTINUOUS  implicit none   real, parameter :: maxweight = 15.0  real :: total_weight = 0, total_value = 0, frac  integer :: i, j   type Item    character(7) :: name    real :: weight    real :: value  end type Item   type(Item) :: items(9), temp   items(1) = Item("beef",    3.8, 36.0)  items(2) = Item("pork",    5.4, 43.0)  items(3) = Item("ham",     3.6, 90.0)  items(4) = Item("greaves", 2.4, 45.0)  items(5) = Item("flitch",  4.0, 30.0)  items(6) = Item("brawn",   2.5, 56.0)  items(7) = Item("welt",    3.7, 67.0)  items(8) = Item("salami",  3.0, 95.0)  items(9) = Item("sausage", 5.9, 98.0)   ! sort items in descending order of their value per unit weight  do i = 2, size(items)     j = i - 1     temp = items(i)     do while (j>=1 .and. items(j)%value / items(j)%weight < temp%value / temp%weight)       items(j+1) = items(j)       j = j - 1     end do    items(j+1) = temp  end do   i = 0  write(*, "(a4, a13, a6)") "Item", "Weight", "Value"  do while(i < size(items) .and. total_weight < maxweight)    i = i + 1    if(total_weight+items(i)%weight < maxweight) then      total_weight = total_weight + items(i)%weight      total_value = total_value + items(i)%value      write(*, "(a7, 2f8.2)") items(i)    else      frac = (maxweight-total_weight) / items(i)%weight      total_weight = total_weight + items(i)%weight * frac      total_value = total_value + items(i)%value * frac      write(*, "(a7, 2f8.2)") items(i)%name, items(i)%weight * frac, items(i)%value * frac    end if   end do   write(*, "(f15.2, f8.2)") total_weight, total_value end program KNAPSACK_CONTINUOUS

## Go

package main import (    "fmt"    "sort") type item struct {    item   string    weight float64    price  float64} type items []item var all = items{    {"beef", 3.8, 36},    {"pork", 5.4, 43},    {"ham", 3.6, 90},    {"greaves", 2.4, 45},    {"flitch", 4.0, 30},    {"brawn", 2.5, 56},    {"welt", 3.7, 67},    {"salami", 3.0, 95},    {"sausage", 5.9, 98},} // satisfy sort interfacefunc (z items) Len() int      { return len(z) }func (z items) Swap(i, j int) { z[i], z[j] = z[j], z[i] }func (z items) Less(i, j int) bool {    return z[i].price/z[i].weight > z[j].price/z[j].weight} func main() {    left := 15.    sort.Sort(all)    for _, i := range all {        if i.weight <= left {            fmt.Println("take all the", i.item)            if i.weight == left {                return            }            left -= i.weight        } else {            fmt.Printf("take %.1fkg %s\n", left, i.item)            return        }    }}

Output:

take all the salami
take all the ham
take all the brawn
take all the greaves
take 3.5kg welt


## Groovy

Solution: obvious greedy algorithm

import static java.math.RoundingMode.* def knapsackCont = { list, maxWeight = 15.0 ->    list.sort{ it.weight / it.value }    def remainder = maxWeight    List sack = []    for (item in list) {        if (item.weight < remainder) {            sack << [name: item.name, weight: item.weight,                        value: (item.value as BigDecimal).setScale(2, HALF_UP)]        } else {            sack << [name: item.name, weight: remainder,                        value: (item.value * remainder / item.weight).setScale(2, HALF_UP)]            break        }        remainder -= item.weight    }    sack}

Test:

def possibleItems = [    [name:'beef',    weight:3.8, value:36],    [name:'pork',    weight:5.4, value:43],    [name:'ham',     weight:3.6, value:90],    [name:'greaves', weight:2.4, value:45],    [name:'flitch',  weight:4.0, value:30],    [name:'brawn',   weight:2.5, value:56],    [name:'welt',    weight:3.7, value:67],    [name:'salami',  weight:3.0, value:95],    [name:'sausage', weight:5.9, value:98],] def contents = knapsackCont(possibleItems)println "Total Value: ${contents*.value.sum()}"contents.each { printf(" name: %-7s weight:${it.weight}  value: ${it.value}\n", it.name)} Output: Total Value: 349.38 name: salami weight: 3.0 value: 95.00 name: ham weight: 3.6 value: 90.00 name: brawn weight: 2.5 value: 56.00 name: greaves weight: 2.4 value: 45.00 name: welt weight: 3.5 value: 63.38 ## Haskell We use a greedy algorithm. import Data.List (sortBy)import Data.Ord (comparing)import Text.Printf (printf)import Control.Monad (forM_)import Data.Ratio (numerator, denominator) maxWgt :: RationalmaxWgt = 15 data Bounty = Bounty { itemName :: String , itemVal, itemWgt :: Rational } items :: [Bounty]items = [ Bounty "beef" 36 3.8 , Bounty "pork" 43 5.4 , Bounty "ham" 90 3.6 , Bounty "greaves" 45 2.4 , Bounty "flitch" 30 4.0 , Bounty "brawn" 56 2.5 , Bounty "welt" 67 3.7 , Bounty "salami" 95 3.0 , Bounty "sausage" 98 5.9 ] solution :: [(Rational, Bounty)]solution = g maxWgt$ sortBy (flip $comparing f) items where g room (b@(Bounty _ _ w):bs) = if w < room then (w, b) : g (room - w) bs else [(room, b)] f (Bounty _ v w) = v / w main :: IO ()main = do forM_ solution$ $$w, b) -> printf "%s kg of %s\n" (mixedNum w) (itemName b) (printf "Total value: %s\n" . mixedNum . sum)  f <> solution where f (w, Bounty _ v wtot) = v * (w / wtot) mixedNum q = if b == 0 then show a else printf "%d %d/%d" a (numerator b) (denominator b) where a = floor q b = q - toEnum a Output: 3 kg of salami 3 3/5 kg of ham 2 1/2 kg of brawn 2 2/5 kg of greaves 3 1/2 kg of welt Total value: 349 14/37 Or similar to above (but more succinct): import Data.List (sortBy)import Data.Ord (comparing)import Text.Printf (printf) -- (name, (value, weight))items = [ ("beef", (36, 3.8)) , ("pork", (43, 5.4)) , ("ham", (90, 3.6)) , ("greaves", (45, 2.4)) , ("flitch", (30, 4.0)) , ("brawn", (56, 2.5)) , ("welt", (67, 3.7)) , ("salami", (95, 3.0)) , ("sausage", (98, 5.9)) ] unitWeight (_, (val, weight)) = fromIntegral val / weight solution k = loop k . sortBy (flip  comparing unitWeight) where loop k ((name, (_, weight)):xs) | weight < k = putStrLn ("Take all the " ++ name) >> loop (k - weight) xs | otherwise = printf "Take %.2f kg of the %s\n" (k :: Float) name main = solution 15 items Output: Take all the salami Take all the ham Take all the brawn Take all the greaves Take 3.50 kg of the welt ## Icon and Unicon This implements the greedy algorithm. This also uses a Unicon extension to reverse which reverses a list. In Icon, an IPL procedure is available to do the same. link printf procedure main()room := 15every (x := !(choices := get_items())).uprice := x.price / x.weight choices := reverse(sortf(choices,4)) every (value := 0, x := !choices) do { if x.weight <= room then { printf("Take all of the %s (%r kg) worth %r\n",x.name,x.weight,x.price) value +:= x.price room -:= x.weight } else { fvalue := x.uprice * room printf("Take (%r kg) of the %s worth %r\n",room,x.name,fvalue) value +:= fvalue break }} printf("Total value of a full knapsack is %r\n",value)end record item(name,weight,price,uprice) procedure get_items() return [ item("beef", 3.8, 36), item("pork", 5.4, 43), item("ham", 3.6, 90), item("greaves", 2.4, 45), item("flitch", 4.0, 30), item("brawn", 2.5, 56), item("welt", 3.7, 67), item("salami", 3.0, 95), item("sausage", 5.9, 98) ]end Output: Take all of the salami (3.000000 kg) worth 95.000000 Take all of the ham (3.600000 kg) worth 90.000000 Take all of the brawn (2.500000 kg) worth 56.000000 Take all of the greaves (2.400000 kg) worth 45.000000 Take (3.500000 kg) of the welt worth 63.378378 Total value of a full knapsack is 349.378378 ## J We take as much as we can of the most valuable items first, and continue until we run out of space. Only one item needs to be cut. 'names numbers'=:|:;:;._2]0 :0beef 3.8 36pork 5.4 43ham 3.6 90greaves 2.4 45flitch 4.0 30brawn 2.5 56welt 3.7 67salami 3.0 95sausage 5.9 98)'weights prices'=:|:".numbersorder=: \:prices%weightstake=: 15&<.&.(+/$$ order{weightsresult=: (*take)#(order{names),.' ',.":,.take

This gives the result:

salami    3
ham     3.6
brawn   2.5
greaves 2.4
welt    3.5


For a total value of:

   +/prices * (take/:order) % weights349.378

See Knapsack_problem/Continuous/J for some comments on intermediate results...

Greedy solution.

 package hu.pj.alg.test; import hu.pj.alg.ContinuousKnapsack;import hu.pj.obj.Item;import java.util.*;import java.text.*; public class ContinousKnapsackForRobber {    final private double tolerance = 0.0005;     public ContinousKnapsackForRobber() {        ContinuousKnapsack cok = new ContinuousKnapsack(15); // 15 kg         // making the list of items that you want to bring        cok.add("beef",     3.8, 36); // marhahús        cok.add("pork",     5.4, 43); // disznóhús        cok.add("ham",      3.6, 90); // sonka        cok.add("greaves",  2.4, 45); // tepertő        cok.add("flitch",   4.0, 30); // oldalas        cok.add("brawn",    2.5, 56); // disznósajt        cok.add("welt",     3.7, 67); // hurka        cok.add("salami",   3.0, 95); // szalámi        cok.add("sausage",  5.9, 98); // kolbász         // calculate the solution:        List<Item> itemList = cok.calcSolution();         // write out the solution in the standard output        if (cok.isCalculated()) {            NumberFormat nf  = NumberFormat.getInstance();             System.out.println(                "Maximal weight           = " +                nf.format(cok.getMaxWeight()) + " kg"            );            System.out.println(                "Total weight of solution = " +                nf.format(cok.getSolutionWeight()) + " kg"            );            System.out.println(                "Total value (profit)     = " +                nf.format(cok.getProfit())            );            System.out.println();            System.out.println(                "You can carry the following materials " +                "in the knapsack:"            );            for (Item item : itemList) {                if (item.getInKnapsack() > tolerance) {                    System.out.format(                        "%1$-10s %2$-15s %3$-15s \n", nf.format(item.getInKnapsack()) + " kg ", item.getName(), "(value = " + nf.format(item.getInKnapsack() * (item.getValue() / item.getWeight())) + ")" ); } } } else { System.out.println( "The problem is not solved. " + "Maybe you gave wrong data." ); } } public static void main(String[] args) { new ContinousKnapsackForRobber(); } } // class  package hu.pj.alg; import hu.pj.obj.Item;import java.util.*; public class ContinuousKnapsack { protected List<Item> itemList = new ArrayList<Item>(); protected double maxWeight = 0; protected double solutionWeight = 0; protected double profit = 0; protected boolean calculated = false; public ContinuousKnapsack() {} public ContinuousKnapsack(double _maxWeight) { setMaxWeight(_maxWeight); } public List<Item> calcSolution() { int n = itemList.size(); setInitialStateForCalculation(); if (n > 0 && maxWeight > 0) { Collections.sort(itemList); for (int i = 0; (maxWeight - solutionWeight) > 0.0 && i < n; i++) { Item item = itemList.get(i); if (item.getWeight() >= (maxWeight - solutionWeight)) { item.setInKnapsack(maxWeight - solutionWeight); solutionWeight = maxWeight; profit += item.getInKnapsack() / item.getWeight() * item.getValue(); break; } else { item.setInKnapsack(item.getWeight()); solutionWeight += item.getInKnapsack(); profit += item.getValue(); } } calculated = true; } return itemList; } // add an item to the item list public void add(String name, double weight, double value) { if (name.equals("")) name = "" + (itemList.size() + 1); itemList.add(new Item(name, weight, value)); setInitialStateForCalculation(); } public double getMaxWeight() {return maxWeight;} public double getProfit() {return profit;} public double getSolutionWeight() {return solutionWeight;} public boolean isCalculated() {return calculated;} public void setMaxWeight(double _maxWeight) { maxWeight = Math.max(_maxWeight, 0); } // set the member with name "inKnapsack" by all items: private void setInKnapsackByAll(double inKnapsack) { for (Item item : itemList) item.setInKnapsack(inKnapsack); } // set the data members of class in the state of starting the calculation: protected void setInitialStateForCalculation() { setInKnapsackByAll(-0.0001); calculated = false; profit = 0.0; solutionWeight = 0.0; } } // class  package hu.pj.obj; public class Item implements Comparable { protected String name = ""; protected double weight = 0; protected double value = 0; protected double inKnapsack = 0; // the weight of item in solution public Item() {} public Item(Item item) { setName(item.name); setWeight(item.weight); setValue(item.value); } public Item(double _weight, double _value) { setWeight(_weight); setValue(_value); } public Item(String _name, double _weight, double _value) { setName(_name); setWeight(_weight); setValue(_value); } public void setName(String _name) {name = _name;} public void setWeight(double _weight) {weight = Math.max(_weight, 0);} public void setValue(double _value) {value = Math.max(_value, 0);} public void setInKnapsack(double _inKnapsack) { inKnapsack = Math.max(_inKnapsack, 0); } public void checkMembers() { setWeight(weight); setValue(value); setInKnapsack(inKnapsack); } public String getName() {return name;} public double getWeight() {return weight;} public double getValue() {return value;} public double getInKnapsack() {return inKnapsack;} // implementing of Comparable interface: public int compareTo(Object item) { int result = 0; Item i2 = (Item)item; double rate1 = value / weight; double rate2 = i2.value / i2.weight; if (rate1 > rate2) result = -1; // if greater, put it previously else if (rate1 < rate2) result = 1; return result; } } // class output: Maximal weight = 15 kg Total weight of solution = 15 kg Total value (profit) = 349,378 You can carry the following materials in the knapsack: 3 kg salami (value = 95) 3,6 kg ham (value = 90) 2,5 kg brawn (value = 56) 2,4 kg greaves (value = 45) 3,5 kg welt (value = 63,378) ## jq Works with: jq version 1.4 # continuous_knapsack(W) expects the input to be# an array of objects {"name": _, "weight": _, "value": _}# where "value" is the value of the given weight of the object. def continuous_knapsack(W): map( .price = (if .weight > 0 then (.value/.weight) else 0 end) ) | sort_by( .price ) | reverse | reduce .[] as$item      # state: [array, capacity]      ([[], W];       .[1] as $c | if$c <= 0 then .         else ( [$item.weight,$c] | min) as $min | [.[0] + [$item | (.weight = $min) | .value = (.price *$min)],                 ($c -$min) ]         end)  | .[1] as $remainder | .[0] | (.[] | {name, weight}), "Total value: \( map(.value) | add)", "Total weight: \(W -$remainder)" ;

def items: [ { "name": "beef",    "weight":  3.8, "value": 36}, { "name": "pork",    "weight":  5.4, "value": 43}, { "name": "ham",     "weight":  3.6, "value": 90}, { "name": "greaves", "weight":  2.4, "value": 45}, { "name": "flitch",  "weight":  4.0, "value": 30}, { "name": "brawn",   "weight":  2.5, "value": 56}, { "name": "welt",    "weight":  3.7, "value": 67}, { "name": "salami",  "weight":  3.0, "value": 95}, { "name": "sausage", "weight":  5.9, "value": 98} ]; items | continuous_knapsack(15)
Output:
$jq -r -c -n -f knapsack_continuous.jq{"name":"salami","weight":3}{"name":"ham","weight":3.6}{"name":"brawn","weight":2.5}{"name":"greaves","weight":2.4}{"name":"welt","weight":3.5000000000000004}Total value: 349.3783783783784Total weight: 15 ## Julia This solution is built around the immutable type KPCSupply, which holds an item's data including its unit value (uvalue). When the store's inventory is kept in this way, the solution to the continuous knapsack problem (provided by solve), is straightforward. The thief should pack as much of the highest value items as are available until full capacity is reached, topping off with as much of the last item as the knapsack will hold. (If the store contains less than the thief's knapsack will hold, he'll take the store's entire inventory.) An outer constructor method is used to create instances of KPCSupply when only the item, weight and value are supplied. The isless method is provided for KPCSupply objects so that items are transparently sorted by their unit value. KPCSupply supports any real type for weight, value and uvalue (though this simple implementation does not support mixed types or promotion). This solution uses Rational numbers to avoid rounding errors until the results are printed. Type and Functions: struct KPCSupply{T<:Real} item::String weight::T value::T uvalue::Tendfunction KPCSupply(item::AbstractString, weight::Real, value::Real) w, v = promote(weight, value) KPCSupply(item, w, v, v / w)end Base.show(io::IO, s::KPCSupply) = print(io, s.item, @sprintf " (%.2f kg, %.2f €, %.2f €/kg)" s.weight s.value s.uvalue)Base.isless(a::KPCSupply, b::KPCSupply) = a.uvalue < b.uvalue function solve(store::Vector{KPCSupply{T}}, capacity::Real) where T<:Real sack = similar(store, 0) # vector like store, but of length 0 kweight = zero(T) for s in sort(store, rev = true) if kweight + s.weight ≤ capacity kweight += s.weight push!(sack, s) else w = capacity - kweight v = w * s.uvalue push!(sack, KPCSupply(s.item, w, v, s.value)) break end end return sackend Main: store = [KPCSupply("beef", 38//10, 36), KPCSupply("pork", 54//10, 43), KPCSupply("ham", 36//10, 90), KPCSupply("greaves", 24//10, 45), KPCSupply("flitch", 4//1, 30), KPCSupply("brawn", 25//10, 56), KPCSupply("welt", 37//10, 67), KPCSupply("salami", 3//1, 95), KPCSupply("sausage", 59//10, 98)] sack = solve(store, 15)println("The store contains:\n - ", join(store, "\n - "))println("\nThe thief should take::\n - ", join(sack, "\n - "))@printf("\nTotal value in the sack: %.2f €\n", sum(getfield.(sack, :value))) Output: The store contains: - beef (3.80 kg, 36.00 €, 9.47 €/kg) - pork (5.40 kg, 43.00 €, 7.96 €/kg) - ham (3.60 kg, 90.00 €, 25.00 €/kg) - greaves (2.40 kg, 45.00 €, 18.75 €/kg) - flitch (4.00 kg, 30.00 €, 7.50 €/kg) - brawn (2.50 kg, 56.00 €, 22.40 €/kg) - welt (3.70 kg, 67.00 €, 18.11 €/kg) - salami (3.00 kg, 95.00 €, 31.67 €/kg) - sausage (5.90 kg, 98.00 €, 16.61 €/kg) The thief should take:: - salami (3.00 kg, 95.00 €, 31.67 €/kg) - ham (3.60 kg, 90.00 €, 25.00 €/kg) - brawn (2.50 kg, 56.00 €, 22.40 €/kg) - greaves (2.40 kg, 45.00 €, 18.75 €/kg) - welt (3.50 kg, 63.38 €, 67.00 €/kg) Total value in the sack: 349.38 € ## Kotlin // version 1.1.2 data class Item(val name: String, val weight: Double, val value: Double) val items = mutableListOf( Item("beef", 3.8, 36.0), Item("pork", 5.4, 43.0), Item("ham", 3.6, 90.0), Item("greaves", 2.4, 45.0), Item("flitch", 4.0, 30.0), Item("brawn", 2.5, 56.0), Item("welt", 3.7, 67.0), Item("salami", 3.0, 95.0), Item("sausage", 5.9, 98.0)) const val MAX_WEIGHT = 15.0 fun main(args: Array<String>) { // sort items by value per unit weight in descending order items.sortByDescending { it.value / it.weight } println("Item Chosen Weight Value Percentage") println("----------- ------ ------ ----------") var w = MAX_WEIGHT var itemCount = 0 var sumValue = 0.0 for (item in items) { itemCount++ if (item.weight <= w) { sumValue += item.value print("${item.name.padEnd(11)}     ${"%3.1f".format(item.weight)}${"%5.2f".format(item.value)}")           println("    100.00")        }        else {           val value  = Math.round((w / item.weight * item.value * 100.0)) / 100.0           val percentage = Math.round((w / item.weight * 10000.0)) / 100.0           sumValue += value           print("${item.name.padEnd(11)}${"%3.1f".format(w)}   ${"%5.2f".format(value)}") println("$percentage")           break        }        w -= item.weight        if (w == 0.0) break    }    println("-----------   ------ ------")    println("${itemCount} items 15.0${"%6.2f".format(sumValue)}")}
Output:
Item Chosen   Weight  Value  Percentage
-----------   ------ ------  ----------
salami          3.0   95.00    100.00
ham             3.6   90.00    100.00
brawn           2.5   56.00    100.00
greaves         2.4   45.00    100.00
welt            3.5   63.38     94.59
-----------   ------ ------
5 items        15.0  349.38

Translation of: Fortran

Using QuickSort (a generic form, non recursive)

## M2000 Interpreter

 Module Knapsack {      Form 60, 40      Cls 5, 0      Pen 14      Class Quick {      Private:            partition=lambda-> {                  Read &A(), p, r : i = p-1 : x=A(r)                  For j=p to r-1 {If .LE(A(j), x) Then i++:Swap A(i),A(j)                  } : Swap A(i+1), A(r) :  Push  i+2, i             }      Public:            LE=Lambda->Number<=Number            \\ module for strings erased here            Function quicksort {                 Read ref${ loop : If Stackitem() >= Stackitem(2) Then Drop 2 : if empty then {Break} else continue over 2,2 : call .partition(ref$) :shift 3                  }            }      }      Class Item {            name$, weight, aValue ' can't use Value has other meaning class: Module Item (.name$, .weight, .aValue) {}      }      Def Double max_weight=15, total_weight, total_value, frac      Def long I      Dim Items(1 to 9)      Flush  ' empty stack      \\ now fill stack      Data  "beef", 3.8, 36,"pork", 5.4, 43,"ham", 3.6, 90, "greaves", 2.4, 45, "flitch", 4, 30      Data "brawn", 2.5, 56, "welt", 3.7, 67, "salami", 3, 95, "sausage", 5.9, 98      For i=1 to 9 : Items(i)=Item(Letter$, Number, Number): Next i \\ Setup QuickSort Quick=Quick() Quick.LE=lambda (b, a)-> { =a.avalue/a.weight<=b.avalue/b.weight } Call Quick.QuickSort(&items(), 1, 9) \\ So now we have a sorted array of objects i=0 \\ Setup console to print Dim Back(-1 to 0) Back(-1)=#666666, #444444 Alter=True \\$("0.00", 20) Set number rounding for print, and 14 chars column width      \\ $(2) set center justify for non proportional print \\$(0) set default - strings justify left, numbers right      Print  $("0.00", 20),$(2),"", "Knapsack"      Pen 0 {            Print @(pos, row,width,row+1, 7),"Item", "Weight (Kg)", "Price (value)", $(0) } While i<Len(Items()) and total_weight<max_weight { i++ if total_weight+items(i).weight<max_weight Then { total_weight+=items(i).weight total_value+=items(i).avalue WriteItem(i, 1) } Else { frac=(max_weight-total_weight)/items(i).weight total_weight+=items(i).weight*frac total_value+=items(i).avalue*frac WriteItem(i, frac ) } } Print Pen 0 { Print @(pos+1, row,width,row+1, 7, 7), "Total Weight",total_weight Print @(pos+1, row,width,row+1, 7, 7), "Total Value", total_value } End Sub WriteItem(i, frac) For Items(i) { Print @(pos+1, row,width,row+1, back(alter), 14), .name$, .weight*frac, .avalue*frac                  Alter~            }      End Sub}Knapsack 

Output the same as other examples, with some color.

## Mathematica

The problem is solved by sorting the original table by price to weight ratio, finding the accumlated weight, and the index of the item which exedes the carrying capacity (overN) The output is then all items prior to this one, along with that item corrected for it's excess weighter (overW)

Knapsack[shop_, capacity_] :=  Block[{sortedTable, overN, overW, output}, sortedTable = SortBy[{#1, #2, #3, #3/#2} & @@@ shop, -#[[4]] &]; overN = Position[Accumulate[sortedTable[[1 ;;, 2]]], a_ /; a > capacity, 1,1][[1, 1]]; overW = Accumulate[sortedTable[[1 ;;, 2]]][[overN]] - capacity;  output = [email protected][[Ordering[sortedTable[[1 ;;, 4]], -overN]]]; output[[-1, 2]] = output[[-1, 2]] - overW; output[[-1, 3]] = output[[-1, 2]] output[[-1, 4]]; Append[output[[1 ;;, 1 ;; 3]], {"Total",Sequence @@ Total[output[[1 ;;, 2 ;; 3]]]}]]

A test using the specified data:

weightPriceTable = {{"beef", 3.8, 36}, {"pork", 5.4, 43}, {"ham", 3.6, 90}, {"greaves", 2.4, 45}, {"flitch", 4., 30}, {"brawn", 2.5, 56}, {"welt", 3.7, 67}, {"salami", 3., 95}, {"sausage",  5.9, 98}};carryCapacity = 15;Knapsack[weightPriceTable, carryCapacity] // Grid salami	3.	95ham	3.6	90brawn	2.5	56greaves	2.4	45welt	3.5	63.3784Total	15.	349.378 

## Mathprog

/*Knapsack   This model finds the optimal packing of a knapsack   Nigel_Galloway  January 10th., 2012*/set Items;param weight{t in Items};param value{t in Items}; var take{t in Items}, >=0, <=weight[t]; knap_weight : sum{t in Items} take[t] <= 15; maximize knap_value: sum{t in Items} take[t] * (value[t]/weight[t]); data; param : Items          : weight   value :=        beef 	          3.8     36            pork 	          5.4	  43	        ham 		  3.6	  90            greaves           2.4     45        flitch 	          4.0     30        brawn 	          2.5     56        welt 	          3.7     67        salami 	          3.0     95        sausage           5.9     98                                       ;                                                        end;

The solution is here at Knapsack problem/Continuous/Mathprog.

## OCaml

 This example does not show the output mentioned in the task description on this page (or a page linked to from here). reason Please ensure that it meets all task requirements and remove this message. Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution.

let items =  [ "beef",     3.8,  36;    "pork",     5.4,  43;    "ham",      3.6,  90;    "greaves",  2.4,  45;    "flitch",   4.0,  30;    "brawn",    2.5,  56;    "welt",     3.7,  67;    "salami",   3.0,  95;    "sausage",  5.9,  98; ] let () =  let items = List.map (fun (name, w, p) -> (name, w, p, float p /. w)) items in  let items = List.sort (fun (_,_,_,v1) (_,_,_,v2) -> compare v2 v1) items in  let rec loop acc weight = function  | ((_,w,_,_) as item) :: tl ->      if w +. weight > 15.0      then (weight, acc, item)      else loop (item::acc) (w +. weight) tl  | [] -> assert false  in  let weight, res, (last,w,p,v) = loop [] 0.0 items in  print_endline "    Items  Weight Price";  let price =    List.fold_left (fun price (name,w,p,_) ->      Printf.printf " %7s: %6.2f %3d\n" name w p;      (p + price)    ) 0 res  in  let rem_weight = 15.0 -. weight in  let last_price = v *. rem_weight in  Printf.printf " %7s: %6.2f %6.2f\n" last rem_weight last_price;  Printf.printf " Total Price: %.3f\n" (float price +. last_price);;;

## Oforth

[   [ "beef",    3.8, 36 ], [ "pork",    5.4, 43 ], [ "ham",     3.6, 90 ],   [ "greaves", 2.4, 45 ], [ "flitch",  4.0, 30 ], [ "brawn",  	2.5, 56 ],   [ "welt",  	3.7, 67 ], [ "salami",  3.0, 95 ], [ "sausage", 5.9, 98 ]] const: Items : rob| item value |  0.0 ->value  15.0 #[ dup second swap third / ] Items sortBy forEach: item [     dup 0.0 == ifTrue: [ return ]     dup item second >= ifTrue: [         "Taking" . item first . " :" . item second dup .cr -        item third value + ->value continue         ]     "And part of" . item first . " :" . dup .cr     item third * item second / value + "Total value :" . .cr break     ] ;
Output:
>rob
Taking salami  : 3
Taking ham  : 3.6
Taking brawn  : 2.5
Taking greaves  : 2.4
And part of welt  : 3.5
Total value : 349.378378378378
ok


## ooRexx

### version 1

/*--------------------------------------------------------------------* 20.09.2014 Walter Pachl translated from REXX version 2*            utilizing ooRexx features like objects, array(s) and sort*-------------------------------------------------------------------*/  maxweight = 15.0  items=.array~new  items~append(.item~new('beef',    3.8, 36.0))  items~append(.item~new('pork',    5.4, 43.0))  items~append(.item~new('ham',     3.6, 90.0))  items~append(.item~new('greaves', 2.4, 45.0))  items~append(.item~new('flitch',  4.0, 30.0))  items~append(.item~new('brawn',   2.5, 56.0))  items~append(.item~new('welt',    3.7, 67.0))  items~append(.item~new('salami',  3.0, 95.0))  items~append(.item~new('sausage', 5.9, 98.0))   /* show the input */  Say '#    vpu name    weight   value'  i=0  Do x over items    i+=1    Say i format(x~vpu,2,3) left(x~name,7) format(x~weight,2,3) format(x~value,3,3)    End   /* sort the items by descending value per unit of weight */  items~sortWith(.DescendingComparator~new)   total_weight=0  total_value =0  Say ' '  Say 'Item     Weight   Value'  i=0  Do x over items    i+=1    Parse Var item.i name '*' weight '*' value    if total_weight+x~weight<maxweight then Do      total_weight = total_weight + x~weight      total_value  = total_value + x~value      Say left(x~name,7) format(x~weight,3,3) format(x~value,3,3)      End    Else Do      weight=maxweight-total_weight      value=weight*x~vpu      total_value = total_value + value      total_weight = maxweight      Say left(x~name,7) format(weight,3,3) format(value,3,3)      Leave      End    End  Say copies('-',23)  Say 'total ' format(total_weight,4,3) format(total_value,3,3)  Exit ::class item  ::attribute vpu  ::attribute name  ::attribute weight  ::attribute value ::method init  Expose vpu  Use Arg name, weight, value  self~name=name  self~weight=weight  self~value=value  self~vpu=value/weight ::CLASS 'DescendingComparator' MIXINCLASS Comparator::METHOD compareuse strict arg a, bSelect  When (a~vpu)<(b~vpu) Then res='1'  Otherwise res='-1'  EndReturn res
Output:
#    vpu name    weight   value
1  9.474 beef     3.800  36.000
2  7.963 pork     5.400  43.000
3 25.000 ham      3.600  90.000
4 18.750 greaves  2.400  45.000
5  7.500 flitch   4.000  30.000
6 22.400 brawn    2.500  56.000
7 18.108 welt     3.700  67.000
8 31.667 salami   3.000  95.000
9 16.610 sausage  5.900  98.000

Item     Weight   Value
salami    3.000  95.000
ham       3.600  90.000
brawn     2.500  56.000
greaves   2.400  45.000
welt      3.500  63.378
-----------------------
total    15.000 349.378

### version 2

/*--------------------------------------------------------------------* 20.09.2014 Walter Pachl translated from REXX version 2*            utilizing ooRexx features like objects, array(s) and sort* 21.09.2014 simplified (courtesy Rony Flatscher)*            (sort uses now the method "compareTo" defined for item)*-------------------------------------------------------------------*/  maxweight = 15.0  items=.array~new  items~append(.item~new('beef',    3.8, 36.0))  items~append(.item~new('pork',    5.4, 43.0))  items~append(.item~new('ham',     3.6, 90.0))  items~append(.item~new('greaves', 2.4, 45.0))  items~append(.item~new('flitch',  4.0, 30.0))  items~append(.item~new('brawn',   2.5, 56.0))  items~append(.item~new('welt',    3.7, 67.0))  items~append(.item~new('salami',  3.0, 95.0))  items~append(.item~new('sausage', 5.9, 98.0))   /* show the input */  Say '#    vpu name    weight   value'  i=0  Do x over items    i+=1    Say i format(x~vpu,2,3) left(x~name,7) format(x~weight,2,3) format(x~value,3,3)    End   /* sort the items by descending value per unit of weight */  items~sort          /* using the method compareTo used for item */   total_weight=0  total_value =0  Say ' '  Say 'Item     Weight   Value'  i=0  Do x over items    i+=1    Parse Var item.i name '*' weight '*' value    if total_weight+x~weight<maxweight then Do      total_weight = total_weight + x~weight      total_value  = total_value + x~value      Say left(x~name,7) format(x~weight,3,3) format(x~value,3,3)      End    Else Do      weight=maxweight-total_weight      value=weight*x~vpu      total_value = total_value + value      total_weight = maxweight      Say left(x~name,7) format(weight,3,3) format(value,3,3)      Leave      End    End  Say copies('-',23)  Say 'total ' format(total_weight,4,3) format(total_value,3,3)  Exit ::class item  ::attribute vpu  ::attribute name  ::attribute weight  ::attribute value ::method init  Expose vpu  Use Arg name, weight, value  self~name=name  self~weight=weight  self~value=value  self~vpu=value/weight ::method compareTo   -- default sort order  Expose vpu  use Arg other  return -sign(vpu - other~vpu)

Output is the same as for version 1.

## Perl

my @items = sort { $b->[2]/$b->[1] <=> $a->[2]/$a->[1] }(        [qw'beef    3.8 36'],        [qw'pork    5.4 43'],        [qw'ham     3.6 90'],        [qw'greaves 2.4 45'],        [qw'flitch  4.0 30'],        [qw'brawn   2.5 56'],        [qw'welt    3.7 67'],        [qw'salami  3.0 95'],        [qw'sausage 5.9 98'],); my ($limit,$value) = (15, 0); print "item   fraction weight value\n";for (@items) {        my $ratio =$_->[1] > $limit ?$limit/$_->[1] : 1; print "$_->[0]\t";        $value +=$_->[2] * $ratio;$limit -= $_->[1]; if ($ratio == 1) {                print "  all\t$_->[1]\t$_->[2]\n";        } else {                printf "%5.3f   %s   %8.3f\n", $ratio,$_->[1] * $ratio,$_->[2] * $ratio; last; }} print "-" x 40, "\ntotal value:$value\n"; 
Output:
item   fraction weight value
salami    all   3.0     95
ham       all   3.6     90
brawn     all   2.5     56
greaves   all   2.4     45
welt    0.946   3.5     63.378
----------------------------------------
total value: 349.378378378378


## Perl 6

Works with: rakudo version 2015-09-16

This Solutions sorts the item by WEIGHT/VALUE

class KnapsackItem {  has $.name; has$.weight is rw;  has $.price is rw; has$.ppw;   method new (Str $n, Rat$w, Int $p) { self.bless(:name($n), :weight($w), :price($p), :ppw($w/$p))  }   method cut-maybe ($max-weight) { return False if$max-weight > $.weight;$.price = $max-weight /$.ppw;    $.weight =$.ppw * $.price; return True; } method gist () { sprintf "%8s %1.2f %3.2f",$.name,                                $.weight,$.price }} my $max-w = 15;say "Item Portion Value"; .say for gather for < beef 3.8 36 pork 5.4 43 ham 3.6 90 greaves 2.4 45 flitch 4.0 30 brawn 2.5 56 welt 3.7 67 salami 3.0 95 sausage 5.9 98 > ==> map({ KnapsackItem.new($^a, $^b,$^c) })        ==> sort *.ppw    {        my $last-one = .cut-maybe($max-w);        take $_;$max-w -= .weight;        last if $last-one; } Output: %perl6 knapsack_continous.p6 Item Portion Value salami 3.00 95.00 ham 3.60 90.00 brawn 2.50 56.00 greaves 2.40 45.00 welt 3.50 63.38  ## Phix constant meats = {--Item Weight (kg) Price (Value){"beef", 3.8, 36},{"pork", 5.4, 43},{"ham", 3.6, 90},{"greaves", 2.4, 45},{"flitch", 4.0, 30},{"brawn", 2.5, 56},{"welt", 3.7, 67},{"salami", 3.0, 95},{"sausage", 5.9, 98}} function by_weighted_value(integer i, j) atom {?,weighti,pricei} = meats[i], {?,weightj,pricej} = meats[j] return compare(pricej/weightj,pricei/weighti)end function sequence tags = custom_sort(routine_id("by_weighted_value"),tagset(length(meats))) atom w = 15, worth = 0for i=1 to length(tags) do object {desc,wi,price} = meats[tags[i]] atom c = min(wi,w) printf(1,"%3.1fkg%s of %s\n",{c,iff(c=wi?" (all)":""),desc}) worth += (c/wi)*price w -= c if w=0 then exit end ifend forprintf(1,"Total value: %f\n",{worth}) Output: 3.0kg (all) of salami 3.6kg (all) of ham 2.5kg (all) of brawn 2.4kg (all) of greaves 3.5kg of welt Total value: 349.378378  ## PicoLisp (scl 2) (de *Items ("beef" 3.8 36.0) ("pork" 5.4 43.0) ("ham" 3.6 90.0) ("greaves" 2.4 45.0) ("flitch" 4.0 30.0) ("brawn" 2.5 56.0) ("welt" 3.7 67.0) ("salami" 3.0 95.0) ("sausage" 5.9 98.0) ) (let K (make (let Weight 0 (for I (by '((L) (*/ (caddr L) -1.0 (cadr L))) sort *Items) (T (= Weight 15.0)) (inc 'Weight (cadr I)) (T (> Weight 15.0) (let W (- (cadr I) Weight -15.0) (link (list (car I) W (*/ W (caddr I) (cadr I)))) ) ) (link I) ) ) ) (for I K (tab (3 -9 8 8) NIL (car I) (format (cadr I) *Scl) (format (caddr I) *Scl) ) ) (tab (12 8 8) NIL (format (sum cadr K) *Scl) (format (sum caddr K) *Scl) ) ) Output:  salami 3.00 95.00 ham 3.60 90.00 brawn 2.50 56.00 greaves 2.40 45.00 welt 3.50 63.38 15.00 349.38 ## PL/I *process source xref attributes; KNAPSACK_CONTINUOUS: Proc Options(main); /*-------------------------------------------------------------------- * 19.09.2014 Walter Pachl translated from FORTRAN *-------------------------------------------------------------------*/ Dcl (divide,float,hbound,repeat) Builtin; Dcl SYSPRINT Print; Dcl maxweight Dec Fixed(15,3); maxweight = 15.0; Dcl (total_weight,total_value) Dec Fixed(15,3) Init(0); Dcl vpu Dec Float(15); Dcl (i,j) Bin Fixed(31); Dcl 1 item(9), 2 name Char(7), 2 weight Dec Fixed(15,3), 2 value Dec Fixed(15,3); Dcl temp Like item; Call init_item(1,'beef', 3.8, 36.0); Call init_item(2,'pork', 5.4, 43.0); Call init_item(3,'ham', 3.6, 90.0); Call init_item(4,'greaves', 2.4, 45.0); Call init_item(5,'flitch', 4.0, 30.0); Call init_item(6,'brawn', 2.5, 56.0); Call init_item(7,'welt', 3.7, 67.0); Call init_item(8,'salami', 3.0, 95.0); Call init_item(9,'sausage', 5.9, 98.0); /* sort item in descending order of their value per unit weight */ do i = 2 To hbound(item); j = i - 1; temp = item(i); do while(j>=1&item(j).value/item(j).weight<temp.value/temp.weight); item(j+1) = item(j); j = j - 1; end; item(j+1) = temp; end; Do i=1 To hbound(item); Put Edit(i,item(i))(Skip,f(2),x(2),a(7),2(f(8,3))); End; i = 0; Put Skip; Put Edit('Item Weight Value')(Skip,a); do i=1 By 1 while(i < hbound(item) & total_weight < maxweight); if total_weight+item(i).weight < maxweight then Do; total_weight = total_weight + item(i).weight; total_value = total_value + item(i).value; Put Edit(item(i))(Skip,a(7),2(f(8,3))); End; Else Do; vpu=divide(item(i).value,item(i).weight,15,8); item(i).weight=maxweight-total_weight; item(i).value=float(item(i).weight)*vpu; total_value = total_value + item(i).value; total_weight = total_weight + item(i).weight; Put Edit(item(i).name, item(i).weight, item(i).value) (Skip,a(7),2(f(8,3))); Leave Loop; end; end; Put Edit(repeat('-',22))(Skip,a); Put Edit('total',total_weight, total_value)(Skip,a(6),f(9,3),f(8,3)); init_item: Proc(i,name,weight,value); Dcl i Bin Fixed(31); Dcl name Char(*); Dcl (weight,value) Dec Fixed(15,3); item(i).name = name; item(i).weight = weight; item(i).value = value; End; End; Output:  1 salami 3.000 95.000 2 ham 3.600 90.000 3 brawn 2.500 56.000 4 greaves 2.400 45.000 5 welt 3.700 67.000 6 sausage 5.900 98.000 7 beef 3.800 36.000 8 pork 5.400 43.000 9 flitch 4.000 30.000 Item Weight Value salami 3.000 95.000 ham 3.600 90.000 brawn 2.500 56.000 greaves 2.400 45.000 welt 3.500 63.378 ----------------------- total 15.000 349.378 ## Prolog Works with SWI-Prolog and library(simplex) written by Markus Triska :- use_module(library(simplex)).% tuples (name, weights, value).knapsack :- L = [( beef, 3.8, 36), ( pork, 5.4, 43), ( ham, 3.6, 90), ( greaves, 2.4, 45), ( flitch, 4.0, 30), ( brawn, 2.5, 56), ( welt, 3.7, 67), ( salami, 3.0, 95), ( sausage, 5.9, 98)], gen_state(S0), length(L, N), numlist(1, N, LN), ( ( create_constraint_N(LN, L, S0, S1, [], LW, [], LV), constraint(LW =< 15.0, S1, S2), maximize(LV, S2, S3) )), compute_lenword(L, 0, Len), sformat(A1, '~~w~~t~~~w|', [Len]), sformat(A2, '~~t~~2f~~~w|', [10]), sformat(A3, '~~t~~2f~~~w|', [10]), print_results(S3, A1,A2,A3, L, LN, 0, 0). create_constraint_N([], [], S, S, LW, LW, LV, LV). create_constraint_N([HN|TN], [(_, W, V) | TL], S1, SF, LW, LWF, LV, LVF) :- constraint([x(HN)] >= 0, S1, S2), constraint([x(HN)] =< W, S2, S3), X is V/W, create_constraint_N(TN, TL, S3, SF, [x(HN) | LW], LWF, [X * x(HN) | LV], LVF). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%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, A1, A2, A3, [], [], WM, VM) :- sformat(W1, A1, [' ']), sformat(W2, A2, [WM]), sformat(W3, A3, [VM]), format('~w~w~w~n', [W1,W2,W3]). print_results(S, A1, A2, A3, [(Name, W, V)|T], [N|TN], W1, V1) :- variable_value(S, x(N), X), ( X = 0 -> W1 = W2, V1 = V2 ; sformat(S1, A1, [Name]), sformat(S2, A2, [X]), Vtemp is X * V/W, sformat(S3, A3, [Vtemp]), format('~w~w~w~n', [S1,S2,S3]), W2 is W1 + X, V2 is V1 + Vtemp ), print_results(S, A1, A2, A3, T, TN, W2, V2).  Output :  ?- knapsack. ham 3.60 90.00 greaves 2.40 45.00 brawn 2.50 56.00 welt 3.50 63.38 salami 3.00 95.00 15.00 349.38 true . ## PureBasic Using the greedy algorithm. Structure item name.s weight.f ;units are kilograms (kg) Value.f vDensity.f ;the density of the value, i.e. value/weight, and yes I made up the term ;)EndStructure #maxWeight = 15Global itemCount = 0 ;this will be increased as needed to match actual countGlobal Dim items.item(itemCount) Procedure addItem(name.s, weight.f, Value.f) If itemCount >= ArraySize(items()) Redim items.item(itemCount + 10) EndIf With items(itemCount) \name = name \weight = weight \Value = Value If Not \weight \vDensity = \Value Else \vDensity = \Value / \weight EndIf EndWith itemCount + 1EndProcedure ;build item listaddItem("beef", 3.8, 36)addItem("pork", 5.4, 43)addItem("ham", 3.6, 90)addItem("greaves", 2.4, 45)addItem("flitch", 4.0, 30)addItem("brawn", 2.5, 56)addItem("welt", 3.7, 67)addItem("salami", 3.0, 95)addItem("sausage", 5.9, 98)SortStructuredArray(items(), #PB_Sort_descending, OffsetOf(item\vDensity), #PB_Sort_Float, 0, itemCount - 1) Define TotalWeight.f, TotalValue.f, iNewList knapsack.item()For i = 0 To itemCount If TotalWeight + items(i)\weight < #maxWeight AddElement(knapsack()) knapsack() = items(i) TotalWeight + items(i)\weight TotalValue + items(i)\Value Else AddElement(knapsack()) knapsack() = items(i) knapsack()\weight = #maxWeight - TotalWeight knapsack()\Value = knapsack()\weight * knapsack()\vDensity TotalWeight = #maxWeight TotalValue + knapsack()\Value Break EndIf Next If OpenConsole() PrintN(LSet("Maximal weight", 26, " ") + "= " + Str(#maxWeight) + " kg") PrintN(LSet("Total weight of solution", 26, " ") + "= " + Str(#maxWeight) + " kg") PrintN(LSet("Total value", 26, " ") + "= " + StrF(TotalValue, 3) + " " + #CRLF$)  PrintN("You can carry the following materials in the knapsack: ")  ForEach knapsack()    PrintN(RSet(StrF(knapsack()\weight, 1), 5, " ") + " kg  " + LSet(knapsack()\name, 10, " ") + "  (Value = " + StrF(knapsack()\Value, 3) + ")")  Next    Print(#CRLF$+ #CRLF$ + "Press ENTER to exit")  Input()  CloseConsole()EndIf 

Sample output:

Maximal weight            = 15 kg
Total weight of solution  = 15 kg
Total value               = 349.378

You can carry the following materials in the knapsack:
3.0 kg  salami      (Value = 95.000)
3.6 kg  ham         (Value = 90.000)
2.5 kg  brawn       (Value = 56.000)
2.4 kg  greaves     (Value = 45.000)
3.5 kg  welt        (Value = 63.378)

## Python

I think this greedy algorithm of taking the largest amounts of items ordered by their value per unit weight is maximal:

#        NAME, WEIGHT, VALUE (for this weight)items = [("beef",    3.8, 36.0),         ("pork",    5.4, 43.0),         ("ham",     3.6, 90.0),         ("greaves", 2.4, 45.0),         ("flitch",  4.0, 30.0),         ("brawn",   2.5, 56.0),         ("welt",    3.7, 67.0),         ("salami",  3.0, 95.0),         ("sausage", 5.9, 98.0)] MAXWT = 15.0 sorted_items = sorted(((value/amount, amount, name)                       for name, amount, value in items),                      reverse = True)wt = val = 0bagged = []for unit_value, amount, name in sorted_items:    portion = min(MAXWT - wt, amount)    wt     += portion    addval  = portion * unit_value    val    += addval    bagged += [(name, portion, addval)]    if wt >= MAXWT:        break print("    ITEM   PORTION VALUE")print("\n".join("%10s %6.2f %6.2f" % item for item in bagged))print("\nTOTAL WEIGHT: %5.2f\nTOTAL VALUE: %5.2f" % (wt, val))

Sample Output

    ITEM   PORTION VALUE
salami   3.00  95.00
ham   3.60  90.00
brawn   2.50  56.00
greaves   2.40  45.00
welt   3.50  63.38

TOTAL WEIGHT: 15.00
TOTAL VALUE: 349.38

## R

Translated into r-script by Shana White ([email protected]) from pseudocode found in 'Algorithms: Sequential Parallel and Distributed', by Kenneth A. Berman and Jerome L. Paul

 knapsack<- function(Value, Weight, Objects, Capacity){  Fraction = rep(0, length(Value))  Cost = Value/Weight  #print(Cost)  W = Weight[order(Cost, decreasing = TRUE)]  Obs = Objects[order(Cost, decreasing = TRUE)]  Val = Value[order(Cost, decreasing = TRUE)]  #print(W)  RemainCap = Capacity  i = 1  n = length(Cost)  if (W[1] <= Capacity){    Fits <- TRUE  }  else{    Fits <- FALSE   }  while (Fits && i <= n ){    Fraction[i] <- 1    RemainCap <- RemainCap - W[i]    i <- i+1    #print(RemainCap)    if (W[i] <= RemainCap){      Fits <- TRUE    }    else{      Fits <- FALSE    }  }  #print(RemainCap)  if (i <= n){    Fraction[i] <- RemainCap/W[i]  }  names(Fraction) = Obs  Quantity_to_take = W*Fraction  Total_Value = sum(Val*Fraction)  print("Fraction of available quantity to take:")  print(round(Fraction, 3))  print("KG of each to take:")  print(Quantity_to_take)  print("Total value of tasty meats:")  print(Total_Value)}

Sample Input

o = c("beef", "pork", "ham", "greaves", "flitch", "brawn", "welt", "salami", "sausage")
w = c(3.8,5.4,3.6,2.4,4.0,2.5,3.7,3.0,5.9)
v = c(36,43,90,45,30,56,67,95,98)
knapsack(v, w, o, 15)

Sample Output

[1] "Fraction of available quantity to take:"
salami     ham   brawn greaves    welt sausage    beef    pork  flitch
1.000   1.000   1.000   1.000   0.946   0.000   0.000   0.000   0.000
[1] "KG of each to take:"
salami     ham   brawn greaves    welt sausage    beef    pork  flitch
3.0     3.6     2.5     2.4     3.5     0.0     0.0     0.0     0.0
[1] "Total value of tasty meats:"
[1] 349.3784

## Racket

#lang racket(define shop-inventory  '((beef 	3.8 	36)    (pork 	5.4 	43)    (ham 	3.6 	90)    (greaves 	2.4 	45)    (flitch 	4.0 	30)    (brawn 	2.5 	56)    (welt 	3.7 	67)    (salami 	3.0 	95)    (sausage 	5.9 	98)))  (define (continuous-knapsack shop sack sack-capacity sack-total-value)  ;; solved by loading up on the highest value item...  (define (value/kg item) (/ (third item) (second item)))  (if (zero? sack-capacity)      (values (reverse sack) sack-total-value)      (let* ((best-value-item (argmax value/kg shop))             (bvi-full-weight (second best-value-item))             (amount-can-take (min sack-capacity bvi-full-weight))             (bvi-full-value  (third best-value-item))             (bvi-taken-value (* bvi-full-value (/ amount-can-take bvi-full-weight))))        (continuous-knapsack (remove best-value-item shop)                             (cons (list (first best-value-item)                                         (if (= amount-can-take bvi-full-weight)                                             'all-of amount-can-take) bvi-taken-value)                                   sack)                             (- sack-capacity amount-can-take)                             (+ sack-total-value bvi-taken-value))))) (define (report-knapsack sack total-value)  (for-each (lambda (item)               (if (eq? 'all-of (second item))                  (printf "Take all of the ~a (for ~a)~%"                          (first item) (third item))                  (printf "Take ~a of the ~a (for ~a)~%"                          (real->decimal-string (second item))                          (first item)                          (real->decimal-string (third item)))))            sack)  (printf "For a grand total of: ~a" (real->decimal-string total-value))) (call-with-values (lambda () (continuous-knapsack shop-inventory null 15 0))                  report-knapsack)
Output:
Take all of the salami (for 95.0)
Take all of the ham (for 90.0)
Take all of the brawn (for 56.0)
Take all of the greaves (for 45.0)
Take 3.50 of the welt (for 63.38)
For a grand total of: 349.38

## REXX

### version 1

Originally used the Fortran program as a prototype.
Some amount of code was added to format the output better.

/*REXX pgm solves the continuous burglar's knapsack problem; items with weight and value*/@.=               /*═══════  name    weight  value  ══════*/                     @.1 = 'flitch     4       30  '                     @.2 = 'beef       3.8     36  '                     @.3 = 'pork       5.4     43  '                     @.4 = 'greaves    2.4     45  '                     @.5 = 'brawn      2.5     56  '                     @.6 = 'welt       3.7     67  '                     @.7 = 'ham        3.6     90  '                     @.8 = 'salami     3       95  '                     @.9 = 'sausage    5.9     98  'parse arg maxW d .                               /*get possible arguments from the C.L. */if maxW=='' | maxW==","  then maxW=15            /*the burglar's knapsack maximum weight*/if    d=='' |    d==","  then    d= 3            /*# decimal digits shown with  FORMAT. */wL=d+length('weight');   nL=d+length("total weight");    vL=d+length('value')  /*lengths*/totW=0;  totV=0                                  /* [↓]  assign item to separate lists. */                 do #=1  while @.#\=='';    parse var @.# n.# w.# v.# .;   end;      #=#-1call show  'unsorted item list'                  /*display the header and the   @  list.*/call sortD                                       /*invoke descemdomg sort for:  n. w. v.*/call hdr "burglar's knapsack contents"                 do j=1  for #      while totW<maxW;   f=1        /*process the items.  */                 if totW+w.j>=maxW  then f=(maxW-totW)/w.j        /*calculate fraction. */                 totW=totW+w.j*f;        totV=totV+v.j*f          /*add it ───► totals. */                 call syf  left(word('{all}',1+(f\==1)),5)   n.j,  w.j*f,  v.j*f                 end   /*j*/                     /* [↑]  display item, maybe with {all} */call sep;  say                                   /* [↓]   $suppresses trailing zeroes.*/call sy left('total weight', nL, "─"),$(format(totW,,d))call sy  left('total  value', nL, "─"),      ,       $(format(totV,,d))exit /*stick a fork in it, we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/sortD: do s=2 to #; a=n.s; !=w.s; u=v.s /* [↓] this is a descending sort. */ do k=s-1 by -1 to 1 while v.k/w.k<u/!; ?=k+1; n.?=n.k; w.?=w.k; v.?=v.k; end ?=k+1; n.?=a; w.?=!; v.?=u end /*s*/; return /* ↑↑↑ algorithm is OK for small arrays*//*──────────────────────────────────────────────────────────────────────────────────────*/hdr: say; say; say center(arg(1),50,'─'); say; call title; call sep; returnsep: call sy copies('═', nL), copies("═", wL), copies('═', vL); returnshow: call hdr arg(1); do j=1 for #; call syf n.j, w.j, v.j; end; returnsy: say left('',9) left(arg(1),nL) right(arg(2),wL) right(arg(3),vL); returnsyf: call sy arg(1),$(format(arg(2), , d)),    $(format(arg(3), , d)); returntitle: call sy center('item',nL), center("weight", wL), center('value', vL); return$:     parse arg x;if pos(.,x)>1 then x=left(strip(strip(x,'T',0),,.),length(x)); return x

output   using the default inputs of:   15   3

────────────────unsorted item list────────────────

item        weight    value
═══════════════ ═════════ ════════
flitch              4       30
beef                3.8     36
pork                5.4     43
greaves             2.4     45
brawn               2.5     56
welt                3.7     67
ham                 3.6     90
salami              3       95
sausage             5.9     98

───────────burglar's knapsack contents────────────

item        weight    value
═══════════════ ═════════ ════════
{all} salami        3       95
{all} ham           3.6     90
{all} brawn         2.5     56
{all} greaves       2.4     45
welt          3.5     63.378
═══════════════ ═════════ ════════

total weight───    15
total  value───            349.378


### version 2

 /*-------------------------------------------------------------------- * 19.09.2014 Walter Pachl translated from FORTRAN * While this program works with all REXX interpreters, * see section ooRexx for a version that utilizes the ooRexx features *-------------------------------------------------------------------*/  maxweight = 15.0  input.0=0  Call init_input 'beef',    3.8, 36.0  Call init_input 'pork',    5.4, 43.0  Call init_input 'ham',     3.6, 90.0  Call init_input 'greaves', 2.4, 45.0  Call init_input 'flitch',  4.0, 30.0  Call init_input 'brawn',   2.5, 56.0  Call init_input 'welt',    3.7, 67.0  Call init_input 'salami',  3.0, 95.0  Call init_input 'sausage', 5.9, 98.0   /* sort the items by descending value per unit of weight */  Do i = 1 to input.0    Parse Var input.i name '*' weight '*' value    vpu=value/weight;    If i=1 Then Do      item.0=1      item.1=input.1      vpu.1=vpu      End    Else Do      Do ii=1 To item.0        If vpu.ii<vpu Then          Leave        End      Do jj=item.0 To ii By -1        jj1=jj+1        item.jj1=item.jj        vpu.jj1=vpu.jj        End      item.ii=input.i      vpu.ii=vpu      item.0=item.0+1      End    End  Say '#    vpu name    weight   value'  Do i=1 To item.0    Parse Var item.i name '*' weight '*' value    Say i format(vpu.i,2,3) left(name,7) format(weight,2,3) format(value,3,3)    End   total_weight=0  total_value =0  Say ' '  Say 'Item     Weight   Value'  Do i=1 To item.0    Parse Var item.i name '*' weight '*' value    if total_weight+weight < maxweight then Do      total_weight = total_weight + weight      total_value  = total_value + value      Say left(name,7) format(weight,3,3) format(value,3,3)      End    Else Do      weight=maxweight-total_weight      value=weight*vpu.i      total_value = total_value + value      total_weight = maxweight      Say left(name,7) format(weight,3,3) format(value,3,3)      Leave      End    End  Say copies('-',23)  Say 'total ' format(total_weight,4,3) format(total_value,3,3)  Exit init_input: Procedure Expose input.  Parse Arg name,weight,value  i=input.0+1  input.i=name'*'weight'*'value  input.0=i  Return
Output:
#    vpu name    weight   value
1 31.667 salami   3.000  95.000
2 25.000 ham      3.600  90.000
3 22.400 brawn    2.500  56.000
4 18.750 greaves  2.400  45.000
5 18.108 welt     3.700  67.000
6 16.610 sausage  5.900  98.000
7  9.474 beef     3.800  36.000
8  7.963 pork     5.400  43.000
9  7.500 flitch   4.000  30.000

Item     Weight   Value
salami    3.000  95.000
ham       3.600  90.000
brawn     2.500  56.000
greaves   2.400  45.000
welt      3.500  63.378
-----------------------
total    15.000 349.378

## Ruby

items = [ [:beef   , 3.8, 36],          [:pork   , 5.4, 43],          [:ham    , 3.6, 90],          [:greaves, 2.4, 45],          [:flitch , 4.0, 30],          [:brawn  , 2.5, 56],          [:welt   , 3.7, 67],          [:salami , 3.0, 95],          [:sausage, 5.9, 98] ].sort_by{|item, weight, price| -price / weight}maxW, value = 15.0, 0items.each do |item, weight, price|  if (maxW -= weight) > 0    puts "Take all #{item}"    value += price  else    puts "Take %gkg of %s" % [t=weight+maxW, item], "",         "Total value of swag is %g" % (value+(price/weight)*t)    break  endend
Output:
Take all salami
Take all ham
Take all brawn
Take all greaves
Take 3.5kg of welt

Total value of swag is 349.378


## Run BASIC

 This example is incorrect. It does not accomplish the given task. Please fix the code and remove this message.
dim name$(9)dim wgt(9)dim price(9)dim tak$(100) name$(1) = "beef" : wgt(1) = 3.8 : price(1) = 36 name$(2) = "pork"      : wgt(2) = 5.4 : price(2) = 43 name$(3) = "ham" : wgt(3) = 3.6 : price(3) = 90 name$(4) = "greaves"   : wgt(4) = 2.4 : price(4) = 45 name$(5) = "flitch" : wgt(5) = 4.0 : price(5) = 30 name$(6) = "brawn"     : wgt(6) = 2.5 : price(6) = 56 name$(7) = "welt" : wgt(7) = 3.7 : price(7) = 67 name$(8) = "salami"    : wgt(8) = 3.0 : price(8) = 95 name$(9) = "sausage" : wgt(9) = 5.9 : price(9) = 98 for beef = 0 to 15 step 3.8 for pork = 0 to 15 step 5.4 for ham = 0 to 15 step 3.6 for greaves = 0 to 15 step 2.4 for flitch = 0 to 15 step 4.0 for brawn = 0 to 15 step 2.5 for welt = 0 to 15 step 3.7 for salami = 0 to 15 step 3.0 for sausage = 0 to 15 step 5.9 if beef + pork + ham + greaves + flitch + brawn + welt + salami + sausage <= 15 then totPrice = beef / 3.8 * 36 + _ pork / 5.4 * 43 + _ ham / 3.6 * 90 + _ greaves / 2.4 * 45 + _ flitch / 4.0 * 30 + _ brawn / 2.5 * 56 + _ welt / 3.7 * 67 + _ salami / 3.0 * 95 + _ sausage / 5.9 * 98 if totPrice >= maxPrice then maxPrice = totPrice theMax = max(totPrice,maxPrice) t = t + 1 tak$(t)  = str$(maxPrice);",";beef;",";pork;",";ham;",";greaves;",";flitch;",";brawn;",";welt;",";salami;",";sausage end if end ifnext:next :next :next :next :next :next :next :next print "Best 2 Options":printfor i = t-1 to t totTake = val(word$(tak$(i),1,",")) if totTake > 0 then totWgt = 0 for j = 2 to 10 wgt = val(word$(tak$(i),j,",")) totWgt = totWgt + wgt value = wgt / wgt(j - 1) * price(j - 1) if wgt <> 0 then print name$(j-1);chr$(9);"Value: ";using("###.#",value);chr$(9);"Weight: ";using("##.#",wgt)   next j    print "-------- Total ";using("###.#",totTake);chr$(9);"Weight: ";totWgt end ifnext i Output: Best 2 Options salami Value: 285.0 Weight: 9.0 sausage Value: 98.0 Weight: 5.9 -------- Total 383.0 Weight: 14.9 salami Value: 475.0 Weight: 15.0 -------- Total 475.0 Weight: 15.0 ## SAS Use LP solver in SAS/OR: /* create SAS data set */data mydata; input item$ weight value;   datalines;beef    3.8  36  pork    5.4  43  ham     3.6  90  greaves 2.4  45  flitch  4.0  30  brawn   2.5  56  welt    3.7  67  salami  3.0  95  sausage 5.9  98  ; /* call OPTMODEL procedure in SAS/OR */proc optmodel;   /* declare sets and parameters, and read input data */   set <str> ITEMS;   num weight {ITEMS};   num value {ITEMS};   read data mydata into ITEMS=[item] weight value;    /* declare variables, objective, and constraints */   var WeightSelected {i in ITEMS} >= 0 <= weight[i];   max TotalValue = sum {i in ITEMS} (value[i]/weight[i]) * WeightSelected[i];   con WeightCon:      sum {i in ITEMS} WeightSelected[i] <= 15;    /* call linear programming (LP) solver */   solve;    /* print optimal solution */   print TotalValue;   print {i in ITEMS: WeightSelected[i].sol > 1e-3} WeightSelected;quit;

Output:

TotalValue
349.38

[1] WeightSelected
brawn 2.5
greaves 2.4
ham 3.6
salami 3.0
welt 3.5 

import scala.annotation.tailrec object ContinousKnapsackForRobber extends App {  val MaxWeight = 15.0  val items = Seq(    Item("Beef",    3.8, 3600),    Item("Pork",    5.4, 4300),    Item("Ham",     3.6, 9000),    Item("Greaves", 2.4, 4500),    Item("Flitch",  4.0, 3000),    Item("Brawn",   2.5, 5600),    Item("Welt",    3.7, 6700),    Item("Salami",  3.0, 9500),    Item("Sausage", 5.9, 9800))   // sort items by value per unit weight in descending order  def sortedItems = items.sortBy(it => -it.value / it.weight)   @tailrec  def packer(notPacked: Seq[Item], packed: Lootsack): Lootsack = {     if (!packed.isNotFull || notPacked.isEmpty) packed    else {      val try2fit = packed.copy(bagged = notPacked.head +: packed.bagged)      if (try2fit.isNotFull) packer(notPacked.tail, try2fit)      else {        try2fit.copy(lastPiece = packed.weightLeft / notPacked.head.weight)      }    }  }   case class Item(name: String, weight: Double, value: Int)   case class Lootsack(bagged: Seq[Item], lastPiece: Double = 1.0) {    private val totWeight = if (bagged.isEmpty) 0.0    else bagged.tail.map(_.weight).sum + bagged.head.weight * lastPiece     def isNotFull: Boolean = weightLeft > 0     def weightLeft: Double = MaxWeight - totWeight     override def toString = f"${show(bagged, lastPiece)}Totals: weight:$totWeight%4.1f, value: $totValue%6.2f" private def totValue: BigDecimal = if (bagged.isEmpty) 0.0 else (bagged.tail.map(_.value).sum + bagged.head.value * lastPiece) / 100 private def show(is: Seq[Item], percentage: Double) = { def toStr(is: Seq[Item], percentage: Double = 1): String = is.map(it => f"${percentage * 100}%6.2f%% ${it.name}%-7s${          it.weight * percentage}%4.1f ${it.value * percentage / 100}%6.2f\n").mkString toStr(is.tail.reverse) + toStr(Seq(is.head), percentage) } } println(packer(sortedItems, Lootsack(Nil)))} Output: 100.00% Salami 3.0 95.00 100.00% Ham 3.6 90.00 100.00% Brawn 2.5 56.00 100.00% Greaves 2.4 45.00 94.59% Welt 3.5 63.38 Totals: weight: 15.0, value: 349.38 Output: See it in running in your browser by ScalaFiddle (JavaScript) . ## Sidef Translation of: Perl var items =[ [:beef, 3.8, 36], [:pork, 5.4, 43], [:ham, 3.6, 90], [:greaves, 2.4, 45], [:flitch, 4.0, 30], [:brawn, 2.5, 56], [:welt, 3.7, 67], [:salami, 3.0, 95], [:sausage, 5.9, 98],].sort {|a,b| b[2]/b[1] <=> a[2]/a[1] } var (limit, value) = (15, 0);print "Item Fraction Weight Value\n"; items.each { |item| var ratio = (item[1] > limit ? limit/item[1] : 1); value += item[2]*ratio; limit -= item[1]; if (ratio == 1) { printf("%-8s %4s %7.2f %6.2f\n", item[0], 'all', item[1], item[2]); } else { printf("%-8s %-4.2f %7.2f %6.2f\n", item[0], ratio, item[1]*ratio, item[2]*ratio); break; }} say "#{'-'*28}\ntotal value: #{'%.14g' % value }" Output: Item Fraction Weight Value salami all 3.00 95.00 ham all 3.60 90.00 brawn all 2.50 56.00 greaves all 2.40 45.00 welt 0.95 3.50 63.38 ---------------------------- total value: 349.37837837838  ## Tcl package require Tcl 8.5 # Uses the trivial greedy algorithmproc continuousKnapsack {items massLimit} { # Add in the unit prices set idx -1 foreach item$items {	lassign $item name mass value lappend item [expr {$value / $mass}] lset items [incr idx]$item    }     # Sort by unit prices    set items [lsort -decreasing -real -index 3 $items] # Add items, using most valuable-per-unit first set result {} set total 0.0 set totalValue 0 foreach item$items {	lassign $item name mass value unit if {$total + $mass <$massLimit} {	    lappend result [list $name$mass $value] set total [expr {$total + $mass}] set totalValue [expr {$totalValue + $value}] } else { set mass [expr {$massLimit - $total}] set value [expr {$unit * $mass}] lappend result [list$name $mass$value]	    set totalValue [expr {$totalValue +$value}]	    break	}    }     # We return the total value too, purely for convenience    return [list $result$totalValue]}

Driver for this particular problem:

set items {    {beef	3.8	36}    {pork	5.4	43}    {ham	3.6	90}    {greaves	2.4	45}    {flitch	4.0	30}    {brawn	2.5	56}    {welt	3.7	67}    {salami	3.0	95}    {sausage	5.9	98}} lassign [continuousKnapsack $items 15.0] contents totalValueputs [format "total value of knapsack: %.2f"$totalValue]puts "contents:"foreach item $contents { lassign$item name mass value    puts [format "\t%.1fkg of %s, value %.2f" $mass$name $value]} Output: total value of knapsack: 349.38 contents: 3.0kg of salami, value 95.00 3.6kg of ham, value 90.00 2.5kg of brawn, value 56.00 2.4kg of greaves, value 45.00 3.5kg of welt, value 63.38  ## Ursala We might as well leave this one to the experts by setting it up as a linear programming problem and handing it off to an external library (which will be either lpsolve or glpk depending on the run-time system configuration). #import flo#import lin items = # name: (weight,price) < 'beef ': (3.8,36.0), 'pork ': (5.4,43.0), 'ham ': (3.6,90.0), 'greaves': (2.4,45.0), 'flitch ': (4.0,30.0), 'brawn ': (2.5,56.0), 'welt ': (3.7,67.0), 'salami ': (3.0,95.0), 'sausage': (5.9,98.0)> system = # a function to transform the item list to the data structure needed by the solver linear_system$[   lower_bounds: *nS ~&\0.,         # all zeros because we can't steal less than zero   upper_bounds: ~&nmlPXS,          # can't steal more than what's in the shop   costs: * ^|/~& negative+ vid,    # prices divided by weights, negated so as to maximize   equations: ~&iNC\15.+ 1.-*@nS]   # 1 equation constraining the total weight to 15 #cast %em main = solution system items

output:

<
'brawn  ': 2.500000e+00,
'greaves': 2.400000e+00,
'ham    ': 3.600000e+00,
'salami ': 3.000000e+00,
'welt   ': 3.500000e+00>

## XPL0

int  Name, Price, I, BestItem;real    Weight, Best, ItemWt, TotalWt;def     Items = 9;real    PricePerWt(Items);int     Taken(Items);include c:\cxpl\codes; [Name:=  ["beef","pork","ham","greaves","flitch","brawn","welt","salami","sausage"];Weight:= [ 3.8,   5.4,   3.6,  2.4,      4.0,     2.5,    3.7,   3.0,     5.9];Price:=  [ 36,    43,    90,   45,       30,      56,     67,    95,      98]; for I:= 0 to Items-1 do        [PricePerWt(I):= float(Price(I)) / Weight(I);        Taken(I):= false;        ];Format(2,1);TotalWt:= 0.0;repeat  Best:= 0.0;        for I:= 0 to Items-1 do            if not Taken(I) and PricePerWt(I) > Best then                [Best:= PricePerWt(I);  BestItem:= I];        Taken(BestItem):= true;                 \take item        ItemWt:= Weight(BestItem);              \get its weight        TotalWt:= TotalWt + ItemWt;             \add to total weight        if TotalWt > 15.0 then                  \if total is too much, reduce            ItemWt:= ItemWt - (TotalWt-15.0);   \item weight by amount it's over        RlOut(0, ItemWt);  Text(0, " kg of ");  \show weight and item        Text(0, Name(BestItem));  CrLf(0);until   TotalWt >= 15.0;                        \all we can steal]

Output:

 3.0 kg of salami
3.6 kg of ham
2.5 kg of brawn
2.4 kg of greaves
3.5 kg of welt


## zkl

Translation of: C
items:=List( T(3.8, 36.0, "beef"),  T(5.4, 43.0, "pork"),  // weight, value, name	     T(3.6, 90.0, "ham"),   T(2.4, 45.0, "greaves"),	     T(4.0, 30.0, "flitch"),T(2.5, 56.0, "brawn"),	     T(3.7, 67.0, "welt"),  T(3.0, 95.0, "salami"),	     T(5.9, 98.0, "sausage"),);fcn item_cmp(a,b){ a[1]/a[0] > b[1]/b[0] } items.sort(item_cmp);space := 15.0;foreach it in (items){ w,_,nm:=it;   if (space >= w){ println("take all ",nm); space-=w }   else{ println("take %gkg of %gkg of %s".fmt(space,w,nm)); break }}
Output:
take all salami
take all ham
take all brawn
take all greaves
take 3.5kg of 3.7kg of welt
`