Knapsack problem/0-1

From Rosetta Code
Task
Knapsack problem/0-1
You are encouraged to solve this task according to the task description, using any language you may know.

A tourist wants to make a good trip at the weekend with his friends.

They will go to the mountains to see the wonders of nature, so he needs to pack well for the trip.

He has a good knapsack for carrying things, but knows that he can carry a maximum of only 4kg in it,   and it will have to last the whole day.

He creates a list of what he wants to bring for the trip but the total weight of all items is too much.

He then decides to add columns to his initial list detailing their weights and a numerical value representing how important the item is for the trip.


Here is the list:

Table of potential knapsack items
item weight (dag) value
map 9 150
compass 13 35
water 153 200
sandwich 50 160
glucose 15 60
tin 68 45
banana 27 60
apple 39 40
cheese 23 30
beer 52 10
suntan cream 11 70
camera 32 30
T-shirt 24 15
trousers 48 10
umbrella 73 40
waterproof trousers 42 70
waterproof overclothes 43 75
note-case 22 80
sunglasses 7 20
towel 18 12
socks 4 50
book 30 10
knapsack ≤400 dag ?


The tourist can choose to take any combination of items from the list, but only one of each item is available.

He may not cut or diminish the items, so he can only take whole units of any item.


Task

Show which items the tourist can carry in his knapsack so that their total weight does not exceed 400 dag [4 kg],   and their total value is maximized.

[dag = decagram = 10 grams]


Related tasks



11l

Translation of: Python
F totalvalue(comb)
   V totwt = 0
   V totval = 0
   L(item, wt, val) comb
      totwt += wt
      totval += val
   R I totwt <= 400 {(totval, -totwt)} E (0, 0)

V items = [
   (‘map’, 9, 150), (‘compass’, 13, 35), (‘water’, 153, 200), (‘sandwich’, 50, 160),
   (‘glucose’, 15, 60), (‘tin’, 68, 45), (‘banana’, 27, 60), (‘apple’, 39, 40),
   (‘cheese’, 23, 30), (‘beer’, 52, 10), (‘suntan cream’, 11, 70), (‘camera’, 32, 30),
   (‘t-shirt’, 24, 15), (‘trousers’, 48, 10), (‘umbrella’, 73, 40),
   (‘waterproof trousers’, 42, 70), (‘waterproof overclothes’, 43, 75),
   (‘note-case’, 22, 80), (‘sunglasses’, 7, 20), (‘towel’, 18, 12), (‘socks’, 4, 50),
   (‘book’, 30, 10)
]

F knapsack01_dp(items, limit)
   V table = [[0] * (limit + 1)] * (items.len + 1)

   L(j) 1 .. items.len
      V (item, wt, val) = items[j - 1]
      L(w) 1 .. limit
         I wt > w
            table[j][w] = table[j - 1][w]
         E
            table[j][w] = max(table[j - 1][w], table[j - 1][w - wt] + val)

   [(String, Int, Int)] result
   V w = limit
   L(j) (items.len .< 0).step(-1)
      I table[j][w] != table[j - 1][w]
         V (item, wt, val) = items[j - 1]
         result.append(items[j - 1])
         w -= wt
   R result

V bagged = knapsack01_dp(items, 400)
print("Bagged the following items\n  "sorted(bagged.map((item, _, _2) -> item)).join("\n  "))
V (val, wt) = totalvalue(bagged)
print(‘for a total value of #. and a total weight of #.’.format(val, -wt))
Output:
Bagged the following items
  banana
  compass
  glucose
  map
  note-case
  sandwich
  socks
  sunglasses
  suntan cream
  water
  waterproof overclothes
  waterproof trousers
for a total value of 1030 and a total weight of 396

360 Assembly

Non recurvive brute force version.

*      Knapsack problem/0-1      16/02/2017
KNAPSA01 CSECT
       USING  KNAPSA01,R13
       B      72(R15)
       DC     17F'0'
       STM    R14,R12,12(R13)
       ST     R13,4(R15)
       ST     R15,8(R13)
       LR     R13,R15            end of prolog
       L      R0,N               n
       LA     R1,1
POWER  MH     R1,=H'2'           *2
       BCT    R0,POWER
       BCTR   R1,0               -1
       ST     R1,IMAX            imax=2**n-1
       SR     R6,R6              i=0
       DO WHILE=(C,R6,LE,IMAX)   do i=0 to imax
         SR     R10,R10            im=0
         SR     R8,R8              iw=0
         SR     R9,R9              iv=0
         LA     R7,1               j=1
         DO WHILE=(C,R7,LE,N)      do j=1 to n
           LR     R1,R6              i
           LR     R2,R7              j
           BAL    R14,TSTBIT         call tstbit(i,j)
           IF C,R0,EQ,=F'1' THEN     if tstbit(i,j)=1 then
             LA     R10,1(R10)         im=im+1
             LR     R3,R7              j
             BCTR   R3,0
             SLA    R3,5
             LA     R1,24(R3)
             A      R8,DATA(R1)        iw=iw+data(j).w
             LA     R1,28(R3)
             A      R9,DATA(R1)        iv=iv+data(j).v
           ENDIF  ,                  endif
           LA     R7,1(R7)           j=j+1
         ENDDO  ,                  enddo j
         IF C,R8,LE,MAXW,AND,C,R9,GT,XV THEN  if w<=maxw and iv>xv then
           ST     R6,XB              xb=i
           ST     R10,XM             xm=im
           ST     R8,XW              xw=iw
           ST     R9,XV              xv=iv
         ENDIF  ,                  endif
         LA     R6,1(R6)           i=i+1
       ENDDO  ,                  enddo i
       MVC    PG(2),=C'n='
       L      R1,N               n
       XDECO  R1,XDEC            edit n
       MVC    PG+2(2),XDEC+10
       XPRNT  PG,L'PG            print buffer
       LA     R6,1
       DO WHILE=(C,R6,LE,N)      do i=1 to n
         L      R1,XB              xb
         LR     R2,R6              i
         BAL    R14,TSTBIT         call tstbit(xb,i)
         IF C,R0,EQ,=F'1' THEN     if tstbit(xb,i)=1 then
           LR     R1,R6              i
           BCTR   R1,0
           SLA    R1,5
           LA     R2,DATA(R1)        @data(i).n
           MVC    PG(24),0(R2)
           XPRNT  PG,24              print item
         ENDIF  ,                  endif
         LA     R6,1(R6)           i=i+1
       ENDDO  ,                  enddo i
       L      R1,XM              xm
       XDECO  R1,XDEC            edit xm
       MVC    PGT+6(2),XDEC+10
       L      R1,XW              xw
       XDECO  R1,XDEC            edit xw
       MVC    PGT+16(3),XDEC+9
       L      R1,XV              xv
       XDECO  R1,XDEC            edit xv
       MVC    PGT+26(4),XDEC+8
       XPRNT  PGT,L'PGT          print buffer
       L      R13,4(0,R13)       epilog
       LM     R14,R12,12(R13)
       XR     R15,R15
       BR     R14                exit
TSTBIT EQU    *                  R1 value to test the R2 bit
       LA     R3,32              32
       SR     R3,R2              (32-i)
       STC    R3,XSLL+3         
       LR     R0,R1              n
       EX     0,XSLL             SLL R0,(32-i)
       SRL    R0,31             
       BR     R14                return R0
XSLL   SLL    R0,0               shift left logical     
*
MAXW   DC     F'400'             maximum weight
N      DC     A((DATAE-DATA)/32)
IMAX   DS     F                  number of combinations
XB     DS     F                  max vector
XM     DS     F                  max items 
XW     DS     F                  max weight
XV     DS     F                  max value
PG     DC     CL80' '
PGT    DC     CL32'items=.. weight=... value=....'
XDEC   DS     CL12
DATA   DC     CL24'map',F'9',F'150'
       DC     CL24'compass',F'13',F'35'
       DC     CL24'water',F'153',F'200'
       DC     CL24'sandwich',F'50',F'160'
       DC     CL24'glucose',F'15',F'60'
       DC     CL24'tin',F'68',F'45'
       DC     CL24'banana',F'27',F'60'
       DC     CL24'apple',F'39',F'40'
       DC     CL24'cheese',F'23',F'30'
       DC     CL24'beer',F'52',F'10'
       DC     CL24'suntan cream',F'11',F'70'
       DC     CL24'camera',F'32',F'30'
       DC     CL24'T-shirt',F'24',F'15'
       DC     CL24'trousers',F'48',F'10'
       DC     CL24'umbrella',F'73',F'40'
       DC     CL24'book',F'30',F'10'
       DC     CL24'waterproof trousers',F'42',F'70'
       DC     CL24'waterproof overclothes',F'43',F'75'
       DC     CL24'note-case',F'22',F'80'
       DC     CL24'sunglasses',F'7',F'20'
       DC     CL24'towel',F'18',F'12'
       DC     CL24'socks',F'4',F'50'
DATAE  DC     0C
       YREGS
       END    KNAPSA01
Output:
n=22
map
compass
water
sandwich
glucose
banana
suntan cream
waterproof trousers
waterproof overclothes
note-case
sunglasses
socks
items=12 weight=396 value=1030

Ada

with Ada.Text_IO;
with Ada.Strings.Unbounded;

procedure Knapsack_01 is
   package US renames Ada.Strings.Unbounded;

   type Item is record
      Name   : US.Unbounded_String;
      Weight : Positive;
      Value  : Positive;
      Taken  : Boolean;
   end record;

   type Item_Array is array (Positive range <>) of Item;

   function Total_Weight (Items : Item_Array; Untaken : Boolean := False) return Natural is
      Sum : Natural := 0;
   begin
      for I in Items'Range loop
         if Untaken or else Items (I).Taken then
            Sum := Sum + Items (I).Weight;
         end if;
      end loop;
      return Sum;
   end Total_Weight;

   function Total_Value (Items : Item_Array; Untaken : Boolean := False) return Natural is
      Sum : Natural := 0;
   begin
      for I in Items'Range loop
         if Untaken or else Items (I).Taken then
            Sum := Sum + Items (I).Value;
         end if;
      end loop;
      return Sum;
   end Total_Value;

   function Max (Left, Right : Natural) return Natural is
   begin
      if Right > Left then
         return Right;
      else
         return Left;
      end if;
   end Max;

   procedure Solve_Knapsack_01 (Items : in out Item_Array;
                                Weight_Limit : Positive := 400) is
      type W_Array is array (0..Items'Length, 0..Weight_Limit) of Natural;
      W : W_Array := (others => (others => 0));
   begin
      -- fill W
      for I in Items'Range loop
         for J in 1 .. Weight_Limit loop
            if Items (I).Weight > J then
               W (I, J) := W (I - 1, J);
            else
               W (I, J) := Max (W (I - 1, J),
                                W (I - 1, J - Items (I).Weight) + Items (I).Value);
            end if;
         end loop;
      end loop;
      declare
         Rest : Natural := Weight_Limit;
      begin
         for I in reverse Items'Range loop
            if W (I, Rest) /= W (I - 1, Rest) then
               Items (I).Taken := True;
               Rest := Rest - Items (I).Weight;
            end if;
         end loop;
      end;
   end Solve_Knapsack_01;

   All_Items : Item_Array :=
     ( (US.To_Unbounded_String ("map"),                      9, 150, False),
       (US.To_Unbounded_String ("compass"),                 13,  35, False),
       (US.To_Unbounded_String ("water"),                  153, 200, False),
       (US.To_Unbounded_String ("sandwich"),                50, 160, False),
       (US.To_Unbounded_String ("glucose"),                 15,  60, False),
       (US.To_Unbounded_String ("tin"),                     68,  45, False),
       (US.To_Unbounded_String ("banana"),                  27,  60, False),
       (US.To_Unbounded_String ("apple"),                   39,  40, False),
       (US.To_Unbounded_String ("cheese"),                  23,  30, False),
       (US.To_Unbounded_String ("beer"),                    52,  10, False),
       (US.To_Unbounded_String ("suntan cream"),            11,  70, False),
       (US.To_Unbounded_String ("camera"),                  32,  30, False),
       (US.To_Unbounded_String ("t-shirt"),                 24,  15, False),
       (US.To_Unbounded_String ("trousers"),                48,  10, False),
       (US.To_Unbounded_String ("umbrella"),                73,  40, False),
       (US.To_Unbounded_String ("waterproof trousers"),     42,  70, False),
       (US.To_Unbounded_String ("waterproof overclothes"),  43,  75, False),
       (US.To_Unbounded_String ("note-case"),               22,  80, False),
       (US.To_Unbounded_String ("sunglasses"),               7,  20, False),
       (US.To_Unbounded_String ("towel"),                   18,  12, False),
       (US.To_Unbounded_String ("socks"),                    4,  50, False),
       (US.To_Unbounded_String ("book"),                    30,  10, False) );

begin
   Solve_Knapsack_01 (All_Items, 400);
   Ada.Text_IO.Put_Line ("Total Weight: " & Natural'Image (Total_Weight (All_Items)));
   Ada.Text_IO.Put_Line ("Total Value:  " & Natural'Image (Total_Value  (All_Items)));
   Ada.Text_IO.Put_Line ("Items:");
   for I in All_Items'Range loop
      if All_Items (I).Taken then
         Ada.Text_IO.Put_Line ("   " & US.To_String (All_Items (I).Name));
      end if;
   end loop;
end Knapsack_01;
Output:
Total Weight:  396
Total Value:   1030
Items:
   map
   compass
   water
   sandwich
   glucose
   banana
   suntan cream
   waterproof trousers
   waterproof overclothes
   note-case
   sunglasses
   socks

APL

     retNapSack;sum;b;list;total
[1]   total400
[2]   list("map" 9 150)("compass" 13 35)("water" 153 200)("sandwich" 50 160)("glucose" 15 60) ("tin" 68 45)("banana" 27 60)("apple" 39 40)("cheese" 23 30)("beer" 52 10) ("suntan cream" 11 70)("camera" 32 30)("t-shirt" 24 15)("trousers" 48 10) ("umbrella" 73 40)("waterproof trousers" 42 70)("waterproof overclothes" 43 75) ("note-case" 22 80) ("sunglasses" 7 20) ("towel" 18 12) ("socks" 4 50) ("book" 30 10)
[3]   listlist[3¨list]
[4]   
[5]   ret
[6]   :while 0≠⍴list
[7]       retret,(btotal>sum+\2¨list)/list
[8]       list1(~b)/list
[9]       totaltotal-sum¯1(total>sum)/sum
[10]  :end 
[11]  retret,⊂'TOTALS:' (+/2¨ret)(+/3¨ret)   
    
Output:
NapSack
 water                  153  200
 sandwich                50  160
 map                      9  150
 note-case               22   80
 waterproof overclothes  43   75
 suntan cream            11   70
 waterproof trousers     42   70
 glucose                 15   60
 banana                  27   60
 socks                    4   50
 compass                 13   35
 sunglasses               7   20
 TOTALS:                396 1030

Average runtime: 0.000168 seconds

AWK

# syntax: GAWK -f KNAPSACK_PROBLEM_0-1.AWK
BEGIN {
#   arr["item,weight"] = value
    arr["map,9"] = 150
    arr["compass,13"] = 35
    arr["water,153"] = 200
    arr["sandwich,50"] = 160
    arr["glucose,15"] = 60
    arr["tin,68"] = 45
    arr["banana,27"] = 60
    arr["apple,39"] = 40
    arr["cheese,23"] = 30
    arr["beer,52"] = 10
    arr["suntan cream,11"] = 70
    arr["camera,32"] = 30
    arr["T-shirt,24"] = 15
    arr["trousers,48"] = 10
    arr["umbrella,73"] = 40
    arr["waterproof trousers,42"] = 70
    arr["waterproof overclothes,43"] = 75
    arr["note-case,22"] = 80
    arr["sunglasses,7"] = 20
    arr["towel,18"] = 12
    arr["socks,4"] = 50
    arr["book,30"] = 10
    sack_size = 400 # dag
    PROCINFO["sorted_in"] = "@val_num_desc"
    for (i in arr) {
      if (total_weight >= sack_size) {
        break
      }
      split(i,tmp,",")
      weight = tmp[2]
      if (total_weight + weight <= sack_size) {
        printf("%s\n",tmp[1])
        total_items++
        total_value += arr[i]
        total_weight += weight
      }
    }
    printf("items=%d (out of %d) weight=%d value=%d\n",total_items,length(arr),total_weight,total_value)
    exit(0)
}
Output:
water
sandwich
map
note-case
waterproof overclothes
waterproof trousers
suntan cream
banana
glucose
socks
compass
sunglasses
items=12 (out of 22) weight=396 value=1030

BASIC

QBasic

Works with: QBasic version 1.1
Works with: QuickBasic version 4.5
Translation of: QB64
N = 7: G = 5: a = 2 ^ (N + 1) ' Author: DANILIN & Editor: Jjuanhdez or Unknow
RANDOMIZE TIMER
DIM L(N), C(N), j(N), q(a), d(a), q$(a)

FOR i = a - 1 TO (a - 1) \ 2 STEP -1
    k = i
    DO  ' cipher 0-1
        q$(i) = LTRIM$(STR$(k MOD 2)) + q$(i)
        k = INT(k / 2)
    LOOP UNTIL k = 0
    q$(i) = MID$(q$(i), 2, LEN(q$(i)))
NEXT i

PRINT " #            Mass          Cost"
FOR i = 1 TO N
    L(i) = INT(RND * 3 + 1)' mass & cost
    C(i) = 10 + INT(RND * 9)
    PRINT i, L(i), C(i)
NEXT i  ' origin

PRINT CHR$(10) + "Mass          Cost           Chifer"
FOR h = a - 1 TO (a - 1) / 2 STEP -1
    FOR k = 1 TO N
        j(k) = VAL(MID$(q$(h), k, 1))    ' j() = cipher
        q(h) = q(h) + L(k) * j(k) * C(k) ' 0 or 1
        d(h) = d(h) + L(k) * j(k)
    NEXT k
    IF d(h) <= G THEN PRINT d(h), q(h), q$(h)
NEXT h

PRINT CHR$(10) + "Mass          MAX            Chifer"
max = 0: h = 1
FOR i = 1 TO a
    IF d(i) <= G AND q(i) > max THEN max = q(i): h = i
NEXT i
PRINT d(h), q(h), q$(h)
Output:
Same as QB64 entry.

Yabasic

Translation of: QB64
N = 7 : G = 5 : a = 2^(N+1) ' Author: DANILIN & Editor: Jjuanhdez or Unknow
dim L(N), C(N), j(N), q(a), d(a), q$(a)

for i = a-1 to int((a-1)/2) step -1
    k = i
    repeat    // cipher 0-1
        q$(i) = ltrim$(str$(mod(k, 2))) + q$(i)
        k = int(k / 2)
    until k = 0
    q$(i) = mid$(q$(i), 2, len(q$(i))) 
next i

print " #     Mass    Cost"
for i = 1 to N
    L(i) = int(ran(3)) + 1    // mass & cost
    C(i) = 10 + int(ran(9))
    print i, chr$(9), L(i), chr$(9), C(i)
next i  // origin

print chr$(10) + "Mass   Cost      Chifer"
for h = a-1 to (a-1)/2 step -1
    for k = 1 to N
        j(k) = val(mid$(q$(h), k, 1))     // j() = cipher
        q(h) = q(h) + L(k) * j(k) * C(k)  // 0 or 1
        d(h) = d(h) + L(k) * j(k) 
    next k
    if d(h) <= G  print d(h), chr$(9), q(h), chr$(9), q$(h)
next h

print chr$(10) + "Mass   MAX       Chifer"
maxx = 0 : h = 1 
for i = 1 to a
    if d(i) <= G and q(i) > maxx  maxx = q(i) : h = i
next i
print d(h), chr$(9), q(h), chr$(9), q$(h)
end
Output:
Same as QB64 entry
https://jdoodle.com/iembed/v0/suj

Batch File

:: Initiate command line environment
@echo off
setlocal enabledelayedexpansion

:: Establish arrays we'll be using
set items=map compass water sandwich glucose tin banana apple cheese beer suntancream camera tshirt trousers umbrella waterprooftrousers waterproofoverclothes notecase sunglasses towel socks book
set weight=9 13 153 50 15 68 27 39 23 52 11 32 24 48 73 42 43 22 7 18 4 30
set importance=150 35 200 160 60 45 60 40 30 10 70 30 15 10 40 70 75 80 20 12 50 10

:: Put the above 3 arrays into their own variables with the form of "item[]", "w[]" and "i[]"
set tempnum=0
for %%i in (%items%) do (
  set /a tempnum+=1
  set item!tempnum!=%%i
)
set tempnum=0
for %%i in (%weight%) do (
  set /a tempnum+=1
  set w!tempnum!=%%i
)
set tempnum=0
for %%i in (%importance%) do (
  set /a tempnum+=1
  set i!tempnum!=%%i
)
:: Define the array "r[]" as the ratio between the importance ("i[]") and the weight ("w[]"). 
for /l %%i in (1,1,22) do set /a r%%i=!i%%i!*100/!w%%i! & rem batch doesn't support decimals, so the numerator is multiplied by 100 to get past this

set totalimportance=0
set totalweight=0
set amount=0

:: Find the largest number in "r[]" and define some temp variables based off it
:load
set tempr=0
set tempitem=0
for /l %%i in (1,1,22) do (
  if !r%%i! gtr !tempr! (
    set tempr=!r%%i!
    set tempitem=%%i
    set /a testweight=%totalweight%+!w%%i!
    if !tempr!==0 goto end
    if !testweight! geq 400 goto end
  )
)

:: Do basic error checking using the temp variables from above and either output and end the program or send back to load
set /a totaltempweight=%totalweight%+!w%tempitem%!

if %totaltempweight% gtr 400 (
  set !r%tempitem%!=0
  goto load
)

set totalweight=%totaltempweight%
set /a totalimportance+=!i%tempitem%!
set taken=%taken% !item%tempitem%!
set /a amount+=1
set r%tempitem%=0 & rem set the ratio variable of the item we just added to the knapsack as 0 to stop it repeat

goto load

:end
echo List of things taken [%amount%]: %taken%
echo Total Value: %totalimportance%  Total Weight: %totalweight%
pause>nul
Output:
List of things taken [12]:  map socks suntancream glucose notecase sandwich sunglasses compass banana waterproofoverclothes waterprooftrousers water
Total Value: 1030  Total Weight: 396

BBC BASIC

      HIMEM = PAGE + 8000000
      nItems% = 22
      maxWeight% = 400
      
      DIM Tag{ivalue%, list%(nItems%-1), lp%}
      DIM items{(nItems%-1)name$, weight%, ivalue%}
      FOR item% = 0 TO nItems%-1
        READ items{(item%)}.name$, items{(item%)}.weight%, items{(item%)}.ivalue%
      NEXT
      
      DATA "map", 9, 150, "compass", 13, 35, "water", 153, 200, "sandwich", 50, 160
      DATA "glucose", 15, 60, "tin", 68, 45, "banana", 27, 60, "apple", 39, 40
      DATA "cheese", 23, 30, "beer", 52, 10, "suntan cream", 11, 70, "camera", 32, 30
      DATA "t-shirt", 24, 15, "trousers", 48, 10, "umbrella", 73, 40, "book", 30, 10
      DATA "waterproof trousers", 42, 70, "waterproof overclothes", 43, 75
      DATA "note-case", 22, 80, "sunglasses", 7, 20, "towel", 18, 12, "socks", 4, 50
      
      carry% = FN_Knapsack(items{()}, nItems% - 1, maxWeight%, cache{()})
      FOR i% = 0 TO cache{(carry%)}.lp%-1
        n% = cache{(carry%)}.list%(i%)
        TotalWeight% += items{(n%)}.weight%
        TotalValue% += items{(n%)}.ivalue%
        PRINT items{(n%)}.name$ " "
      NEXT
      PRINT '"Total weight = " ; TotalWeight%
      PRINT "Total value  = " ; TotalValue%
      END
      
      DEF FN_Knapsack(i{()}, i%, w%, RETURN m{()})
      LOCAL included{}, excluded{}, tmp%, index%
      DIM m{(16384)} = Tag{}, included{} = Tag{}, excluded{} = Tag{}
      
      index% = i% << 9 OR w%
      IF m{(index%)}.ivalue% THEN = index%
      
      IF i% = 0 THEN
        IF i{(0)}.weight% > w% THEN
          m{(index%)}.ivalue% = 0 : REM Item doesn't fit
        ELSE
          m{(index%)}.ivalue% = i{(0)}.ivalue%
          m{(index%)}.list%(m{(index%)}.lp%) = 0
          m{(index%)}.lp% += 1
        ENDIF
        = index%
      ENDIF
      
      tmp% = FN_Knapsack(i{()}, i% - 1, w%, m{()})
      excluded{} = m{(tmp%)}
      IF i{(i%)}.weight% > w% THEN
        m{(index%)} = excluded{} : REM Item weighs too much
        = index%
      ELSE
        tmp% = FN_Knapsack(i{()}, i% - 1, w% - i{(i%)}.weight%, m{()})
        included{} = m{(tmp%)}
        included.ivalue% += i{(i%)}.ivalue%
        included.list%(included.lp%) = i%
        included.lp% += 1
      ENDIF
      
      IF included.ivalue% > excluded.ivalue% THEN
        m{(index%)} = included{}
      ELSE
        m{(index%)} = excluded{}
      ENDIF
      = index%
Output:
map
compass
water
sandwich
glucose
banana
suntan cream
waterproof trousers
waterproof overclothes
note-case
sunglasses
socks

Total weight = 396
Total value  = 1030

Bracmat

(knapsack=
  ( things
  =   (map.9.150)
      (compass.13.35)
      (water.153.200)
      (sandwich.50.160)
      (glucose.15.60)
      (tin.68.45)
      (banana.27.60)
      (apple.39.40)
      (cheese.23.30)
      (beer.52.10)
      ("suntan cream".11.70)
      (camera.32.30)
      (T-shirt.24.15)
      (trousers.48.10)
      (umbrella.73.40)
      ("waterproof trousers".42.70)
      ("waterproof overclothes".43.75)
      (note-case.22.80)
      (sunglasses.7.20)
      (towel.18.12)
      (socks.4.50)
      (book.30.10)
  )
& 0:?maxvalue
& :?sack
& ( add
  =     cumwght
        cumvalue
        cumsack
        name
        wght
        val
        tings
        n
        ncumwght
        ncumvalue
    .     !arg
        : (?cumwght.?cumvalue.?cumsack.(?name.?wght.?val) ?tings)
      & -1:?n
      &   whl
        ' ( 1+!n:~>1:?n
          & !cumwght+!n*!wght:~>400:?ncumwght
          & !cumvalue+!n*!val:?ncumvalue
          & (   !tings:
              & (   !ncumvalue:>!maxvalue:?maxvalue
                  &     !cumsack
                        (!n:0&|!name)
                    : ?sack
                |
                )
            |   add
              $ ( !ncumwght
                . !ncumvalue
                .   !cumsack
                    (!n:0&|!name)
                . !tings
                )
            )
          )
  )
& add$(0.0..!things)
& out$(!maxvalue.!sack));
 
!knapsack;
Output:
  1030
.   map
    compass
    water
    sandwich
    glucose
    banana
    suntan cream
    waterproof trousers
    waterproof overclothes
    note-case
    sunglasses
    socks

C

#include <stdio.h>
#include <stdlib.h>

typedef struct {
    char *name;
    int weight;
    int value;
} item_t;

item_t items[] = {
    {"map",                      9,   150},
    {"compass",                 13,    35},
    {"water",                  153,   200},
    {"sandwich",                50,   160},
    {"glucose",                 15,    60},
    {"tin",                     68,    45},
    {"banana",                  27,    60},
    {"apple",                   39,    40},
    {"cheese",                  23,    30},
    {"beer",                    52,    10},
    {"suntan cream",            11,    70},
    {"camera",                  32,    30},
    {"T-shirt",                 24,    15},
    {"trousers",                48,    10},
    {"umbrella",                73,    40},
    {"waterproof trousers",     42,    70},
    {"waterproof overclothes",  43,    75},
    {"note-case",               22,    80},
    {"sunglasses",               7,    20},
    {"towel",                   18,    12},
    {"socks",                    4,    50},
    {"book",                    30,    10},
};

int *knapsack (item_t *items, int n, int w) {
    int i, j, a, b, *mm, **m, *s;
    mm = calloc((n + 1) * (w + 1), sizeof (int));
    m = malloc((n + 1) * sizeof (int *));
    m[0] = mm;
    for (i = 1; i <= n; i++) {
        m[i] = &mm[i * (w + 1)];
        for (j = 0; j <= w; j++) {
            if (items[i - 1].weight > j) {
                m[i][j] = m[i - 1][j];
            }
            else {
                a = m[i - 1][j];
                b = m[i - 1][j - items[i - 1].weight] + items[i - 1].value;
                m[i][j] = a > b ? a : b;
            }
        }
    }
    s = calloc(n, sizeof (int));
    for (i = n, j = w; i > 0; i--) {
        if (m[i][j] > m[i - 1][j]) {
            s[i - 1] = 1;
            j -= items[i - 1].weight;
        }
    }
    free(mm);
    free(m);
    return s;
}

int main () {
    int i, n, tw = 0, tv = 0, *s;
    n = sizeof (items) / sizeof (item_t);
    s = knapsack(items, n, 400);
    for (i = 0; i < n; i++) {
        if (s[i]) {
            printf("%-22s %5d %5d\n", items[i].name, items[i].weight, items[i].value);
            tw += items[i].weight;
            tv += items[i].value;
        }
    }
    printf("%-22s %5d %5d\n", "totals:", tw, tv);
    return 0;
}
Output:
map                        9   150
compass                   13    35
water                    153   200
sandwich                  50   160
glucose                   15    60
banana                    27    60
suntan cream              11    70
waterproof trousers       42    70
waterproof overclothes    43    75
note-case                 22    80
sunglasses                 7    20
socks                      4    50
totals:                  396  1030

C#

Library: System
using System;
using System.Collections.Generic;

namespace Tests_With_Framework_4
{

class Bag : IEnumerable<Bag.Item>
        {
            List<Item> items;
            const int MaxWeightAllowed = 400;

            public Bag()
            {
                items = new List<Item>();
            }

            void AddItem(Item i)
            {
                if ((TotalWeight + i.Weight) <= MaxWeightAllowed)
                    items.Add(i);
            }

            public void Calculate(List<Item> items)
            {
                foreach (Item i in Sorte(items))
                {
                    AddItem(i);
                }
            }

            List<Item> Sorte(List<Item> inputItems)
            {
                List<Item> choosenItems = new List<Item>();
                for (int i = 0; i < inputItems.Count; i++)
                {
                    int j = -1;
                    if (i == 0)
                    {
                        choosenItems.Add(inputItems[i]);
                    }
                    if (i > 0)
                    {
                        if (!RecursiveF(inputItems, choosenItems, i, choosenItems.Count - 1, false, ref j))
                        {
                            choosenItems.Add(inputItems[i]);
                        }
                    }
                }
                return choosenItems;
            }

            bool RecursiveF(List<Item> knapsackItems, List<Item> choosenItems, int i, int lastBound, bool dec, ref int indxToAdd)
            {
                if (!(lastBound < 0))
                {
                    if ( knapsackItems[i].ResultWV < choosenItems[lastBound].ResultWV )
                    {
                        indxToAdd = lastBound;
                    }
                    return RecursiveF(knapsackItems, choosenItems, i, lastBound - 1, true, ref indxToAdd);
                }
                if (indxToAdd > -1)
                {
                    choosenItems.Insert(indxToAdd, knapsackItems[i]);
                    return true;
                }
                return false;
            }

            #region IEnumerable<Item> Members
            IEnumerator<Item> IEnumerable<Item>.GetEnumerator()
            {
                foreach (Item i in items)
                    yield return i;
            }
            #endregion

            #region IEnumerable Members
            System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator()
            {
                return items.GetEnumerator();
            }
            #endregion

            public int TotalWeight
            {
                get
                {
                    var sum = 0;
                    foreach (Item i in this)
                    {
                        sum += i.Weight;
                    }
                    return sum;
                }
            }

            public class Item
            {
                public string Name { get; set; } public int Weight { get; set; } public int Value { get; set; } public int ResultWV { get { return  Weight-Value; } }
                public override string ToString()
                {
                    return "Name : " + Name + "        Wieght : " + Weight + "       Value : " + Value + "     ResultWV : " + ResultWV;
                }
            }
        }

    class Program
    {
        static void Main(string[] args)
        {List<Bag.Item> knapsackItems = new List<Bag.Item>();
            knapsackItems.Add(new Bag.Item() { Name = "Map", Weight = 9, Value = 150 });
            knapsackItems.Add(new Bag.Item() { Name = "Water", Weight = 153, Value = 200 });
            knapsackItems.Add(new Bag.Item() { Name = "Compass", Weight = 13, Value = 35 });
            knapsackItems.Add(new Bag.Item() { Name = "Sandwitch", Weight = 50, Value = 160 });
            knapsackItems.Add(new Bag.Item() { Name = "Glucose", Weight = 15, Value = 60 });
            knapsackItems.Add(new Bag.Item() { Name = "Tin", Weight = 68, Value = 45 });
            knapsackItems.Add(new Bag.Item() { Name = "Banana", Weight = 27, Value = 60 });
            knapsackItems.Add(new Bag.Item() { Name = "Apple", Weight = 39, Value = 40 });
            knapsackItems.Add(new Bag.Item() { Name = "Cheese", Weight = 23, Value = 30 });
            knapsackItems.Add(new Bag.Item() { Name = "Beer", Weight = 52, Value = 10 });
            knapsackItems.Add(new Bag.Item() { Name = "Suntan Cream", Weight = 11, Value = 70 });
            knapsackItems.Add(new Bag.Item() { Name = "Camera", Weight = 32, Value = 30 });
            knapsackItems.Add(new Bag.Item() { Name = "T-shirt", Weight = 24, Value = 15 });
            knapsackItems.Add(new Bag.Item() { Name = "Trousers", Weight = 48, Value = 10 });
            knapsackItems.Add(new Bag.Item() { Name = "Umbrella", Weight = 73, Value = 40 });
            knapsackItems.Add(new Bag.Item() { Name = "WaterProof Trousers", Weight = 42, Value = 70 });
            knapsackItems.Add(new Bag.Item() { Name = "Note-Case", Weight = 22, Value = 80 });
            knapsackItems.Add(new Bag.Item() { Name = "Sunglasses", Weight = 7, Value = 20 });
            knapsackItems.Add(new Bag.Item() { Name = "Towel", Weight = 18, Value = 12 });
            knapsackItems.Add(new Bag.Item() { Name = "Socks", Weight = 4, Value = 50 });
            knapsackItems.Add(new Bag.Item() { Name = "Book", Weight = 30, Value = 10 });
            knapsackItems.Add(new Bag.Item() { Name = "waterproof overclothes ", Weight = 43, Value = 75 });

            Bag b = new Bag();
            b.Calculate(knapsackItems);
            b.All(x => { Console.WriteLine(x); return true; });
            Console.WriteLine(b.Sum(x => x.Weight));
            Console.ReadKey();
        }
    }
}

("Bag" might not be the best name for the class, since "bag" is sometimes also used to refer to a multiset data structure.)


C#, Alternative Version

C# Knapsak 0-1 Russian Binary ciphers

Russian Knapsack 0-1 synthesizes all ciphers from 0 & 1 adding left +1 register and 0 remain on left in cipher

Number of comparisons decreases from N! to 2^N for example N=8 N!=40320 >> 2^N=256

Random values origin are automatically assigned create integral of quantity and quality

using System;		// Knapsack C# binary DANILIN
using System.Text;	// rextester.com/YRFA61366
namespace Knapsack 
{ 
class Knapsack  
    { 
    static void Main()
        { 
            int n = 7; 
            int Inside = 5; 
            int all=Convert.ToInt32(Math.Pow(2,(n+1))); 
            int[] mass = new int[n]; 
            int[] cost = new int[n]; 
            int[] jack = new int[n]; 
            int[] quality = new int[all]; 
            int[] amount = new int[all];   
            int i; 			// circle
            int k; 			// circle
            int dec;  
            string[] bin = new string[all]; 
            int list; 
            int max;
            int max_num;
            Random rand = new Random();

            for (i=0; i<n; i++)
            {
                mass[i]=1+rand.Next(3);
                cost[i]=10+rand.Next(9);
                Console.WriteLine("{0} {1} {2}", i+1, mass[i], cost[i]); 
            } 
            Console.WriteLine();

            for (list = all-1; list>(all-1)/2; list--) 
            { 
                dec=list; 
                while (dec > 0)
                { 
                    bin[list] = dec % 2 + bin[list]; // from 10 to 2 
                    dec/=2; 
                }
                if (bin[list] == "") 
                {
                    bin[list] = "0";
                }
                bin[list]=bin[list].Substring(1,bin[list].Length-1); 
                for (k=0; k<n; k++) // inside 01
                {
                    jack[k]=Convert.ToInt32(bin[list].Substring(k,1));
                    quality[list]=quality[list]+mass[k]*jack[k]*cost[k]; 	// integral of costs
                    amount[list]=amount[list]+mass[k]*jack[k]; 	// integral of mass
                }        
                if (amount[list]<= Inside)		// current mass < Knapsack
                { 
                    Console.WriteLine("{0} {1} {2} {3}", Inside, amount[list], quality[list], bin[list]); 
                } 
            } 
            Console.WriteLine();

            max=0; 
            max_num=1;
            for (i=0; i < all; i++)
            { 
                if (amount[i]<=Inside && quality[i]>max)
                { 
                    max = quality[i]; max_num =i ;
                }
            }
            Console.WriteLine("{0} {1} {2}",amount[max_num],quality[max_num],bin[max_num]);
        }
    }
}
Output:
 # Mass Cost
1 2 12
2 3 17
3 1 14
4 3 17
5 1 13
Chifer Mass Cost 
11000 5 5 75
01001 5 4 64
00111 5 5 78 !!!
00110 5 4 65
00101 5 2 27
Mass MAX Chifer
5 78 00111
Output:
int n = 20; 
int Inside = 400; 
int all=Convert.ToInt32(Math.Pow(2,(n+1))); 
int[] mass = {9,13,153,50,15,68,27,39,23,52,11,32,24,48,73,42,43,22,7,4,30}; 
int[] cost = {150,35,200,160,60,45,60,40,30,10,70,30,15,10,40,70,75,80,20,50,10}; 

396 1030 11111010001000011111

jdoodle.com/ia/rSn

C++

First version

Library: Boost
#include <vector>
#include <string>
#include <iostream>
#include <boost/tuple/tuple.hpp>
#include <set>

int findBestPack( const std::vector<boost::tuple<std::string , int , int> > & , 
      std::set<int> & , const int  ) ;

int main( ) {
   std::vector<boost::tuple<std::string , int , int> > items ;
   //===========fill the vector with data====================
   items.push_back( boost::make_tuple( "" , 0  ,  0 ) ) ;
   items.push_back( boost::make_tuple( "map" , 9 , 150 ) ) ;
   items.push_back( boost::make_tuple( "compass" , 13 , 35 ) ) ;
   items.push_back( boost::make_tuple( "water" , 153 , 200 ) ) ;
   items.push_back( boost::make_tuple( "sandwich", 50 , 160 ) ) ;
   items.push_back( boost::make_tuple( "glucose" , 15 , 60 ) ) ;
   items.push_back( boost::make_tuple( "tin", 68 , 45 ) ) ;
   items.push_back( boost::make_tuple( "banana", 27 , 60 ) ) ;
   items.push_back( boost::make_tuple( "apple" , 39 , 40 ) ) ;
   items.push_back( boost::make_tuple( "cheese" , 23 , 30 ) ) ;
   items.push_back( boost::make_tuple( "beer" , 52 , 10 ) ) ;
   items.push_back( boost::make_tuple( "suntan creme" , 11 , 70 ) ) ;
   items.push_back( boost::make_tuple( "camera" , 32 , 30 ) ) ;
   items.push_back( boost::make_tuple( "T-shirt" , 24 , 15 ) ) ;
   items.push_back( boost::make_tuple( "trousers" , 48 , 10 ) ) ;
   items.push_back( boost::make_tuple( "umbrella" , 73 , 40 ) ) ;
   items.push_back( boost::make_tuple( "waterproof trousers" , 42 , 70 ) ) ;
   items.push_back( boost::make_tuple( "waterproof overclothes" , 43 , 75 ) ) ;
   items.push_back( boost::make_tuple( "note-case" , 22 , 80 ) ) ;
   items.push_back( boost::make_tuple( "sunglasses" , 7 , 20 ) ) ;
   items.push_back( boost::make_tuple( "towel" , 18 , 12 ) ) ;
   items.push_back( boost::make_tuple( "socks" , 4 , 50 ) ) ;
   items.push_back( boost::make_tuple( "book" , 30 , 10 ) ) ;
   const int maximumWeight = 400 ;
   std::set<int> bestItems ; //these items will make up the optimal value
   int bestValue = findBestPack( items , bestItems , maximumWeight ) ;
   std::cout << "The best value that can be packed in the given knapsack is " <<
      bestValue << " !\n" ;
   int totalweight = 0 ;
   std::cout << "The following items should be packed in the knapsack:\n" ;
   for ( std::set<int>::const_iterator si = bestItems.begin( ) ; 
	 si != bestItems.end( ) ; si++ ) { 
      std::cout << (items.begin( ) + *si)->get<0>( ) << "\n" ;
      totalweight += (items.begin( ) + *si)->get<1>( ) ;
   }
   std::cout << "The total weight of all items is " << totalweight << " !\n" ;
   return 0 ;
}
   
int findBestPack( const std::vector<boost::tuple<std::string , int , int> > & items ,std::set<int> & bestItems , const int weightlimit ) {
   //dynamic programming approach sacrificing storage space for execution
   //time , creating a table of optimal values for every weight and a 
   //second table of sets with the items collected so far in the knapsack
   //the best value is in the bottom right corner of the values table,
   //the set of items in the bottom right corner of the sets' table.
   const int n = items.size( ) ;
   int bestValues [ n ][ weightlimit ] ;
   std::set<int> solutionSets[ n ][ weightlimit ] ;
   std::set<int> emptyset ;
   for ( int i = 0 ; i < n ; i++ ) {
      for ( int j = 0 ; j < weightlimit  ; j++ ) {
	 bestValues[ i ][ j ] = 0 ;
	 solutionSets[ i ][ j ] = emptyset ;
       }
    }
    for ( int i = 0 ; i < n ; i++ ) {
       for ( int weight = 0 ; weight < weightlimit ; weight++ ) {
	  if ( i == 0 )
	     bestValues[ i ][ weight ] = 0 ;
	  else  {
	     int itemweight = (items.begin( ) + i)->get<1>( ) ; 
	     if ( weight < itemweight ) {
		bestValues[ i ][ weight ] = bestValues[ i - 1 ][ weight ] ;
		solutionSets[ i ][ weight ] = solutionSets[ i - 1 ][ weight ] ;
	     } else { // weight >= itemweight
		if ( bestValues[ i - 1 ][ weight - itemweight ] + 
		   (items.begin( ) + i)->get<2>( ) >
		        bestValues[ i - 1 ][ weight ] ) {
		   bestValues[ i ][ weight ] = 
		       bestValues[ i - 1 ][ weight - itemweight ] + 
	        	(items.begin( ) + i)->get<2>( ) ;
		  solutionSets[ i ][ weight ] = 
		      solutionSets[ i - 1 ][ weight - itemweight ] ;
		  solutionSets[ i ][ weight ].insert( i ) ;
	     }
	     else {
		bestValues[ i ][ weight ] = bestValues[ i - 1 ][ weight ] ;
		solutionSets[ i ][ weight ] = solutionSets[ i - 1 ][ weight ] ;
	     }
	  }
       }
      }
    }
    bestItems.swap( solutionSets[ n - 1][ weightlimit - 1 ] ) ;
    return bestValues[ n - 1 ][ weightlimit - 1 ] ;
}
Output:
The best value that can be packed in the given knapsack is 1030 !
The following items should be packed in the knapsack:
map
compass
water
sandwich
glucose
banana
suntan creme
waterproof trousers
waterproof overclothes
note-case
sunglasses
socks
The total weight of all items is 396 !

Second version

Works with: C++17
#include <iomanip>
#include <iostream>
#include <set>
#include <string>
#include <tuple>
#include <vector>

std::tuple<std::set<int>, int> findBestPack(const std::vector<std::tuple<std::string, int, int> > &items, const int weightlimit) {
    const auto n = items.size();
    int bestValues[n][weightlimit] = { 0 };
    std::set<int> solutionSets[n][weightlimit];
    std::set<int> bestItems;
    for (auto i = 0u; i < n; i++)
        for (auto weight = 0; weight < weightlimit; weight++) {
            if (i == 0)
                bestValues[i][weight] = 0;
            else {
                auto [_, itemweight, value] = *(items.begin() + i);
                if (weight < itemweight) {
                    bestValues[i][weight] = bestValues[i - 1][weight];
                    solutionSets[i][weight] = solutionSets[i - 1][weight];
                } else {
                    if (bestValues[i - 1][weight - itemweight] + value > bestValues[i - 1][weight]) {
                        bestValues[i][weight] = bestValues[i - 1][weight - itemweight] + value;
                        solutionSets[i][weight] = solutionSets[i - 1][weight - itemweight];
                        solutionSets[i][weight].insert(i);
                    } else {
                        bestValues[i][weight] = bestValues[i - 1][weight];
                        solutionSets[i][weight] = solutionSets[i - 1][weight];
                    }
                }
            }
        }

    bestItems.swap(solutionSets[n - 1][weightlimit - 1]);
    return { bestItems, bestValues[n - 1][weightlimit - 1] };
}

int main() {
    const std::vector<std::tuple<std::string, int, int>> items = {
            { "", 0, 0 },
            { "map", 9, 150 },
            { "compass", 13, 35 },
            { "water", 153, 200 },
            { "sandwich", 50, 160 },
            { "glucose", 15, 60 },
            { "tin", 68, 45 },
            { "banana", 27, 60 },
            { "apple", 39, 40 },
            { "cheese", 23, 30 },
            { "beer", 52, 10 },
            { "suntan creme", 11, 70 },
            { "camera", 32, 30 },
            { "T-shirt", 24, 15 },
            { "trousers", 48, 10 },
            { "umbrella", 73, 40 },
            { "waterproof trousers", 42, 70 },
            { "waterproof overclothes", 43, 75 },
            { "note-case", 22, 80 },
            { "sunglasses", 7, 20 },
            { "towel", 18, 12 },
            { "socks", 4, 50 },
            { "book", 30, 10 } };

    const int maximumWeight = 400;
    const auto &[bestItems, bestValue] = findBestPack(items, maximumWeight);
    int totalweight = 0;
    std::cout << std::setw(24) << "best knapsack:" << std::endl;
    for (auto si = bestItems.begin(); si != bestItems.end(); si++) {
       auto [name, weight, value] = *(items.begin() + *si);
       std::cout << std::setw(24) << name << std::setw(6) << weight << std::setw(6) << value << std::endl;
       totalweight += weight;
    }
    std::cout << std::endl << std::setw(24) << "total:" << std::setw(6) << totalweight << std::setw(6) << bestValue << std::endl;
    return 0;
}
Output:
          best knapsack:
                     map     9   150
                 compass    13    35
                   water   153   200
                sandwich    50   160
                 glucose    15    60
                  banana    27    60
            suntan creme    11    70
     waterproof trousers    42    70
  waterproof overclothes    43    75
               note-case    22    80
              sunglasses     7    20
                   socks     4    50

                  total:   396  1030

C_sharp

All combinations, eight threads, break when weight is to large.

using System;  // 4790@3.6
using System.Threading.Tasks;
class Program
{
    static void Main()
    {
        var sw = System.Diagnostics.Stopwatch.StartNew();
        Console.Write(knapSack(400) + "\n" + sw.Elapsed);  // 60 ms
        Console.Read();
    }

    static string knapSack(uint w1)
    {
        uint sol = 0, v1 = 0;
        Parallel.For(1, 9, t =>
        {
            uint j, wi, k, vi, i1 = 1u << w.Length;
            for (uint i = (uint)t; i < i1; i += 8)
            {
                k = wi = vi = 0;
                for (j = i; j > 0; j >>= 1, k++)
                    if ((j & 1) > 0)
                    {
                        if ((wi += w[k]) > w1) break;
                        vi += v[k];
                    }
                if (wi <= w1 && v1 < vi)
                    lock (locker)
                        if (v1 < vi) { v1 = vi; sol = i; }
            }
        });
        string str = "";
        for (uint k = 0; sol > 0; sol >>= 1, k++)
            if ((sol & 1) > 0) str += items[k] + "\n";
        return str;
    }

    static readonly object locker = new object();

    static byte[] w = { 9, 13, 153, 50, 15, 68, 27, 39, 23, 52, 11,
                          32, 24, 48, 73, 42, 43, 22, 7, 18, 4, 30 },

                  v = { 150, 35, 200, 160, 60, 45, 60, 40, 30, 10, 70,
                          30, 15, 10, 40, 70, 75, 80, 20, 12, 50, 10 };

    static string[] items = {"map","compass","water","sandwich","glucose","tin",
                             "banana","apple","cheese","beer","suntan cream",
                             "camera","T-shirt","trousers","umbrella",
                             "waterproof trousers","waterproof overclothes",
                             "note-case","sunglasses","towel","socks","book"};
}

A dynamic version.

using System
class program
{
    static void Main()
    {
        knapSack(40);
        var sw = System.Diagnostics.Stopwatch.StartNew();
        Console.Write(knapSack(400) + "\n" + sw.Elapsed);  // 31 µs
        Console.Read();
    }

    static string knapSack(uint w1)
    {
        uint n = (uint)w.Length; var K = new uint[n + 1, w1 + 1];
        for (uint vi, wi, w0, x, i = 0; i < n; i++)
            for (vi = v[i], wi = w[i], w0 = 1; w0 <= w1; w0++)
            {
                x = K[i, w0];
                if (wi <= w0) x = max(vi + K[i, w0 - wi], x);
                K[i + 1, w0] = x;
            }
        string str = "";
        for (uint v1 = K[n, w1]; v1 > 0; n--)
            if (v1 != K[n - 1, w1])
            {
                v1 -= v[n - 1]; w1 -= w[n - 1]; str += items[n - 1] + "\n";
            }
        return str;
    }

    static uint max(uint a, uint b) { return a > b ? a : b; }

    static byte[] w =  { 9, 13, 153, 50, 15, 68, 27, 39, 23, 52, 11,
                          32, 24, 48, 73, 42, 43, 22, 7, 18, 4, 30 },

                  v =  { 150, 35, 200, 160, 60, 45, 60, 40, 30, 10, 70,
                          30, 15, 10, 40, 70, 75, 80, 20, 12, 50, 10 };

    static string[] items =  {"map","compass","water","sandwich","glucose","tin",
                              "banana","apple","cheese","beer","suntan cream",
                              "camera","T-shirt","trousers","umbrella",
                              "waterproof trousers","waterproof overclothes",
                              "note-case","sunglasses","towel","socks","book"};
}

Ceylon

module.ceylon:

module knapsack "1.0.0" {
}

run.ceylon:

shared void run() {
    value knapsack = pack(items, empty(400));

    print(knapsack);
}

class Item(name,weight,theValue) {
    String name;
    shared Integer weight;
    shared Float theValue;

    shared actual String string = "item(``name``, ``weight``, ``theValue``)";
}

class Knapsack(items,theValue,weight,available) {
    shared Item[] items;
    shared Float theValue;
    shared Integer weight;
    shared Integer available;

    shared Boolean canAccept(Item item)
        => item.weight <= available;

    String itemsString = items.fold("")((total, remaining) => "``total``\t\n``remaining.string``" );

    shared actual String string = "Total value: ``theValue``\nTotal weight: ``weight``\nItems:\n``itemsString``";
}

Knapsack empty(Integer capacity)
    => Knapsack([], 0.0, 0, capacity);


Item[] items =
        [
         Item("map", 9, 150.0),
         Item("compass", 13, 35.0),
         Item("water", 153, 200.0),
         Item("sandwich", 50, 160.0),
         Item("glucose", 15, 60.0),
         Item("tin", 68, 45.0),
         Item("banana", 27, 60.0),
         Item("apple", 39, 40.0),
         Item("cheese", 23, 30.0),
         Item("beer", 52, 10.0),
         Item("cream", 11, 70.0),
         Item("camera", 32, 30.0),
         Item("tshirt", 24, 15.0),
         Item("trousers", 48, 10.0),
         Item("umbrella", 73, 40.0),
         Item("trousers", 42, 70.0),
         Item("overclothes", 43, 75.0),
         Item("notecase", 22, 80.0),
         Item("sunglasses", 7, 20.0),
         Item("towel", 18, 12.0),
         Item("socks", 4, 50.0),
         Item("book", 30, 10.0)
        ];


Knapsack add(Item item, Knapsack knapsack)
    => Knapsack { items = knapsack.items.withTrailing(item);
                  theValue = knapsack.theValue + item.theValue;
                  weight = knapsack.weight + item.weight;
                  available = knapsack.available - item.weight; };

Float rating(Item item) => item.theValue / item.weight.float;

Knapsack pack(Item[] items, Knapsack knapsack)
    // Sort the items by decreasing rating, that is, value divided by weight
    => let (itemsSorted =
                items.group(rating)
                     .sort(byDecreasing((Float->[Item+] entry) => entry.key))
                     .map(Entry.item)
                     .flatMap((element) => element)
                     .sequence())

    packRecursive(itemsSorted,knapsack);

Knapsack packRecursive(Item[] sortedItems, Knapsack knapsack)
    => if (exists firstItem=sortedItems.first, knapsack.canAccept(firstItem))
        then packRecursive(sortedItems.rest, add(firstItem,knapsack))
        else knapsack;


Output:
Total value: 1030.0
Total weight: 396
Items:
	
item(map, 9, 150.0)	
item(socks, 4, 50.0)	
item(cream, 11, 70.0)	
item(glucose, 15, 60.0)	
item(notecase, 22, 80.0)	
item(sandwich, 50, 160.0)	
item(sunglasses, 7, 20.0)	
item(compass, 13, 35.0)	
item(banana, 27, 60.0)	
item(overclothes, 43, 75.0)	
item(trousers, 42, 70.0)	
item(water, 153, 200.0)

Clojure

Uses the dynamic programming solution from Wikipedia. First define the items data:

(def item-data
  [ "map"         9 150
    "compass"    13  35
    "water"     153 200
    "sandwich"   50 160
    "glucose"    15  60
    "tin"        68  45
    "banana"     27  60
    "apple"      39  40
    "cheese"     23  30
    "beer"       52  10
    "suntan cream"   11  70
    "camera"     32  30
    "t-shirt"    24  15
    "trousers"   48  10
    "umbrella"   73  40
    "waterproof trousers"    42  70
    "waterproof overclothes" 43  75
    "note-case"  22  80
    "sunglasses"  7  20
    "towel"      18  12
    "socks"       4  50
    "book"       30  10])

(defstruct item :name :weight :value)

(def items (vec (map #(apply struct item %) (partition 3 item-data))))

m is as per the Wikipedia formula, except that it returns a pair [value indexes] where indexes is a vector of index values in items. value is the maximum value attainable using items 0..i whose total weight doesn't exceed w; indexes are the item indexes that produces the value.

(declare mm) ;forward decl for memoization function

(defn m [i w]
  (cond
    (< i 0) [0 []]
    (= w 0) [0 []]
    :else
    (let [{wi :weight vi :value} (get items i)]
      (if (> wi w)
        (mm (dec i) w)
        (let [[vn sn :as no]  (mm (dec i) w)
              [vy sy :as yes] (mm (dec i) (- w wi))]
          (if (> (+ vy vi) vn)
            [(+ vy vi) (conj sy i)]
            no))))))

(def mm (memoize m))

Call m and print the result:

(use '[clojure.string :only [join]])

(let [[value indexes] (m (-> items count dec) 400)
      names (map (comp :name items) indexes)]
  (println "items to pack:" (join ", " names))
  (println "total value:" value)
  (println "total weight:" (reduce + (map (comp :weight items) indexes))))
Output:
items to pack: map, compass, water, sandwich, glucose, banana, suntan cream, waterproof trousers, 
waterproof overclothes, note-case, sunglasses, socks
total value: 1030
total weight: 396

Common Lisp

Cached method.

;;; memoize
(defmacro mm-set (p v) `(if ,p ,p (setf ,p ,v)))

(defun knapsack (max-weight items)
  (let ((cache (make-array (list (1+ max-weight) (1+ (length items)))
			   :initial-element nil)))

    (labels ((knapsack1 (spc items)
	(if (not items) (return-from knapsack1 (list 0 0 '())))
	(mm-set (aref cache spc (length items))
		(let* ((i (first items))
		       (w (second i))
		       (v (third i))
		       (x (knapsack1 spc (cdr items))))
		  (if (> w spc) x
		    (let* ((y (knapsack1 (- spc w) (cdr items)))
			   (v (+ v (first y))))
		      (if (< v (first x)) x
			(list v (+ w (second y)) (cons i (third y))))))))))

      (knapsack1 max-weight items))))

(print
  (knapsack 400
	    '((map 9 150) (compass 13 35) (water 153 200) (sandwich 50 160)
	      (glucose 15 60) (tin 68 45)(banana 27 60) (apple 39 40)
	      (cheese 23 30) (beer 52 10) (cream 11 70) (camera 32 30)
	      (T-shirt 24 15) (trousers 48 10) (umbrella 73 40)
	      (trousers 42 70) (overclothes 43 75) (notecase 22 80)
	      (glasses 7 20) (towel 18 12) (socks 4 50) (book 30 10))))
Output:
(1030 396
 ((MAP 9 150) (COMPASS 13 35) (WATER 153 200) (SANDWICH 50 160) (GLUCOSE 15 60)
  (BANANA 27 60) (CREAM 11 70) (TROUSERS 42 70) (OVERCLOTHES 43 75)
  (NOTECASE 22 80) (GLASSES 7 20) (SOCKS 4 50)))

Crystal

Branch and bound solution

require "bit_array"

struct BitArray
  def clone
    BitArray.new(size).tap { |new| new.to_slice.copy_from (to_slice) }
  end
end

record Item, name : String, weight : Int32, value : Int32

record Selection, mask : BitArray, cur_index : Int32, total_value : Int32

class Knapsack
  @threshold_value = 0
  @threshold_choice : Selection?
  getter checked_nodes = 0

  def knapsack_step(taken, items, remaining_weight)
    if taken.total_value > @threshold_value
      @threshold_value = taken.total_value
      @threshold_choice = taken
    end
    candidate_index = items.index(taken.cur_index) { |item| item.weight <= remaining_weight }
    return nil unless candidate_index
    @checked_nodes += 1
    candidate = items[candidate_index]
    # candidate is a best of available items, so if we fill remaining value with it
    # and still don't reach the threshold, the branch is wrong
    return nil if taken.total_value + 1.0 * candidate.value / candidate.weight * remaining_weight < @threshold_value
    # now recursively check both variants
    mask = taken.mask.clone
    mask[candidate_index] = true
    knapsack_step Selection.new(mask, candidate_index + 1, taken.total_value + candidate.value), items, remaining_weight - candidate.weight
    mask = taken.mask.clone
    mask[candidate_index] = false
    knapsack_step Selection.new(mask, candidate_index + 1, taken.total_value), items, remaining_weight
  end

  def select(items, max_weight)
    @checked_variants = 0
    # sort by descending relative value
    list = items.sort_by { |item| -1.0 * item.value / item.weight }
    # use heuristic of relative value as an initial estimate for branch&bounds
    w = max_weight
    heur_list = list.take_while { |item| w -= item.weight; w > 0 }
    nothing = Selection.new(BitArray.new(items.size), 0, 0)
    @threshold_value = heur_list.sum(&.value) - 1
    @threshold_choice = nothing
    knapsack_step(nothing, list, max_weight)
    selected = @threshold_choice.not_nil!
    result = [] of Item
    selected.mask.each_with_index { |v, i| result << list[i] if v }
    result
  end
end

possible = [
  Item.new("map", 9, 150),
  Item.new("compass", 13, 35),
  Item.new("water", 153, 200),
  Item.new("sandwich", 50, 160),
  Item.new("glucose", 15, 60),
  Item.new("tin", 68, 45),
  Item.new("banana", 27, 60),
  Item.new("apple", 39, 40),
  Item.new("cheese", 23, 30),
  Item.new("beer", 52, 10),
  Item.new("suntan cream", 11, 70),
  Item.new("camera", 32, 30),
  Item.new("T-shirt", 24, 15),
  Item.new("trousers", 48, 10),
  Item.new("umbrella", 73, 40),
  Item.new("waterproof trousers", 42, 70),
  Item.new("waterproof overclothes", 43, 75),
  Item.new("note-case", 22, 80),
  Item.new("sunglasses", 7, 20),
  Item.new("towel", 18, 12),
  Item.new("socks", 4, 50),
  Item.new("book", 30, 10),
]

solver = Knapsack.new
used = solver.select(possible, 400)
puts "optimal choice: #{used.map(&.name)}"
puts "total weight #{used.sum(&.weight)}, total value #{used.sum(&.value)}"
puts "checked nodes: #{solver.checked_nodes}"
Output:
optimal choice: ["map", "socks", "suntan cream", "glucose", "note-case", "sandwich", "sunglasses", "compass", "banana", "waterproof overclothes", "waterproof trousers", "water"]
total weight 396, total value 1030
checked nodes: 992

D

Dynamic Programming Version

Translation of: Python
import std.stdio, std.algorithm, std.typecons, std.array, std.range;

struct Item { string name; int weight, value; }

Item[] knapsack01DinamicProgramming(immutable Item[] items, in int limit)
pure nothrow @safe {
    auto tab = new int[][](items.length + 1, limit + 1);

    foreach (immutable i, immutable it; items)
        foreach (immutable w; 1 .. limit + 1)
            tab[i + 1][w] = (it.weight > w) ? tab[i][w] :
                max(tab[i][w], tab[i][w - it.weight] + it.value);

    typeof(return) result;
    int w = limit;
    foreach_reverse (immutable i, immutable it; items)
        if (tab[i + 1][w] != tab[i][w]) {
            w -= it.weight;
            result ~= it;
        }

    return result;
}

void main() @safe {
    enum int limit = 400;
    immutable Item[] items = [
        {"apple",      39,  40}, {"banana",        27,  60},
        {"beer",       52,  10}, {"book",          30,  10},
        {"camera",     32,  30}, {"cheese",        23,  30},
        {"compass",    13,  35}, {"glucose",       15,  60},
        {"map",         9, 150}, {"note-case",     22,  80},
        {"sandwich",   50, 160}, {"socks",          4,  50},
        {"sunglasses",  7,  20}, {"suntan cream",  11,  70},
        {"t-shirt",    24,  15}, {"tin",           68,  45},
        {"towel",      18,  12}, {"trousers",      48,  10},
        {"umbrella",   73,  40}, {"water",        153, 200},
        {"waterproof overclothes", 43, 75},
        {"waterproof trousers",    42, 70}];

    immutable bag = knapsack01DinamicProgramming(items, limit);
    writefln("Items:\n%-(  %s\n%)", bag.map!q{ a.name }.retro);
    const t = reduce!q{ a[] += [b.weight, b.value] }([0, 0], bag);
    writeln("\nTotal weight and value: ", t[0] <= limit ? t : [0, 0]);
}
Output:
Items:
  banana
  compass
  glucose
  map
  note-case
  sandwich
  socks
  sunglasses
  suntan cream
  water
  waterproof overclothes
  waterproof trousers

Total weight and value: [396, 1030]

Brute Force Version

Translation of: C
struct Item { string name; int weight, value; }

immutable Item[] items = [
    {"apple",      39,  40}, {"banana",        27,  60},
    {"beer",       52,  10}, {"book",          30,  10},
    {"camera",     32,  30}, {"cheese",        23,  30},
    {"compass",    13,  35}, {"glucose",       15,  60},
    {"map",         9, 150}, {"note-case",     22,  80},
    {"sandwich",   50, 160}, {"socks",          4,  50},
    {"sunglasses",  7,  20}, {"suntan cream",  11,  70},
    {"t-shirt",    24,  15}, {"tin",           68,  45},
    {"towel",      18,  12}, {"trousers",      48,  10},
    {"umbrella",   73,  40}, {"water",        153, 200},
    {"waterproof overclothes", 43, 75},
    {"waterproof trousers",    42, 70}];

struct Solution { uint bits; int value; }
static assert(items.length <= Solution.bits.sizeof * 8);

void solve(in int weight, in int idx, ref Solution s)
pure nothrow @nogc @safe {
    if (idx < 0) {
        s.bits = s.value = 0;
        return;
    }

    if (weight < items[idx].weight) {
        solve(weight, idx - 1, s);
        return;
     }

    Solution v1, v2;
    solve(weight, idx - 1, v1);
    solve(weight - items[idx].weight, idx - 1, v2);

    v2.value += items[idx].value;
    v2.bits |= (1 << idx);

    s = (v1.value >= v2.value) ? v1 : v2;
}

void main() @safe {
    import std.stdio;

    auto s = Solution(0, 0);
    solve(400, items.length - 1, s);

    writeln("Items:");
    int w = 0;
    foreach (immutable i, immutable it; items)
        if (s.bits & (1 << i)) {
            writeln("  ", it.name);
            w += it.weight;
        }
    writefln("\nTotal value: %d; weight: %d", s.value, w);
}

The runtime is about 0.09 seconds.

Output:
Items:
  banana
  compass
  glucose
  map
  note-case
  sandwich
  socks
  sunglasses
  suntan cream
  water
  waterproof overclothes
  waterproof trousers

Total value: 1030; weight: 396

Short Dynamic Programming Version

Translation of: Haskell
import std.stdio, std.algorithm, std.typecons, std.array, std.range;

struct Item { string name; int w, v; }
alias Pair = Tuple!(int,"tot", string[],"names");

immutable Item[] items = [{"apple",39,40}, {"banana", 27, 60},
    {"beer", 52, 10}, {"book", 30, 10}, {"camera", 32, 30},
    {"cheese", 23, 30}, {"compass", 13, 35}, {"glucose", 15, 60},
    {"map", 9, 150}, {"note-case", 22, 80}, {"sandwich", 50, 160},
    {"socks", 4, 50}, {"sunglasses", 7, 20}, {"suntan cream", 11, 70},
    {"t-shirt", 24, 15}, {"tin", 68, 45}, {"towel", 18, 12},
    {"trousers", 48, 10}, {"umbrella", 73, 40}, {"water", 153, 200},
    {"overclothes", 43, 75}, {"waterproof trousers", 42, 70}];

auto addItem(Pair[] lst, in Item it) pure /*nothrow*/ {
    auto aux = lst.map!(vn => Pair(vn.tot + it.v, vn.names ~ it.name));
    return lst[0..it.w] ~ lst[it.w..$].zip(aux).map!q{ a[].max }.array;
}

void main() {
    reduce!addItem(Pair().repeat.take(400).array, items).back.writeln;
}

Runtime about 0.04 seconds.

Output:
Tuple!(int, "tot", string[], "names")(1030, ["banana", "compass", "glucose", "map", "note-case", "sandwich", "socks", "sunglasses", "suntan cream", "water", "overclothes", "waterproof trousers"])

Delphi

Works with: Delphi version 6.0

This is a good example of using an iterator. The problem involves looking at all different compinations of items in the list. If you increment a number up to a certain maximum, you systematically set all combination of bits in that number. The trick is turning the pattern of bits in a number into indices into the packing list. The iterater handles that and so it can be used in multiple places in the code to step through various the combinations of items in the list.

{Item to store data in}

type TPackItem = record
 Name: string;
 Weight,Value: integer;
 end;

{List of items, weights and values}

const ItemsList: array [0..21] of TPackItem = (
   (Name: 'map'; Weight: 9; Value: 150),
   (Name: 'compass'; Weight: 13; Value: 35),
   (Name: 'water'; Weight: 153; Value: 200),
   (Name: 'sandwich'; Weight: 50; Value: 160),
   (Name: 'glucose'; Weight: 15; Value: 60),
   (Name: 'tin'; Weight: 68; Value: 45),
   (Name: 'banana'; Weight: 27; Value: 60),
   (Name: 'apple'; Weight: 39; Value: 40),
   (Name: 'cheese'; Weight: 23; Value: 30),
   (Name: 'beer'; Weight: 52; Value: 10),
   (Name: 'suntan cream'; Weight: 11; Value: 70),
   (Name: 'camera'; Weight: 32; Value: 30),
   (Name: 't-shirt'; Weight: 24; Value: 15),
   (Name: 'trousers'; Weight: 48; Value: 10),
   (Name: 'umbrella'; Weight: 73; Value: 40),
   (Name: 'waterproof trousers'; Weight: 42; Value: 70),
   (Name: 'waterproof overclothes'; Weight: 43; Value: 75),
   (Name: 'note-case'; Weight: 22; Value: 80),
   (Name: 'sunglasses'; Weight: 7; Value: 20),
   (Name: 'towel'; Weight: 18; Value: 12),
   (Name: 'socks'; Weight: 4; Value: 50),
   (Name: 'book'; Weight: 30; Value: 10));

{Iterater object to step through all the indices
{ corresponding to the bits in "N". This is used }
{ step through all the combinations of items }

type TBitIterator = class(TObject)
 private
   FNumber,FIndex: integer;
 public
  procedure Start(StartNumber: integer);
  function Next(var Index: integer): boolean;
 end;

procedure TBitIterator.Start(StartNumber: integer);
{Set the starting value of the number }
begin
FNumber:=StartNumber;
end;


function TBitIterator.Next(var Index: integer): boolean;
{Return the next available index}
begin
Result:=False;
while FNumber>0 do
	begin
	Result:=(FNumber and 1)=1;
	if Result then Index:=FIndex;
	FNumber:=FNumber shr 1;
	Inc(FIndex);
	if Result then break;
	end;
end;

{=============================================================================}


procedure GetSums(N: integer; var Weight,Value: integer);
{Iterate through all indices corresponding to N}
{Get get the sum of their values}
var Inx: integer;
var BI: TBitIterator;
begin
BI:=TBitIterator.Create;
try
BI.Start(N);
Weight:=0; Value:=0;
while BI.Next(Inx) do
	begin
	Weight:=Weight+ItemsList[Inx].Weight;
	Value:=Value+ItemsList[Inx].Value;
	end;
finally BI.Free; end;
end;



procedure DoKnapsackProblem(Memo: TMemo);
{Find optimized solution to Knapsack problem}
{By iterating through all binary combinations}
var I,J,Inx: integer;
var Max: integer;
var WeightSum,ValueSum: integer;
var BestValue,BestIndex,BestWeight: integer;
var S: string;
var BI: TBitIterator;
begin
BI:=TBitIterator.Create;
try
{Get value that will cover all binary combinations}
Max:=1 shl Length(ItemsList)-1;
BestValue:=0;
{Iterate through all combinations of bits}
for I:=1 to Max do
	begin
	{Get the sum of the weights and values}
	GetSums(I,WeightSum,ValueSum);
	{Ignore any weight greater than 400}
	if WeightSum>400 then continue;
	{Test if this is the best value so far}
	if ValueSum>BestValue then
		begin
		BestValue:=ValueSum;
		BestWeight:=WeightSum;
		BestIndex:=I;
		end;
	end;
{Display the best result}
Memo.Lines.Add('  Item                    Weight  Value');
Memo.Lines.Add('---------------------------------------');
BI.Start(BestIndex);
while BI.Next(Inx) do
	begin
	S:='  '+Format('%-25s',[ItemsList[Inx].Name]);
	S:=S+Format('%5d',[ItemsList[Inx].Weight]);
	S:=S+Format('%7d',[ItemsList[Inx].Value]);
	Memo.Lines.Add(S);
	end;
Memo.Lines.Add('---------------------------------------');
Memo.Lines.Add(Format('Total                     %6d %6d',[BestWeight,BestValue]));
Memo.Lines.Add('Best Inx: '+IntToStr(BestIndex));
Memo.Lines.Add('Best Value: '+IntToStr(BestValue));
Memo.Lines.Add('Best Weight: '+IntToStr(BestWeight));
finally BI.Free; end;
end;
Output:
  Item                    Weight  Value
---------------------------------------
  map                          9    150
  compass                     13     35
  water                      153    200
  sandwich                    50    160
  glucose                     15     60
  banana                      27     60
  suntan cream                11     70
  waterproof trousers         42     70
  waterproof overclothes      43     75
  note-case                   22     80
  sunglasses                   7     20
  socks                        4     50
---------------------------------------
Total                        396   1030
Best Inx: 1541215
Best Value: 1030
Best Weight: 396

Dart

List solveKnapsack(items, maxWeight) {
  int MIN_VALUE=-100;
  int N = items.length; // number of items 
  int W = maxWeight; // maximum weight of knapsack
  
  List profit = new List(N+1);
  List weight = new List(N+1);
  
  // generate random instance, items 1..N
  for(int n = 1; n<=N; n++) {
    profit[n] = items[n-1][2];
    weight[n] = items[n-1][1];
    
  }
  
  // opt[n][w] = max profit of packing items 1..n with weight limit w
  // sol[n][w] = does opt solution to pack items 1..n with weight limit w include item n?
  List<List<int>> opt = new List<List<int>>(N+1);
  for (int i=0; i<N+1; i++) {
    opt[i] = new List<int>(W+1);
    for(int j=0; j<W+1; j++) {
      opt[i][j] = MIN_VALUE;
    }
  }
  
  List<List<bool>> sol = new List<List<bool>>(N+1);
  for (int i=0; i<N+1; i++) {
    sol[i] = new List<bool>(W+1);
    for(int j=0; j<W+1; j++) {
      sol[i][j] = false;
    }
  }
  
  for(int n=1; n<=N; n++) {
    for (int w=1; w <= W; w++) {
      // don't take item n      
      int option1 = opt[n-1][w];
      
      // take item n
      int option2 = MIN_VALUE;
      if (weight[n] <= w) {
        option2 = profit[n] + opt[n-1][w - weight[n]];
      }
            
      // select better of two options
      opt[n][w] = Math.max(option1, option2);
      sol[n][w] = (option2 > option1);
    }
  }
  
  // determine which items to take
  List<List> packItems = new List<List>();
  List<bool> take = new List(N+1);
  for (int n = N, w = W; n > 0; n--) {
    if (sol[n][w]) {
      take[n] = true;
      w = w - weight[n];
      packItems.add(items[n-1]); 
    } else {
      take[n] = false; 
    }
  }
    
  return packItems;
  
}

main() {
  List knapsackItems = [];
  knapsackItems.add(["map", 9, 150]);
  knapsackItems.add(["compass", 13, 35]);
  knapsackItems.add(["water", 153, 200]);
  knapsackItems.add(["sandwich", 50, 160]);
  knapsackItems.add(["glucose", 15, 60]);
  knapsackItems.add(["tin", 68, 45]);
  knapsackItems.add(["banana", 27, 60]);
  knapsackItems.add(["apple", 39, 40]);
  knapsackItems.add(["cheese", 23, 30]);
  knapsackItems.add(["beer", 52, 10]);
  knapsackItems.add(["suntan cream", 11, 70]);
  knapsackItems.add(["camera", 32, 30]);
  knapsackItems.add(["t-shirt", 24, 15]);
  knapsackItems.add(["trousers", 48, 10]);
  knapsackItems.add(["umbrella", 73, 40]);
  knapsackItems.add(["waterproof trousers", 42, 70]);
  knapsackItems.add(["waterproof overclothes", 43, 75]);
  knapsackItems.add(["note-case", 22, 80]);
  knapsackItems.add(["sunglasses", 7, 20]);
  knapsackItems.add(["towel", 18, 12]);
  knapsackItems.add(["socks", 4, 50]);
  knapsackItems.add(["book", 30, 10]);
  int maxWeight = 400;
  Stopwatch sw = new Stopwatch.start();
  List p = solveKnapsack(knapsackItems, maxWeight);
  sw.stop();
  int totalWeight = 0;
  int totalValue = 0;
  print(["item","profit","weight"]);
  p.forEach((var i) { print("${i}"); totalWeight+=i[1]; totalValue+=i[2]; });
  print("Total Value = ${totalValue}");
  print("Total Weight = ${totalWeight}");
  print("Elapsed Time = ${sw.elapsedInMs()}ms");
  
}
Output:
[item, profit, weight]
[socks, 4, 50]
[sunglasses, 7, 20]
[note-case, 22, 80]
[waterproof overclothes, 43, 75]
[waterproof trousers, 42, 70]
[suntan cream, 11, 70]
[banana, 27, 60]
[glucose, 15, 60]
[sandwich, 50, 160]
[water, 153, 200]
[compass, 13, 35]
[map, 9, 150]
Total Value = 1030
Total Weight = 396
Elapsed Time = 6ms

EasyLang

name$[] = [ "map" "compass" "water" "sandwich" "glucose" "tin" "banana" "apple" "cheese" "beer" "suntan cream" "camera" "t-shirt" "trousers" "umbrella" "waterproof trousers" "waterproof overclothes" "note-case" "sunglasses" "towel" "socks" "book" ]
weight[] = [ 9 13 153 50 15 68 27 39 23 52 11 32 24 48 73 42 43 22 7 18 4 30 ]
value[] = [ 150 35 200 160 60 45 60 40 30 10 70 30 15 10 40 70 75 80 20 12 50 10 ]
max_w = 400
# 
proc solve i maxw . items[] wres vres .
   if i <= 0
      wres = 0
      vres = 0
      items[] = [ ]
   elif weight[i] > maxw
      solve i - 1 maxw items[] wres vres
   else
      solve i - 1 maxw items[] wres vres
      solve i - 1 maxw - weight[i] items1[] w1 v1
      v1 += value[i]
      if v1 > vres
         swap items[] items1[]
         items[] &= i
         wres = w1 + weight[i]
         vres = v1
      .
   .
.
solve len weight[] max_w items[] w v
print "weight: " & w
print "value: " & v
print "items:"
for item in items[]
   print "  " & name$[item]
.

EchoLisp

(require 'struct)
(require 'hash)
(require 'sql)

(define H (make-hash))
(define T (make-table (struct goodies (name poids valeur ))))
(define-syntax-rule (name i) (table-xref T i 0))
(define-syntax-rule (poids i) (table-xref T i 1))
(define-syntax-rule (valeur i) (table-xref T i 2))

;;  make an unique hash-key from (i rest)
(define (t-idx i r)  (string-append i "|" r))
;; retrieve best score for item i, remaining r availbble weight
(define (t-get i r)  (or (hash-ref H (t-idx i r)) 0))

;; compute best score (i), assuming best (i-1 rest) is known
(define (score i restant)
	(if (< i 0) 0
	(hash-ref! H (t-idx i restant)
		(if ( >= restant (poids i)) 
			(max 
				(score (1- i) restant) 
			    (+ (score (1- i) (- restant (poids i))) (valeur i)))
		    (score (1- i) restant)))))

;; compute best scores, starting from last item
(define (task W)
        (define restant W)
        (define N (1- (table-count T)))
		(writeln 'total-value (score N W))
		(for/list  ((i (in-range N -1 -1)))
			#:continue (= (t-get i restant) (t-get (1- i) restant))
			(set! restant (- restant (poids i)))
			(name i)))
Output:
;; init table
(define goodies
          '((map 9 150) ; 9 is weight, 150 is value
            (compass 13 35) (water 153 200) (sandwich 50 160)
            (glucose 15 60) (tin 68 45)(banana 27 60) (apple 39 40)
            (fromage 23 30) (beer 52 10) (🌞-suntan-cream 11 70) (camera 32 30)
            (T-shirt 24 15) (pantalons 48 10) (umbrella 73 40)
            (☔️-trousers 42 70) (☔️-overclothes 43 75) (note-case 22 80)
            (🌞-sun-glasses 7 20) (towel 18 12) (socks 4 50) (book 30 10)))
(list->table goodies T)


(task 400)
total-value     1030    
     (socks 🌞-sun-glasses note-case ☔️-overclothes ☔️-trousers 🌞-suntan-cream banana 
    glucose sandwich water compass map)


(length (hash-keys H))
    4939  ;; number of entries "i | weight" in hash table

Eiffel

class
	APPLICATION

create
	make

feature {NONE} -- Initialization

	make
		local
			knapsack: KNAPSACKZEROONE
		do
			create knapsack.make (400)
			knapsack.add_item (create {ITEM}.make ("", 0, 0))
			knapsack.add_item (create {ITEM}.make ("map", 9, 150))
			knapsack.add_item (create {ITEM}.make ("compass", 13, 35))
			knapsack.add_item (create {ITEM}.make ("water", 153, 200))
			knapsack.add_item (create {ITEM}.make ("sandwich", 50, 160))
			knapsack.add_item (create {ITEM}.make ("glucose", 15, 60))
			knapsack.add_item (create {ITEM}.make ("tin", 68, 45))
			knapsack.add_item (create {ITEM}.make ("banana", 27, 60))
			knapsack.add_item (create {ITEM}.make ("apple", 39, 40))
			knapsack.add_item (create {ITEM}.make ("cheese", 23, 30))
			knapsack.add_item (create {ITEM}.make ("beer", 52, 10))
			knapsack.add_item (create {ITEM}.make ("suntan cream", 11, 70))
			knapsack.add_item (create {ITEM}.make ("camera", 32, 30))
			knapsack.add_item (create {ITEM}.make ("T-shirt", 24, 15))
			knapsack.add_item (create {ITEM}.make ("trousers", 48, 10))
			knapsack.add_item (create {ITEM}.make ("umbrella, ella ella", 73, 40))
			knapsack.add_item (create {ITEM}.make ("waterproof trousers", 42, 70))
			knapsack.add_item (create {ITEM}.make ("waterproof overclothes", 43, 75))
			knapsack.add_item (create {ITEM}.make ("note-case", 22, 80))
			knapsack.add_item (create {ITEM}.make ("sunglasses", 7, 20))
			knapsack.add_item (create {ITEM}.make ("towel", 18, 12))
			knapsack.add_item (create {ITEM}.make ("socks", 4, 50))
			knapsack.add_item (create {ITEM}.make ("book", 30, 10))
			knapsack.compute_solution
		end

end
class
	ITEM

create
	make, make_from_other

feature

	name: STRING

	weight: INTEGER

	value: INTEGER

	make_from_other (other: ITEM)
			-- Item with name, weight and value set to 'other's name, weight and value.
		do
			name := other.name
			weight := other.weight
			value := other.value
		end

	make (a_name: String; a_weight, a_value: INTEGER)
			-- Item with name, weight and value set to 'a_name', 'a_weight' and 'a_value'.
		require
			a_name /= Void
			a_weight >= 0
			a_value >= 0
		do
			name := a_name
			weight := a_weight
			value := a_value
		end

end
class
	KNAPSACKZEROONE

create
	make

feature

	items: ARRAY [ITEM]

	max_weight: INTEGER

feature

	make (a_max_weight: INTEGER)
			-- Make an empty knapsack.
		require
			a_max_weight >= 0
		do
			create items.make_empty
			max_weight := a_max_weight
		end

	add_item (item: ITEM)
			-- Add 'item' to knapsack.
		local
			temp: ITEM
		do
			create temp.make_from_other (item)
			items.force (item, items.count + 1)
		end

	compute_solution
		local
			M: ARRAY [INTEGER]
			n: INTEGER
			i, j: INTEGER
			w_i, v_i: INTEGER
			item_i: ITEM
			final_items: LINKED_LIST [ITEM]
		do
			n := items.count
			create M.make_filled (0, 1, n * max_weight)
			from
				i := 2
			until
				(i > n)
			loop
				from
					j := 1
				until
					j > max_weight
				loop
					item_i := items [i]
					w_i := item_i.weight
					if w_i <= j then
						v_i := item_i.value
						M [(i - 1) * max_weight + j] := max (M [(i - 2) * max_weight + j], M [(i - 2) * max_weight + j - w_i + 1] + v_i)
					else
						M [(i - 1) * max_weight + j] := M [(i - 2) * max_weight + j]
					end
					j := j + 1
				end
				i := i + 1
			end
			io.put_string ("The final value of the knapsack will be: ")
			io.put_integer (M [(n - 1) * max_weight + max_weight]);
			io.new_line
				--compute the items that fit into the knapsack
			create final_items.make
			io.put_string ("We'll take the following items: %N");
			from
				i := n
				j := max_weight
			until
				i <= 1 or j <= 1
			loop
				item_i := items [i]
				w_i := item_i.weight
				if w_i <= j then
					v_i := item_i.value
					if M [(i - 1) * max_weight + j] = M [(i - 2) * max_weight + j] then
					else
						final_items.extend (item_i)
						io.put_string (item_i.name)
						io.new_line
						j := j - w_i
					end
				else
				end
				i := i - 1
			end
		end

feature {NONE}

	max (a, b: INTEGER): INTEGER
			-- Max of 'a' and 'b'.
		do
			Result := a
			if a < b then
				Result := b
			end
		end

end
Output:
The final value of the knapsack will be: 1030
We'll take the following items:
socks
sunglasses
note-case
waterproof overclothes
waterproof trousers
suntan cream
banana
glucose
sandwich
water
compass
map

Elixir

Translation of: Erlang
defmodule Knapsack do
  def solve([], _total_weight, item_acc, value_acc, weight_acc), do:
    {item_acc, value_acc, weight_acc}
  def solve([{_item, item_weight, _item_value} | t],
            total_weight,
            item_acc,
            value_acc,
            weight_acc) when item_weight > total_weight, do:
    solve(t, total_weight, item_acc, value_acc, weight_acc)
  def solve([{item_name, item_weight, item_value} | t],
            total_weight,
            item_acc,
            value_acc,
            weight_acc) do
    {_tail_item_acc, tail_value_acc, _tail_weight_acc} = tail_res =
        solve(t, total_weight, item_acc, value_acc, weight_acc)
    {_head_item_acc, head_value_acc, _head_weight_acc} = head_res =
        solve(t,
              total_weight - item_weight,
              [item_name | item_acc],
              value_acc + item_value,
              weight_acc + item_weight)
    if tail_value_acc > head_value_acc, do: tail_res, else: head_res
  end
end

stuff = [{"map",                      9,   150},
         {"compass",                 13,    35},
         {"water",                  153,   200},
         {"sandwich",                50,   160},
         {"glucose",                 15,    60},
         {"tin",                     68,    45},
         {"banana",                  27,    60},
         {"apple",                   39,    40},
         {"cheese",                  23,    30},
         {"beer",                    52,    10},
         {"suntan cream",            11,    70},
         {"camera",                  32,    30},
         {"T-shirt",                 24,    15},
         {"trousers",                48,    10},
         {"umbrella",                73,    40},
         {"waterproof trousers",     42,    70},
         {"waterproof overclothes",  43,    75},
         {"note-case",               22,    80},
         {"sunglasses",               7,    20},
         {"towel",                   18,    12},
         {"socks",                    4,    50},
         {"book",                    30,    10}]
max_weight = 400

go = fn (stuff, max_weight) ->
  {time, {item_list, total_value, total_weight}} = :timer.tc(fn ->
    Knapsack.solve(stuff, max_weight, [], 0, 0)
  end)
  IO.puts "Items:"
  Enum.each(item_list, fn item -> IO.inspect item end)
  IO.puts "Total value: #{total_value}"
  IO.puts "Total weight: #{total_weight}"
  IO.puts "Time elapsed in milliseconds: #{time/1000}"
end
go.(stuff, max_weight)
Output:
Items:
"socks"
"sunglasses"
"note-case"
"waterproof overclothes"
"waterproof trousers"
"suntan cream"
"banana"
"glucose"
"sandwich"
"water"
"compass"
"map"
Total value: 1030
Total weight: 396
Time elapsed in milliseconds: 733.0

Emacs Lisp

Translation of: Common Lisp

with changes (memoization without macro)

(defun ks (max-w items)
  (let ((cache (make-vector (1+ (length items)) nil)))
    (dotimes (n (1+ (length items)))
      (setf (aref cache n) (make-hash-table :test 'eql)))  
    (defun ks-emb (spc items)
      (let ((slot (gethash spc (aref cache (length items)))))
        (cond 
         ((null items) (list 0 0 '()))
         (slot slot)
         (t (puthash spc 
                  (let*
                      ((i (car items))
                       (w (nth 1 i))
                       (v (nth 2 i))
                       (x (ks-emb spc (cdr items))))
                    (cond 
                     ((> w spc) x)
                     (t
                      (let* ((y (ks-emb (- spc w) (cdr items)))
                             (v (+ v (car y))))
                        (cond 
                         ((< v (car x)) x)
                         (t 
                          (list v (+ w (nth 1 y)) (cons i (nth 2 y)))))))))
                  (aref cache (length items)))))))
    (ks-emb max-w items)))

(ks 400
    '((map 9 150) (compass 13 35) (water 153 200) (sandwich 50 160)
      (glucose 15 60) (tin 68 45)(banana 27 60) (apple 39 40)
      (cheese 23 30) (beer 52 10) (cream 11 70) (camera 32 30)
      (T-shirt 24 15) (trousers 48 10) (umbrella 73 40)
      (waterproof-trousers 42 70) (overclothes 43 75) (notecase 22 80)
      (glasses 7 20) (towel 18 12) (socks 4 50) (book 30 10)))
Output:
(1030 396 ((map 9 150) (compass 13 35) (water 153 200) (sandwich 50 160) (glucose 15 60) 
(banana 27 60) (cream 11 70) (waterproof-trousers 42 70) (overclothes 43 75) (notecase 22 80) 
(glasses 7 20) (socks 4 50)))

Another way without cache :

(defun best-rate (l1 l2)
  "predicate for sorting a list of elements regarding the value/weight rate"
  (let*
      ((r1 (/ (* 1.0 (nth 2 l1)) (nth 1 l1)))
       (r2 (/ (* 1.0 (nth 2 l2)) (nth 1 l2))))
    (cond
     ((> r1 r2) t)
     (t nil))))

(defun ks1 (l max)
  "return a complete list - complete means 'less than max-weight
but add the next element is impossible'"
(let ((l (sort l 'best-rate)))
  (cond
   ((null l) l)
   ((<= (nth 1 (car l)) max) 
    (cons (car l) (ks1 (cdr l) (- max (nth 1 (car l))))))
   (t (ks1 (cdr l) max)))))

(defun totval (lol)
  "totalize values of a list - lol is not for laughing 
but for list of list"
  (cond 
   ((null lol) 0)
   (t
    (+
     (nth 2 (car lol))
     (totval (cdr lol))))))

(defun ks (l max)
  "browse the list to find the best subset to put in the f***ing knapsack"
    (cond
     ((null (cdr l)) (list (car l)))
     (t
      (let*
          ((x (ks1 l max))
           (y (ks (cdr l) max)))
        (cond
         ((> (totval x) (totval y)) x)
         (t y))))))

        (ks '((map 9 150) (compass 13 35) (water 153 200) (sandwich 50 160)
              (glucose 15 60) (tin 68 45)(banana 27 60) (apple 39 40)
              (cheese 23 30) (beer 52 10) (cream 11 70) (camera 32 30)
              (T-shirt 24 15) (trousers 48 10) (umbrella 73 40)
              (waterproof-trousers 42 70) (overclothes 43 75) (notecase 22 80)
              (glasses 7 20) (towel 18 12) (socks 4 50) (book 30 10)) 400)
Output:

with org-babel in Emacs

| map                 |   9 |  150 |
| socks               |   4 |   50 |
| cream               |  11 |   70 |
| glucose             |  15 |   60 |
| notecase            |  22 |   80 |
| sandwich            |  50 |  160 |
| glasses             |   7 |   20 |
| compass             |  13 |   35 |
| banana              |  27 |   60 |
| overclothes         |  43 |   75 |
| waterproof-trousers |  42 |   70 |
| water               | 153 |  200 |
|                     | 396 | 1030 |

Erlang

-module(knapsack_0_1).

-export([go/0,
         solve/5]).

-define(STUFF,
        [{"map",                      9,   150},
         {"compass",                 13,    35},
         {"water",                  153,   200},
         {"sandwich",                50,   160},
         {"glucose",                 15,    60},
         {"tin",                     68,    45},
         {"banana",                  27,    60},
         {"apple",                   39,    40},
         {"cheese",                  23,    30},
         {"beer",                    52,    10},
         {"suntan cream",            11,    70},
         {"camera",                  32,    30},
         {"T-shirt",                 24,    15},
         {"trousers",                48,    10},
         {"umbrella",                73,    40},
         {"waterproof trousers",     42,    70},
         {"waterproof overclothes",  43,    75},
         {"note-case",               22,    80},
         {"sunglasses",               7,    20},
         {"towel",                   18,    12},
         {"socks",                    4,    50},
         {"book",                    30,    10}
        ]).

-define(MAX_WEIGHT, 400).

go() ->
    StartTime = os:timestamp(),
    {ItemList, TotalValue, TotalWeight} =
        solve(?STUFF, ?MAX_WEIGHT, [], 0, 0),
    TimeElapsed = timer:now_diff(os:timestamp(), StartTime),
    io:format("Items: ~n"),
    [io:format("~p~n", [Item]) || Item <- ItemList],
    io:format(
      "Total value: ~p~nTotal weight: ~p~nTime elapsed in milliseconds: ~p~n",
      [TotalValue, TotalWeight, TimeElapsed/1000]).

solve([], _TotalWeight, ItemAcc, ValueAcc, WeightAcc) ->
    {ItemAcc, ValueAcc, WeightAcc};
solve([{_Item, ItemWeight, _ItemValue} | T],
      TotalWeight,
      ItemAcc,
      ValueAcc,
      WeightAcc) when ItemWeight > TotalWeight ->
    solve(T, TotalWeight, ItemAcc, ValueAcc, WeightAcc);
solve([{ItemName, ItemWeight, ItemValue} | T],
      TotalWeight,
      ItemAcc,
      ValueAcc,
      WeightAcc) ->
    {_TailItemAcc, TailValueAcc, _TailWeightAcc} = TailRes =
        solve(T, TotalWeight, ItemAcc, ValueAcc, WeightAcc),
    {_HeadItemAcc, HeadValueAcc, _HeadWeightAcc} = HeadRes =
        solve(T,
              TotalWeight - ItemWeight,
              [ItemName | ItemAcc],
              ValueAcc + ItemValue,
              WeightAcc + ItemWeight),

    case TailValueAcc > HeadValueAcc of
        true ->
            TailRes;
        false ->
            HeadRes
    end.
Output:
1> knapsack_0_1:go().
Items: 
"socks"
"sunglasses"
"note-case"
"waterproof overclothes"
"waterproof trousers"
"suntan cream"
"banana"
"glucose"
"sandwich"
"water"
"compass"
"map"
Total value: 1030
Total weight: 396
Time elapsed in milliseconds: 133.445
ok

Euler Math Toolbox

>items=["map","compass","water","sandwich","glucose", ...
>  "tin","banana","apple","cheese","beer","suntan creame", ...
>  "camera","t-shirt","trousers","umbrella","waterproof trousers", ...
>  "waterproof overclothes","note-case","sunglasses", ...
>  "towel","socks","book"];
>ws = [9,13,153,50,15,68,27,39,23,52,11, ...
>  32,24,48,73,42,43,22,7,18,4,30];
>vs = [150,35,200,160,60,45,60,40,30,10,70, ...
>  30,15,10,40,70,75,80,20,12,50,10];
>A=ws_id(cols(ws));
>c=vs;
>b=[400]_ones(cols(vs),1);
>sol = intsimplex(A,b,c,eq=-1,>max,>check);
>items[nonzeros(sol)]
 map
 compass
 water
 sandwich
 glucose
 banana
 suntan creame
 waterproof trousers
 waterproof overclothes
 note-case
 sunglasses
 socks

F#

Using A* Algorithm

//Solve Knapsack 0-1 using A* algorithm
//Nigel Galloway, August 3rd., 2018
let knapStar items maxW=
  let l=List.length items
  let p=System.Collections.Generic.SortedSet<float*int*float*float*list<int>>() //H*; level; value of items taken so far; weight so far
  p.Add (0.0,0,0.0,0.0,[])|>ignore
  let H items maxW=let rec H n g a=match g with |(_,w,v)::e->let t=n+w
                                                             if t<=maxW then H t e (a+v) else a+(v/w)*(maxW-n)
                                                |_->a
                   H 0.0 items 0.0
  let pAdd ((h,_,_,_,_) as n) bv=if h>bv then p.Add n |> ignore
  let fH n (bv,t) w' v' t'=let _,w,v=List.item n items
                           let e=max bv (if w<=(maxW-w') then v'+v else bv)
                           let rt=n::t'
                           if n+1<l then pAdd ((v'+H (List.skip (n+1) items) maxW),n+1,v',w',t') bv
                                         if w<=(maxW-w') then pAdd ((v'+v+H (List.skip (n+1) items) (maxW-w')),n+1,v'+v,w'+w,rt) bv
                           if e>bv then (e,rt) else (bv,t)
  let rec fN (bv,t)=
    let h,zl,zv,zw,zt as r=p.Max
    p.Remove r |> ignore
    if bv>=h then t else fN (fH zl (bv,t) zw zv zt)
  fN (fH 0 (0.0,[]) 0.0 0.0 [])
Output:
let itemsf = [
  "map",                     9.0,  150.0;
  "compass",                13.0,   35.0;
  "water",                 153.0,  200.0;
  "sandwich",               50.0,  160.0;
  "glucose",                15.0,   60.0;
  "tin",                    68.0,   45.0;
  "banana",                 27.0,   60.0;
  "apple",                  39.0,   40.0;
  "cheese",                 23.0,   30.0;
  "beer",                   52.0,   10.0;
  "suntan cream",           11.0,   70.0;
  "camera",                 32.0,   30.0;
  "t-shirt",                24.0,   15.0;
  "trousers",               48.0,   10.0;
  "umbrella",               73.0,   40.0;
  "waterproof trousers",    42.0,   70.0;
  "waterproof overclothes", 43.0,   75.0;
  "note-case",              22.0,   80.0;
  "sunglasses",              7.0,   20.0;
  "towel",                  18.0,   12.0;
  "socks",                   4.0,   50.0;
  "book",                   30.0,   10.0;]|> List.sortBy(fun(_,n,g)->n/g)
> let x=knapStar itemsf 400.0;;
> x|>Seq.map (fun n->Seq.item n itemsf)|>Seq.sumBy(fun (_,_,n)->(+n));;                                                                 
val it : float = 1030.0
> x|>Seq.map (fun n->Seq.item n itemsf)|>Seq.sumBy(fun (_,n,_)->(+n));;
val it : float = 396.0
> x|>Seq.iter(fun n->printfn "%A" (List.item n itemsf));; 
("map", 9.0, 150.0)
("socks", 4.0, 50.0)
("suntan cream", 11.0, 70.0)
("glucose", 15.0, 60.0)
("note-case", 22.0, 80.0)
("sandwich", 50.0, 160.0)
("sunglasses", 7.0, 20.0)
("compass", 13.0, 35.0)
("banana", 27.0, 60.0)
("waterproof overclothes", 43.0, 75.0)
("waterproof trousers", 42.0, 70.0)
("water", 153.0, 200.0)

Factor

Using dynamic programming:

USING: accessors arrays fry io kernel locals make math
math.order math.parser math.ranges sequences sorting ;
IN: rosetta.knappsack.0-1

TUPLE: item
    name weight value ;

CONSTANT: items {
        T{ item f "map" 9 150 }
        T{ item f "compass" 13 35 }
        T{ item f "water" 153 200 }
        T{ item f "sandwich" 50 160 }
        T{ item f "glucose" 15 60 }
        T{ item f "tin" 68 45 }
        T{ item f "banana" 27 60 }
        T{ item f "apple" 39 40 }
        T{ item f "cheese" 23 30 }
        T{ item f "beer" 52 10 }
        T{ item f "suntan cream" 11 70 }
        T{ item f "camera" 32 30 }
        T{ item f "t-shirt" 24 15 }
        T{ item f "trousers" 48 10 }
        T{ item f "umbrella" 73 40 }
        T{ item f "waterproof trousers" 42 70 }
        T{ item f "waterproof overclothes" 43 75 }
        T{ item f "note-case" 22 80 }
        T{ item f "sunglasses" 7 20 }
        T{ item f "towel" 18 12 }
        T{ item f "socks" 4 50 }
        T{ item f "book" 30 10 }
    }

CONSTANT: limit 400

: make-table ( -- table )
    items length 1 + [ limit 1 + 0 <array> ] replicate ;

:: iterate ( item-no table -- )
    item-no table nth :> prev
    item-no 1 + table nth :> curr
    item-no items nth :> item
    limit [1,b] [| weight |
        weight prev nth
        weight item weight>> - dup 0 >=
        [ prev nth item value>> + max ]
        [ drop ] if
        weight curr set-nth
    ] each ;

: fill-table ( table -- )
    [ items length iota ] dip
    '[ _ iterate ] each ;

:: extract-packed-items ( table -- items )
    [
        limit :> weight!
        items length iota <reversed> [| item-no |
            item-no table nth :> prev
            item-no 1 + table nth :> curr
            weight [ curr nth ] [ prev nth ] bi =
            [
                item-no items nth
                [ name>> , ] [ weight>> weight swap - weight! ] bi
            ] unless
        ] each
    ] { } make ;

: solve-knappsack ( -- items value )
    make-table [ fill-table ]
    [ extract-packed-items ] [ last last ] tri ;

: main ( -- )
    solve-knappsack
    "Total value: " write number>string print
    "Items packed: " print
    natural-sort
    [ "   " write print ] each ;
 ( scratchpad ) main
 Total value: 1030
 Items packed: 
    banana
    compass
    glucose
    map
    note-case
    sandwich
    socks
    sunglasses
    suntan cream
    water
    waterproof overclothes
    waterproof trousers

Forth

\ Rosetta Code Knapp-sack 0-1 problem.  Tested under GForth 0.7.3.
\ 22 items. On current processors a set fits nicely in one CELL (32 or 64 bits).
\ Brute force approach: for every possible set of 22 items,
\ check for admissible solution then for optimal set.

: offs HERE over - ;
        400 VALUE WLIMIT
        0 VALUE ITEM
        0 VALUE VAL
        0 VALUE /ITEM
        0 VALUE ITEMS#
Create Sack
HERE
        9 ,                     offs TO VAL
        150 ,                   offs TO ITEM
        s" map            " s,  offs TO /ITEM
DROP
 13 ,  35 , s" compass        " s,
153 , 200 , s" water          " s,
 50 , 160 , s" sandwich       " s,
 15 ,  60 , s" glucose        " s,
 68 ,  45 , s" tin            " s,
 27 ,  60 , s" banana         " s,
 39 ,  40 , s" apple          " s,
 23 ,  30 , s" cheese         " s,
 52 ,  10 , s" beer           " s,
 11 ,  70 , s" suntan cream   " s,
 32 ,  30 , s" camera         " s,
 24 ,  15 , s" T-shirt        " s,
 48 ,  10 , s" trousers       " s,
 73 ,  40 , s" umbrella       " s,
 42 ,  70 , s" wp trousers    " s,
 43 ,  75 , s" wp overclothes " s,
 22 ,  80 , s" note-case      " s,
  7 ,  20 , s" sunglasses     " s,
 18 ,  12 , s" towel          " s,
  4 ,  50 , s" socks          " s,
 30 ,  10 , s" book           " s,
        HERE VALUE END-SACK
        VARIABLE Sol            \ Solution  Set
        VARIABLE Vmax           \ Temporary Maximum Value
        VARIABLE Sum            \ Temporary Sum (for speed-up)
: ]sum          ( Rtime: set -- sum  ;Ctime: hilimit.a start.a -- )
\ Loop unwinding & precomputing addresses
        ]
        ]] Sum OFF [[
        DO              ]] dup [[  1  ]] LITERAL AND IF [[  I  ]] LITERAL @ Sum +! THEN 2/ [[
        /ITEM +LOOP     ]] drop Sum @ [[
; IMMEDIATE
: solve         ( -- )
        Vmax OFF
        [ 1 END-SACK Sack - /ITEM / lshift 1- ]L 0
        DO
                I [ END-SACK Sack ]sum ( by weight ) WLIMIT <
                IF
                        I [ END-SACK VAL + Sack VAL + ]sum ( by value )
                        dup Vmax @ >
                        IF  Vmax ! I Sol !  ELSE  drop  THEN
                THEN
        LOOP
;
: .solution     ( -- )
        Sol @ END-SACK ITEM + Sack ITEM +
        DO
                dup 1 AND  IF  I count type cr  THEN
                2/
        /ITEM +LOOP
        drop
        ." Weight: " Sol @ [ END-SACK Sack ]sum .  ."  Value: " Sol @ [ END-SACK VAL + Sack VAL + ]sum .
;
Output:
map            
compass        
water          
sandwich       
glucose        
banana         
suntan cream   
wp trousers    
wp overclothes 
note-case      
sunglasses     
socks          
Weight: 396  Value: 1030 


  1. Numbered list item

Fortran

Translation of: Pascal
Program Knapsack01
! Translation of Pascal version on Rosetta Code.
  implicit none
  integer, parameter :: NUM_ITEMS = 22
  integer, parameter :: MAX_WEIGHT = 400
  type :: TItem
    character(len=20) :: Name
    integer :: Weight, Value
  end type TItem
  type(TItem), dimension(0:NUM_ITEMS-1) :: ITEMS
  integer, dimension(0:NUM_ITEMS, 0:MAX_WEIGHT) :: D
  integer :: I, W, V, MaxWeight
  ! Init Arrays
  d = 0
  ITEMS =  [ TItem('compass', 13, 35), &
            TItem('water', 153, 200), &
            TItem('sandwich', 50, 160), &
            TItem('glucose', 15, 60), &
            TItem('tin', 68, 45), &
            TItem('banana', 27, 60), &
            TItem('apple', 39, 40), &
            TItem('cheese', 23, 30), &
            TItem('beer', 52, 10), &
            TItem('suntan cream', 11, 70), &
            TItem('camera', 32, 30), &
            TItem('T-shirt', 24, 15), &
            TItem('trousers', 48, 10), &
            TItem('umbrella', 73, 40), &
            TItem('waterproof trousers', 43, 70), &
            TItem('waterproof overclothes', 42, 75), &
            TItem('note-case', 22, 80), &
            TItem('sunglasses', 7, 20), &
            TItem('towel', 18, 12), &
            TItem('map', 9, 150), &
            TItem('socks', 4, 50), &
            TItem('book', 30, 10) ]
    !
  do I = 0, NUM_ITEMS-1
    do W = 0, MAX_WEIGHT
      if (ITEMS(I)%Weight > W) then
        D(I+1, W) = D(I, W)
      else
        D(I+1, W) = max(D(I, W), D(I, W - ITEMS(I)%Weight) + ITEMS(I)%Value)
      end if
    end do
  end do
  W = MAX_WEIGHT
  V = D(NUM_ITEMS, W)
  MaxWeight = 0
    !
  write(*, "(/,'bagged:')")
  do I = NUM_ITEMS-1, 0, -1 !Pete
    if (D(I+1, W) == V) then
        if((D(I, (W - ITEMS(I)%Weight)) == V - ITEMS(I)%Value)) then
      write(*, "('  ', A,t25,i0,t35,i0)", advance='yes') ITEMS(I)%Name,ITEMS(I)%weight,ITEMS(I)%value
      MaxWeight = MaxWeight + ITEMS(I)%Weight
      W = W - ITEMS(I)%Weight
      V = V - ITEMS(I)%Value
        end if
        end if
  end do
    !
  write(*, "('value  = ', I0)") D(NUM_ITEMS, MAX_WEIGHT)
  write(*, "('weight = ', I0)") MaxWeight
end program Knapsack01
Output:
bagged:
  socks                 4         50
  map                   9         150
  sunglasses            7         20
  note-case             22        80
  waterproof overcloth  42        75
  waterproof trousers   43        70
  suntan cream          11        70
  banana                27        60
  glucose               15        60
  sandwich              50        160
  water                 153       200
  compass               13        35
value  = 1030
weight = 396
knapsack time =           94 Milliseconds

Branch and Bound Version

Translation of: Fortran 77
 
      module ksack2
!
! THIS SUBROUTINE SOLVES THE 0-1 SINGLE KNAPSACK PROBLEM
!
! MAXIMIZE  Z = P(1)*X(1) + ... + P(N)*X(N)
!
! SUBJECT TO:   W(1)*X(1) + ... + W(N)*X(N) .LE. C ,
!               X(J) = 0 OR 1  FOR J=1,...,N.
!
! THE PROGRAM IS INCLUDED IN THE VOLUME
! S. MARTELLO, P. TOTH, "KNAPSACK PROBLEMS: ALGORITHMS
! AND COMPUTER IMPLEMENTATIONS", JOHN WILEY, 1990
! (https://dl.acm.org/doi/book/10.5555/98124)
! AND IMPLEMENTS THE BRANCH-AND-BOUND ALGORITHM DESCRIBED IN
! SECTION  2.5.2 .
! THE PROGRAM DERIVES FROM AN EARLIER CODE PRESENTED IN
! S. MARTELLO, P. TOTH, "ALGORITHM FOR THE SOLUTION OF THE 0-1 SINGLE
! KNAPSACK PROBLEM", COMPUTING, 1978.

! The orignal program was written in Fortran 77 and was an amazing tangle of GOTO statements.
! I have reworked the code in such a manner as to eliminate the GOTO statements and bring it
! to Fortran 2018 LANGUAGE compliance though the code logic remains somewhat untractable.
!
! The routine requires a large parameter string which includes 4 dummy arrays for it's calculations.
! As well, it offers an option to check the input data for correctness.
! Rather than modify the original algorithm, I wrote a simple wrapper called "start_knapsack" that
! allocates those arrays as well as defaulting the input parameter check to "on", hiding them from the user.
! Having said that, the algorithm works very well and is very fast. I've included it in this
! Rosetta Code listing because it scales well and can be used with a large dataset.
! Which a potential user may desire.
! Peter.kelly@acm.org (28-December-2023)
!
! THE INPUT PROBLEM MUST SATISFY THE CONDITIONS
!
!   1) 2 .LE. N .LE. JDIM - 1 ;
!   2) P(J), W(J), C  POSITIVE INTEGERS;
!   3) MAX (W(J)) .LE. C ;
!   4) W(1) + ... + W(N) .GT. C ;
!   5) P(J)/W(J) .GE. P(J+1)/W(J+1) FOR J=1,...,N-1. <-- Note well. They need to be sorted in the greatest ratio of (p(j)/w(j)) down to the smallest one
!
! MT1 CALLS  1  PROCEDURE: CHMT1.
!
! MT1 NEEDS  8  ARRAYS ( P ,  W ,  X ,  XX ,  MIN ,  PSIGN ,  WSIGN
!                        AND  ZSIGN ) OF LENGTH AT LEAST  N + 1 .
!
! MEANING OF THE INPUT PARAMETERS:
! N    = NUMBER OF ITEMS;
! P(J) = PROFIT OF ITEM  J  (J=1,...,N);
! W(J) = WEIGHT OF ITEM  J  (J=1,...,N);
! C    = CAPACITY OF THE KNAPSACK;
! JDIM = DIMENSION OF THE 8 ARRAYS;
! JCK  = 1 IF CHECK ON THE INPUT DATA IS DESIRED,
!      = 0 OTHERWISE.
!
! MEANING OF THE OUTPUT PARAMETERS:
! Z    = VALUE OF THE OPTIMAL SOLUTION IF  Z .GT. 0 ,
!      = ERROR IN THE INPUT DATA (WHEN JCK=1) IF Z .LT. 0 : CONDI-
!        TION  - Z  IS VIOLATED;
! X(J) = 1 IF ITEM  J  IS IN THE OPTIMAL SOLUTION,
!      = 0 OTHERWISE.
!
! ARRAYS XX, MIN, PSIGN, WSIGN AND ZSIGN ARE DUMMY.
!
! ALL THE PARAMETERS ARE INTEGER. ON RETURN OF MT1 ALL THE INPUT
! PARAMETERS ARE UNCHANGED.
!
          implicit none
      contains
          subroutine mt1(n , p , w , c , z , x , jdim , jck , xx , min , psign , wsign , zsign)
              implicit none
              integer :: jdim
              integer :: n
              integer , intent(inout) , dimension(jdim) :: p
              integer , intent(inout) , dimension(jdim) :: w
              integer :: c
              integer , intent(inout) :: z
              integer , intent(out) , dimension(jdim) :: x
              integer , intent(in) :: jck
              integer , intent(inout) , dimension(jdim) :: xx
              integer , intent(inout) , dimension(jdim) :: min
              integer , intent(inout) , dimension(jdim) :: psign
              integer , intent(inout) , dimension(jdim) :: wsign
              integer , intent(inout) , dimension(jdim) :: zsign
!
              real :: a
              real :: b
              integer :: ch
              integer :: chs
              integer :: diff
              integer :: ii
              integer :: ii1
              integer :: in
              integer :: ip
              integer :: iu
              integer :: j
              integer :: j1
              integer :: jj
              integer :: jtemp
              integer :: kk
              integer :: lim
              integer :: lim1
              integer :: ll
              integer :: lold
              integer :: mink
              integer :: n1
              integer :: nn
              integer :: profit
              integer :: r
              integer :: t
              integer :: next_code_block
!*Code
              next_code_block = 1
dispatch_loop: do
                  select case(next_code_block)
                  case(1)
                      z = 0
                      if( jck==1 )call chmt1(n , p , w , c , z , jdim)
                      if( z<0 )return
! INITIALIZE.
                      ch = c
                      ip = 0
                      chs = ch
          first_loop: do ll = 1 , n
                          if( w(ll)>chs )exit first_loop
                          ip = ip + p(ll)
                          chs = chs - w(ll)
                      end do first_loop
                      ll = ll - 1
                      if( chs==0 )then
                          z = ip
                          x(1:ll) = 1
                          nn = ll + 1
                          x(nn:n) = 0
                          return
                      else
                          p(n + 1) = 0
                          w(n + 1) = ch + 1
                          lim = ip + chs*p(ll + 2)/w(ll + 2)
                          a = w(ll + 1) - chs
                          b = ip + p(ll + 1)
                          lim1 = b - a*float(p(ll))/float(w(ll))
                          if( lim1>lim )lim = lim1
                          mink = ch + 1
                          min(n) = mink
                          do j = 2 , n
                              kk = n + 2 - j
                              if( w(kk)<mink )mink = w(kk)
                              min(kk - 1) = mink
                          end do
                          xx(1:n) = 0
                          z = 0
                          profit = 0
                          lold = n
                          ii = 1
                          next_code_block = 4
                          cycle dispatch_loop
                      end if
                  case(2)
! TRY TO INSERT THE II-TH ITEM INTO THE CURRENT SOLUTION.
                      do while ( w(ii)>ch )
                          ii1 = ii + 1
                          if( z>=ch*p(ii1)/w(ii1) + profit )then
                              next_code_block = 5
                              cycle dispatch_loop
                          end if
                          ii = ii1
                      end do
! BUILD A NEW CURRENT SOLUTION.
                      ip = psign(ii)
                      chs = ch - wsign(ii)
                      in = zsign(ii)
                      ll = in
                      do while ( ll<=n )
                          if( w(ll)>chs )then
                              iu = chs*p(ll)/w(ll)
                              ll = ll - 1
                              if( iu==0 )then
                                  next_code_block = 3
                                  cycle dispatch_loop
                              end if
                              if( z>=profit + ip + iu )then
                                  next_code_block = 5
                                  cycle dispatch_loop
                              end if
                              next_code_block = 4
                              cycle dispatch_loop
                          else
                              ip = ip + p(ll)
                              chs = chs - w(ll)
                          end if
                      end do
                      ll = n
                      next_code_block = 3
                  case(3)
                      if( z>=ip + profit )then
                          next_code_block = 5
                          cycle dispatch_loop
                      end if
                      z = ip + profit
                      nn = ii - 1
                      x(1:nn) = xx(1:nn)
                      x(ii:ll) = 1
                      if( ll/=n )then
                          nn = ll + 1
                          x(nn:n) = 0
                      end if
                      if( z/=lim )then
                          next_code_block = 5
                          cycle dispatch_loop
                      end if
                      return
                  case(4)
! SAVE THE CURRENT SOLUTION.
                      wsign(ii) = ch - chs
                      psign(ii) = ip
                      zsign(ii) = ll + 1
                      xx(ii) = 1
                      nn = ll - 1
                      if( nn>=ii )then
                          do j = ii , nn
                              wsign(j + 1) = wsign(j) - w(j)
                              psign(j + 1) = psign(j) - p(j)
                              zsign(j + 1) = ll + 1
                              xx(j + 1) = 1
                          end do
                      end if
                      j1 = ll + 1
                      wsign(j1:lold) = 0
                      psign(j) = 0
                      zsign(j1:lold) = [(jtemp, jtemp = j1,lold)]
                      lold = ll
                      ch = chs
                      profit = profit + ip
                      if( ll<(n - 2) )then
                          ii = ll + 2
                          if( ch>=min(ii - 1) )then
                              next_code_block = 2
                              cycle dispatch_loop
                          end if
                      else if( ll==(n - 2) )then
                          if( ch>=w(n) )then
                              ch = ch - w(n)
                              profit = profit + p(n)
                              xx(n) = 1
                          end if
                          ii = n - 1
                      else
                          ii = n
                      end if
! SAVE THE CURRENT OPTIMAL SOLUTION.
                      if( z<profit )then
                          z = profit
                          x(1:n) = xx(1:n)
                          if( z==lim )return
                      end if
                      if( xx(n)/=0 )then
                          xx(n) = 0
                          ch = ch + w(n)
                          profit = profit - p(n)
                      end if
                      next_code_block = 5
                  case(5)
           outer_loop: do ! BACKTRACK.
                          nn = ii - 1
                          if( nn==0 )return
               middle_loop: do j = 1 , nn
                              kk = ii - j
                              if( xx(kk)==1 )then
                                  r = ch
                                  ch = ch + w(kk)
                                  profit = profit - p(kk)
                                  xx(kk) = 0
                                  if( r<min(kk) )then
                                      nn = kk + 1
                                      ii = kk
! TRY TO SUBSTITUTE THE NN-TH ITEM FOR THE KK-TH.
                            inner_loop: do while ( z<profit + ch*p(nn)/w(nn) )
                                          diff = w(nn) - w(kk)
                                          if( diff<0 )then
                                              t = r - diff
                                              if( t>=min(nn) )then
                                                  if( z>=profit + p(nn) + t*p(nn + 1)/w(nn + 1) )exit inner_loop
                                                  ch = ch - w(nn)
                                                  profit = profit + p(nn)
                                                  xx(nn) = 1
                                                  ii = nn + 1
                                                  wsign(nn) = w(nn)
                                                  psign(nn) = p(nn)
                                                  zsign(nn) = ii
                                                  n1 = nn + 1
                                                  wsign(n1:lold) = 0
                                                  psign(n1:lold) = 0
                                                  zsign(n1:lold) = [(jtemp, jtemp = n1,lold)]
                                                  lold = nn
                                                  next_code_block = 2
                                                  cycle dispatch_loop
                                              end if
                                          else if( diff/=0 )then
                                              if( diff<=r )then
                                                  if( z<profit + p(nn) )then
                                                      z = profit + p(nn)
                                                      x(1:kk) = xx(1:kk)
                                                      jj = kk + 1
                                                      x(jj:n) = 0
                                                      x(nn) = 1
                                                      if( z==lim )return
                                                      r = r - diff
                                                      kk = nn
                                                      nn = nn + 1
                                                      cycle inner_loop
                                                  end if
                                              end if
                                          end if
                                          nn = nn + 1
                                      end do inner_loop
                                      cycle outer_loop
                                  else
                                      ii = kk + 1
                                      next_code_block = 2
                                      cycle dispatch_loop
                                  end if
                              end if
                          end do middle_loop
                          exit outer_loop
                      end do outer_loop
                      exit dispatch_loop
                  end select
              end do dispatch_loop
          end subroutine mt1
!
          subroutine chmt1(n , p , w , c , z , jdim)
              integer , intent(in) :: jdim
              integer , intent(in) :: n
              integer , intent(in) , dimension(jdim) :: p
              integer , intent(in) , dimension(jdim) :: w
              integer , intent(in) :: c
              integer , intent(out) :: z
!
! Local variable declarations
!
              integer :: j
              integer :: jsw
              real :: r
              real :: rr
!
! CHECK THE INPUT DATA.
!
              if(( n<2) .or. (n>jdim - 1) )then
                  z = -1
                  return
              else if( c>0 )then
                  jsw = 0
                  rr = float(p(1))/float(w(1))
                  do j = 1 , n
                      r = rr
                      if(( p(j)<=0 ).or.( w(j)<=0 ))then
                          z = -2
                          return
                      end if
                      jsw = jsw + w(j)
                      if( w(j)<=c )then
                          rr = float(p(j))/float(w(j))
                          if( rr>r )then
                              z = -5
                              return
                          end if
                      else
                          z = -3
                          return
                      end if
                  end do
                  if( jsw>c )return
                  z = -4
                  return
              end if
            z = -2
            return
          end subroutine chmt1

          subroutine start_knapsack(n , profit , weight , capacity , result_val , members)
!
! Dummy argument declarations
!
              integer , intent(in) :: n
              integer , intent(inout) , dimension(n) :: profit
              integer , intent(inout) , dimension(n) :: weight
              integer , intent(in) :: capacity
              integer , intent(inout) :: result_val
              integer , intent(inout) , dimension(n) :: members
!
! Local variable declarations
              integer :: bigger
              integer :: jck
              integer , allocatable , dimension(:) :: mini
              integer , allocatable , dimension(:) :: psign
              integer , allocatable , dimension(:) :: wsign
              integer , allocatable , dimension(:) :: xx
              integer , allocatable , dimension(:) :: zsign
!
!Designed to invoke MT1
!MT1 NEEDS  8  ARRAYS ( P ,  W ,  X ,  XX ,  MIN ,  PSIGN ,  WSIGN
!                        AND  ZSIGN ) OF LENGTH AT LEAST  N + 1 .

! MEANING OF THE INPUT PARAMETERS:
! N    = NUMBER OF ITEMS;
! P(J) = PROFIT OF ITEM  J  (J=1,...,N);
! W(J) = WEIGHT OF ITEM  J  (J=1,...,N);
! C    = CAPACITY OF THE KNAPSACK;
! JDIM = DIMENSION OF THE 8 ARRAYS;
! JCK  = 1 IF CHECK ON THE INPUT DATA IS DESIRED,
!      = 0 OTHERWISE.
!
! MEANING OF THE OUTPUT PARAMETERS:
! Z    = VALUE OF THE OPTIMAL SOLUTION IF  Z .GT. 0 ,
!      = ERROR IN THE INPUT DATA (WHEN JCK=1) IF Z .LT. 0 : CONDI-
!        TION  - Z  IS VIOLATED;
! X(J) = 1 IF ITEM  J  IS IN THE OPTIMAL SOLUTION,
!      = 0 OTHERWISE.
!
! ARRAYS XX, MIN, PSIGN, WSIGN AND ZSIGN ARE DUMMY.
!
! ALL THE PARAMETERS ARE INTEGER. ON RETURN OF MT1 ALL THE INPUT
! PARAMETERS ARE UNCHANGED.
!
              jck = 1   !Set parameter checking on
              bigger = n + 100
!
!        Allocate the dummy arrays
              allocate(xx(bigger))
              allocate(mini(bigger))
              allocate(psign(bigger))
              allocate(wsign(bigger))
              allocate(zsign(bigger))
              call mt1(n , profit , weight , capacity , result_val , members , bigger , jck , xx , mini , psign , wsign , zsign)
              deallocate(xx)
              deallocate(mini)
              deallocate(psign)
              deallocate(wsign)
              deallocate(zsign)

          end subroutine start_knapsack
      end module ksack2
!
program serious_knapsack
    use ksack2
    integer, parameter :: list_size=22
    integer:: p(list_size) ! The weights
    integer::n,profit(list_size),capacity,result_val,members(size(p)),valuez,t1,t2,j
    character(len=25) :: names(list_size),tempnam
    real :: ratio(list_size),rats
    logical :: swapped
    capacity =400
    members = 0
    result_val = 0
    n = list_size
    p(1:list_size) =     (/13,153, 50,15,68,27,39,23,52,11,32,24,48,73,43,42,22,07,18,009,04,30/)
    profit(1:list_size) =(/35,200,160,60,45,60,40,30,10,70,30,15,10,40,70,75,80,20,12,150,50,10/)

    names(1:22) =[character(len=25) ::'compass','water','sandwich','glucose','tin','banana','apple', 'cheese', &
    'beer','suntan cream','camera','T-shirt','trousers','umbrella','waterproof trousers', 'waterproof overclothes', &
    'note-case','sunglasses','towel','map','socks', 'book']
    ratio(1:22) = float(profit(1:22))/float(p(1:22))
    ! The mt1 algorithm wants the data sorted downwards(large-->small) by the ration of profit/weight
    ! So, I implemented a quick bubble sort to order the lists
    swapped = .true.
    do while (swapped)
        swapped = .false.
        do j = 1,21
            if(ratio(j).lt.ratio(j+1))then ! Swaps everywhere
                swapped = .true.
                t1 = p(j+1)   ! Swap the weights
                p(j+1) = p(j)
                p(j) = t1
                t2 = profit(j+1) !Swap the profits
                profit(j+1) = profit(j)
                profit(j) = t2
                tempnam = names(j+1) ! Swap the names around
                names(j+1) = names(j)
                names(j) = tempnam
                rats = ratio(j+1)   ! Swap the ratios
                ratio(j+1) = ratio(j)
                ratio(j) = rats
            endif
        end do
    end do
    !
    call system_clock(count=xx)
    call startup(n,profit(1:22),p(1:22),capacity,result_val,members)
    call system_clock(count=yy)
    print*,'Total of the sack = ',result_val
    capacity = 0
    valuez = 0
    n = 0
    do i = 1,size(members)
        if(members(i) /=0)then
            capacity = capacity +p(i)
            valuez = profit(i) + valuez
            n = n+1
            print*, names(i),p(i),profit(i)
        endif

    end do
    print*,'Filled capacity = ',capacity,'Value = ',valuez!,'No items = ',n,sum(profit(1:22)),sum(p(1:22))
    print*
    print*,'First knapsack time = ',(yy-xx),'Milliseconds'
    stop 'All done'
end program serious_knapsack
Output:
 map                                 9         150
 socks                               4          50
 suntan cream                       11          70
 glucose                            15          60
 note-case                          22          80
 sandwich                           50         160
 sunglasses                          7          20
 compass                            13          35
 banana                             27          60
 waterproof overclothes             42          75
 waterproof trousers                43          70
 water                             153         200
 Filled capacity =          396 Value =         1030

 First knapsack time =            0 Milliseconds

FreeBASIC

Translation of: XPL0
#define Tabu = Chr(9)
Dim As Integer i, A, P, V, N
Dim As Integer MejorArticulo, MejorValor = 0
Type Knapsack
    articulo As String*22
    peso As Integer
    valor As Integer
End Type
Dim item(1 To 22) As Knapsack => { _
("map                   ",   9, 150), ("compass               ",  13,  35), _
("water                 ", 153, 200), ("sandwich              ",  50, 160), _
("glucose               ",  15,  60), ("tin                   ",  68,  45), _
("banana                ",  27,  60), ("apple                 ",  39,  40), _
("cheese                ",  23,  30), ("beer                  ",  52,  10), _
("suntan cream          ",  11,  70), ("camera                ",  32,  30), _
("T-shirt               ",  24,  15), ("trousers              ",  48,  10), _
("umbrella              ",  73,  40), ("waterproof trousers   ",  42,  70), _
("waterproof overclothes",  43,  75), ("note-case             ",  22,  80), _
("sunglasses            ",   7,  20), ("towel                 ",  18,  12), _
("socks                 ",   4,  50), ("book                  ",  30,  10)}

For i = 1 To (1 Shl 22)-1
    A = i : P = 0 : V = 0 : N = 1
    While A
        If A And 1 Then
            P += item(N).peso
            V += item(N).valor
        End If
        A Shr= 1 
        N += 1
    Wend
    If V > MejorValor  And  P <= 400 Then
        MejorValor = V 
        MejorArticulo = i
    End If
Next

A = MejorArticulo : P = 0 : V = 0 : N = 1
While A
    If A And 1 Then
        Print "  "; item(N).articulo; Tabu;
        Print item(N).peso; Tabu; item(N).valor
        P += item(N).peso
        V += item(N).valor
    End If
    A Shr= 1 : N += 1
Wend
Print "Totals:"; Spc(25); P; Tabu; V
Sleep
Output:
Same as XLP0 entry.

Free Pascal

Dynamic programming solution(tested with FPC 3.2.2).

program Knapsack01;
{$mode objfpc}{$j-}
uses
  Math;

type
  TItem = record
    Name: string;
    Weight, Value: Integer;
  end;

const
  NUM_ITEMS = 22;
  ITEMS: array[0..NUM_ITEMS-1] of TItem = (
    (Name: 'map';                    Weight:   9; Value: 150),
    (Name: 'compass';                Weight:  13; Value:  35),
    (Name: 'water';                  Weight: 153; Value: 200),
    (Name: 'sandwich';               Weight:  50; Value: 160),
    (Name: 'glucose';                Weight:  15; Value:  60),
    (Name: 'tin';                    Weight:  68; Value:  45),
    (Name: 'banana';                 Weight:  27; Value:  60),
    (Name: 'apple';                  Weight:  39; Value:  40),
    (Name: 'cheese';                 Weight:  23; Value:  30),
    (Name: 'beer';                   Weight:  52; Value:  10),
    (Name: 'suntan cream';           Weight:  11; Value:  70),
    (Name: 'camera';                 Weight:  32; Value:  30),
    (Name: 'T-shirt';                Weight:  24; Value:  15),
    (Name: 'trousers';               Weight:  48; Value:  10),
    (Name: 'umbrella';               Weight:  73; Value:  40),
    (Name: 'waterproof trousers';    Weight:  42; Value:  70),
    (Name: 'waterproof overclothes'; Weight:  43; Value:  75),
    (Name: 'note-case';              Weight:  22; Value:  80),
    (Name: 'sunglasses';             Weight:   7; Value:  20),
    (Name: 'towel';                  Weight:  18; Value:  12),
    (Name: 'socks';                  Weight:   4; Value:  50),
    (Name: 'book';                   Weight:  30; Value:  10)
  );
  MAX_WEIGHT = 400;

var
  D: array of array of Integer;
  I, W, V, MaxWeight: Integer;
begin
  SetLength(D, NUM_ITEMS + 1, MAX_WEIGHT + 1);
  for I := 0 to High(ITEMS) do
    for W := 0 to MAX_WEIGHT do
      if ITEMS[I].Weight > W then
        D[I+1, W] := D[I, W]
      else
        D[I+1, W] := Max(D[I, W], D[I, W - ITEMS[I].Weight] + ITEMS[I].Value);

  W := MAX_WEIGHT;
  V := D[NUM_ITEMS, W];
  MaxWeight := 0;
  WriteLn('bagged:');
  for I := High(ITEMS) downto 0 do
    if (D[I+1, W] = V)and(D[I, W - ITEMS[I].Weight] = V - ITEMS[I].Value)then begin
      WriteLn('  ', ITEMS[I].Name);
      Inc(MaxWeight, ITEMS[I].Weight);
      Dec(W, ITEMS[I].Weight);
      Dec(V, ITEMS[I].Value);
    end;
  WriteLn('value  = ', D[NUM_ITEMS, MAX_WEIGHT]);
  WriteLn('weight = ', MaxWeight);
end.
Output:
bagged:
  socks
  sunglasses
  note-case
  waterproof overclothes
  waterproof trousers
  suntan cream
  banana
  glucose
  sandwich
  water
  compass
  map
value  = 1030
weight = 396

FutureBasic

window 1, @"Knapsack Problem", (0,0,480,270)

_maxWeight = 400

void local fn FillKnapsack
  long              totalWeight = 0, totalValue = 0, itemWeight, unusedWeight
  CFDictionaryRef   item, extraItem = NULL
  SortDescriptorRef sd
  CFMutableArrayRef packedItems
  
  CFArrayRef items = @[
  @{@"item":@"map",                    @"weight":@9,   @"value":@150},
  @{@"item":@"compass",                @"weight":@13,  @"value":@35 },
  @{@"item":@"water",                  @"weight":@153, @"value":@200},
  @{@"item":@"sandwich",               @"weight":@50,  @"value":@160},
  @{@"item":@"glucose",                @"weight":@15,  @"value":@60 },
  @{@"item":@"tin",                    @"weight":@68,  @"value":@45 },
  @{@"item":@"banana",                 @"weight":@27,  @"value":@60 },
  @{@"item":@"apple",                  @"weight":@39,  @"value":@40 },
  @{@"item":@"cheese",                 @"weight":@23,  @"value":@30 },
  @{@"item":@"beer",                   @"weight":@52,  @"value":@10 },
  @{@"item":@"suntan cream",           @"weight":@11,  @"value":@70 },
  @{@"item":@"camera",                 @"weight":@32,  @"value":@30 },
  @{@"item":@"T-shirt",                @"weight":@24,  @"value":@15 },
  @{@"item":@"trousers",               @"weight":@48,  @"value":@10 },
  @{@"item":@"umbrella",               @"weight":@73,  @"value":@40 },
  @{@"item":@"waterproof trousers",    @"weight":@42,  @"value":@70 },
  @{@"item":@"waterproof overclothes", @"weight":@43,  @"value":@75 },
  @{@"item":@"note-case",              @"weight":@22,  @"value":@80 },
  @{@"item":@"sunglasses",             @"weight":@7,   @"value":@20 },
  @{@"item":@"towel",                  @"weight":@18,  @"value":@12 },
  @{@"item":@"socks",                  @"weight":@4,   @"value":@50 },
  @{@"item":@"book",                   @"weight":@30,  @"value":@10 }
  ]
  
  sd = fn SortDescriptorWithKey( @"value", NO )
  items = fn ArraySortedArrayUsingDescriptors( items, @[sd] )
  packedItems = fn MutableArrayWithCapacity(0)
  for item in items
    itemWeight = fn NumberIntegerValue(item[@"weight"])
    if ( totalWeight + itemWeight <= _maxWeight )
      MutableArrayAddObject( packedItems, item )
      totalWeight += itemWeight
      totalValue += fn NumberIntegerValue(item[@"value"])
    end if
  next
  
  text @"Menlo-Bold",,, fn ColorWithRGB(1.0,0.0,1.0,0.25),, 170
  print @"Item",@"Weight",@"Value"
  text @"Menlo",,, fn ColorClear
  for item in packedItems
    printf @"%@\t%6ld\t%5ld",item[@"item"],fn NumberIntegerValue(item[@"weight"]),fn NumberIntegerValue(item[@"value"])
  next
  text ,,, fn ColorWithRGB(1.0,0.0,1.0,0.25)
  printf @"knapsack\t%6ld\t%5ld",totalWeight,totalValue
  
  text
  print
  
  unusedWeight = _maxWeight - totalWeight
  
  for item in items
    if ( fn NumberIntegerValue(item[@"weight"]) <= unusedWeight )
      extraItem = item : break
    end if
  next
  
  if ( extraItem ) then printf @"There's just enough room for extra %@!", extraItem[@"item"]
end fn

fn FillKnapsack

HandleEvents
Output:
Item                    Weight              Value
water                      153                200
sandwich                    50                160
map                          9                150
note-case                   22                 80
waterproof overclothes      43                 75
suntan cream                11                 70
waterproof trousers         42                 70
glucose                     15                 60
banana                      27                 60
socks                        4                 50
compass                     13                 35
sunglasses                   7                 20

knapsack                   396               1030

There's just enough room for extra socks!

Go

From WP, "0-1 knapsack problem" under The Knapsack Problem, although the solution here simply follows the recursive defintion and doesn't even use the array optimization.

package main

import "fmt"

type item struct {
    string
    w, v int
}

var wants = []item{
    {"map", 9, 150},
    {"compass", 13, 35},
    {"water", 153, 200},
    {"sandwich", 50, 160},
    {"glucose", 15, 60},
    {"tin", 68, 45},
    {"banana", 27, 60},
    {"apple", 39, 40},
    {"cheese", 23, 30},
    {"beer", 52, 10},
    {"suntan cream", 11, 70},
    {"camera", 32, 30},
    {"T-shirt", 24, 15},
    {"trousers", 48, 10},
    {"umbrella", 73, 40},
    {"waterproof trousers", 42, 70},
    {"waterproof overclothes", 43, 75},
    {"note-case", 22, 80},
    {"sunglasses", 7, 20},
    {"towel", 18, 12},
    {"socks", 4, 50},
    {"book", 30, 10},
}

const maxWt = 400

func main() {
    items, w, v := m(len(wants)-1, maxWt)
    fmt.Println(items)
    fmt.Println("weight:", w)
    fmt.Println("value:", v)
}

func m(i, w int) ([]string, int, int) {
    if i < 0 || w == 0 {
        return nil, 0, 0
    } else if wants[i].w > w {
        return m(i-1, w)
    }
    i0, w0, v0 := m(i-1, w)
    i1, w1, v1 := m(i-1, w-wants[i].w)
    v1 += wants[i].v
    if v1 > v0 {
        return append(i1, wants[i].string), w1 + wants[i].w, v1
    }
    return i0, w0, v0
}
Output:
[map compass water sandwich glucose banana suntan cream waterproof trousers waterproof overclothes note-case sunglasses socks]
weight: 396
value: 1030

Alternative test case

Data for which a greedy algorithm might give an incorrect result:

var wants = []item{
    {"sunscreen", 15, 2},
    {"GPS", 25, 2},
    {"beer", 35, 3},
}

const maxWt = 40
Output:
[sunscreen GPS]
weight: 40
value: 4

Groovy

Solution #1: brute force

def totalWeight = { list -> list*.weight.sum() }
def totalValue = { list -> list*.value.sum() }
 
def knapsack01bf = { possibleItems ->
    possibleItems.subsequences().findAll{ ss ->
        def w = totalWeight(ss)
        350 < w && w < 401
    }.max(totalValue)
}

Solution #2: dynamic programming

def knapsack01dp = { possibleItems ->
    def n = possibleItems.size()
    def m = (0..n).collect{ i -> (0..400).collect{ w -> []} }
    (1..400).each { w ->
        (1..n).each { i ->
            def wi = possibleItems[i-1].weight
            m[i][w] = wi > w ? m[i-1][w] : ([m[i-1][w], m[i-1][w-wi] + [possibleItems[i-1]]].max(totalValue))
        }
    }
    m[n][400]
}

Test:

def items = [ 
        [name:"map", weight:9, value:150],
        [name:"compass", weight:13, value:35],
        [name:"water", weight:153, value:200],
        [name:"sandwich", weight:50, value:160],
        [name:"glucose", weight:15, value:60],
        [name:"tin", weight:68, value:45],
        [name:"banana", weight:27, value:60],
        [name:"apple", weight:39, value:40],
        [name:"cheese", weight:23, value:30],
        [name:"beer", weight:52, value:10],
        [name:"suntan cream", weight:11, value:70],
        [name:"camera", weight:32, value:30],
        [name:"t-shirt", weight:24, value:15],
        [name:"trousers", weight:48, value:10],
        [name:"umbrella", weight:73, value:40],
        [name:"waterproof trousers", weight:42, value:70],
        [name:"waterproof overclothes", weight:43, value:75],
        [name:"note-case", weight:22, value:80],
        [name:"sunglasses", weight:7, value:20],
        [name:"towel", weight:18, value:12],
        [name:"socks", weight:4, value:50],
        [name:"book", weight:30, value:10],
]

[knapsack01bf, knapsack01dp].each { knapsack01 ->
    def start = System.currentTimeMillis()
    def packingList = knapsack01(items)
    def elapsed = System.currentTimeMillis() - start
    
    println "\n\n\nElapsed Time: ${elapsed/1000.0} s"
    println "Total Weight: ${totalWeight(packingList)}"
    println " Total Value: ${totalValue(packingList)}"
    packingList.each {
        printf ("  item: %-25s  weight:%4d  value:%4d\n", it.name, it.weight, it.value)
    }
}
Output:
Elapsed Time: 132.267 s
Total Weight: 396
 Total Value: 1030
  item: map                        weight:   9  value: 150
  item: compass                    weight:  13  value:  35
  item: water                      weight: 153  value: 200
  item: sandwich                   weight:  50  value: 160
  item: glucose                    weight:  15  value:  60
  item: banana                     weight:  27  value:  60
  item: suntan cream               weight:  11  value:  70
  item: waterproof trousers        weight:  42  value:  70
  item: waterproof overclothes     weight:  43  value:  75
  item: note-case                  weight:  22  value:  80
  item: sunglasses                 weight:   7  value:  20
  item: socks                      weight:   4  value:  50



Elapsed Time: 0.27 s
Total Weight: 396
 Total Value: 1030
  item: map                        weight:   9  value: 150
  item: compass                    weight:  13  value:  35
  item: water                      weight: 153  value: 200
  item: sandwich                   weight:  50  value: 160
  item: glucose                    weight:  15  value:  60
  item: banana                     weight:  27  value:  60
  item: suntan cream               weight:  11  value:  70
  item: waterproof trousers        weight:  42  value:  70
  item: waterproof overclothes     weight:  43  value:  75
  item: note-case                  weight:  22  value:  80
  item: sunglasses                 weight:   7  value:  20
  item: socks                      weight:   4  value:  50

Haskell

Brute force:

inv = [("map",9,150), ("compass",13,35), ("water",153,200), ("sandwich",50,160),
	("glucose",15,60), ("tin",68,45), ("banana",27,60), ("apple",39,40),
	("cheese",23,30), ("beer",52,10), ("cream",11,70), ("camera",32,30),
	("tshirt",24,15), ("trousers",48,10), ("umbrella",73,40), ("trousers",42,70),
	("overclothes",43,75), ("notecase",22,80), ("sunglasses",7,20), ("towel",18,12),
	("socks",4,50), ("book",30,10)]

-- get all combos of items under total weight sum; returns value sum and list
combs [] _ = [ (0, []) ]
combs ((name,w,v):rest) cap = combs rest cap ++ 
		      if w > cap then [] else map (prepend (name,w,v)) (combs rest (cap - w))
		      	where prepend (name,w,v) (v2, lst) = (v2 + v, (name,w,v):lst)

main = do
	putStr "Total value: "; print value
	mapM_ print items
		where (value, items) = maximum $ combs inv 400
Output:
Total value: 1030
("map",9,150)
("compass",13,35)
("water",153,200)
("sandwich",50,160)
("glucose",15,60)
("banana",27,60)
("cream",11,70)
("trousers",42,70)
("overclothes",43,75)
("notecase",22,80)
("sunglasses",7,20)
("socks",4,50)

Much faster brute force solution that computes the maximum before prepending, saving most of the prepends:

inv = [("map",9,150), ("compass",13,35), ("water",153,200), ("sandwich",50,160),
	("glucose",15,60), ("tin",68,45), ("banana",27,60), ("apple",39,40),
	("cheese",23,30), ("beer",52,10), ("cream",11,70), ("camera",32,30),
	("tshirt",24,15), ("trousers",48,10), ("umbrella",73,40), ("trousers",42,70),
	("overclothes",43,75), ("notecase",22,80), ("sunglasses",7,20), ("towel",18,12),
	("socks",4,50), ("book",30,10)]

combs [] _ = (0, [])
combs ((name,w,v):rest) cap
	| w <= cap  = max skipthis $ prepend (name,w,v) (combs rest (cap - w))
	| otherwise = skipthis
	where	prepend (name,w,v) (v2, lst) = (v2 + v, (name,w,v):lst)
		skipthis = combs rest cap

main = do print $ combs inv 400
Output:
(1030,[("map",9,150),("compass",13,35),("water",153,200),("sandwich",50,160),("glucose",15,60),("banana",27,60),("cream",11,70),("trousers",42,70),("overclothes",43,75),("notecase",22,80),("sunglasses",7,20),("socks",4,50)])

Dynamic programming with a list for caching (this can be adapted to bounded problem easily):

inv = [("map",9,150), ("compass",13,35), ("water",153,200), ("sandwich",50,160),
       ("glucose",15,60), ("tin",68,45), ("banana",27,60), ("apple",39,40),
       ("cheese",23,30), ("beer",52,10), ("cream",11,70), ("camera",32,30),
       ("tshirt",24,15), ("trousers",48,10), ("umbrella",73,40),
       ("waterproof trousers",42,70), ("overclothes",43,75), ("notecase",22,80),
       ("sunglasses",7,20), ("towel",18,12), ("socks",4,50), ("book",30,10)]

knapsack = foldr addItem (repeat (0,[])) where
	addItem (name,w,v) list = left ++ zipWith max right newlist where
		newlist = map (\(val, names)->(val + v, name:names)) list
		(left,right) = splitAt w list

main = print $ (knapsack inv) !! 400
Output:
(1030,["map","compass","water","sandwich","glucose","banana","cream","waterproof trousers","overclothes","notecase","sunglasses","socks"])

Icon and Unicon

Translation from Wikipedia pseudo-code. Memoization can be enabled with a command line argument that causes the procedure definitions to be swapped which effectively hooks the procedure.

link printf

global wants                    # items wanted for knapsack

procedure main(A) # kanpsack 0-1
   if !A == ("--trace"|"-t") then &trace := -1     # trace everything (debug)
   if !A == ("--memoize"|"-m") then m :=: Memo_m   # hook (swap) procedure

   printf("Knapsack-0-1: with maximum weight allowed=%d.\n",maxw  := 400)
   showwanted(wants := get_wants())
   showcontents(bag := m(*wants,maxw))
   printf("Performance: time=%d ms collections=%d\n",&time,&collections)
end

record packing(items,weight,value)

procedure Memo_m(i,w)           #: Hook procedure to memoize the knapsack 
static memoT
initial memoT := table()
   return \memoT[k := i||","||w] | ( memoT[k] := Memo_m(i,w) )
end

procedure m(i,w)                #: Solve the Knapsack 0-1 as per Wikipedia
static nil
initial nil := packing([],0,0) 
   if 0 = (i | w) then 
      return nil          
   else if wants[i].weight > w then
           return m(i-1, w)
        else {
            x0 := m(i-1,w)
            x1 := m(i-1,w-wants[i].weight)  
            if ( x1.value + wants[i].value) > x0.value then 
               return packing(x1.items ||| wants[i].items,    
                              x1.weight + wants[i].weight, 
                              x1.value + wants[i].value)
            else
               return x0
        }
end

procedure showwanted(wants)     #: show the list of wanted items
   every (tw := 0) +:= (!wants).weight
   printf("Packing list has total weight=%d and includes %d items [",tw,*wants)
   every printf(" %s",!(!wants).items|"]\n")   
end

procedure showcontents(bag)     #: show the list of the packed bag
   printf("The bag weighs=%d holding %d items [",bag.weight,*bag.items)
   every printf(" %s",!bag.items|"]\n")   
end

procedure get_wants()           #: setup list of wanted items
   return  [ packing(["map"], 9, 150),
             packing(["compass"], 13, 35),
             packing(["water"], 153, 200),
             packing(["sandwich"], 50, 160),
             packing(["glucose"], 15, 60),
             packing(["tin"], 68, 45),
             packing(["banana"], 27, 60),
             packing(["apple"], 39, 40),
             packing(["cheese"], 23, 30),
             packing(["beer"], 52, 10),
             packing(["suntan cream"], 11, 70),
             packing(["camera"], 32, 30),
             packing(["T-shirt"], 24, 15),
             packing(["trousers"], 48, 10),
             packing(["umbrella"], 73, 40),
             packing(["waterproof trousers"], 42, 70),
             packing(["waterproof overclothes"], 43, 75),
             packing(["note-case"], 22, 80),
             packing(["sunglasses"], 7, 20),
             packing(["towel"], 18, 12),
             packing(["socks"], 4, 50),
             packing(["book"], 30, 10) ]
end

printf.icn provides printf

Output:
Knapsack-0-1: with maximum weight allowed=400.
Packing list has total weight=803 and includes 22 items [ map compass water sandwich glucose tin banana apple cheese beer suntan cream camera T-shirt trousers umbrella waterproof trousers waterproof overclothes note-case sunglasses towel socks book ]
The bag weighs=396 holding 12 items [ map compass water sandwich glucose banana suntan cream waterproof trousers waterproof overclothes note-case sunglasses socks ]
Performance: time=37 ms collections=0

The above shows memoized performance. Un-memoized results on the same PC took time=9728 ms collections=4.

J

Static solution:

'names values'=:|:".;._2]0 :0
  'map';                       9         150
  'compass';                  13          35
  'water';                   153         200
  'sandwich';                 50         160
  'glucose';                  15          60
  'tin';                      68          45
  'banana';                   27          60
  'apple';                    39          40
  'cheese';                   23          30
  'beer';                     52          10
  'suntan cream';             11          70
  'camera';                   32          30
  'tshirt';                   24          15
  'trousers';                 48          10
  'umbrella';                 73          40
  'waterproof trousers';      42          70
  'waterproof overclothes';   43          75
  'notecase';                 22          80
  'sunglasses';                7          20
  'towel';                    18          12
  'socks';                     4          50
  'book';                     30          10
)

X=: +/ .*"1
plausible=: (] (] #~ 400 >: X) #:@i.@(2&^)@#)@:({."1)
best=: (plausible ([ {~  [ (i. >./)@:X {:"1@]) ]) values

Illustration of answer:

   +/best#values  NB. total weight and value
396 1030
   best#names
map                   
compass               
water                 
sandwich              
glucose               
banana                
suntan cream          
waterproof trousers   
waterproof overclothes
notecase              
sunglasses            
socks

Alternative test case

'names values'=:|:".;._2]0 :0
    'sunscreen'; 15 2
    'GPS'; 25 2
    'beer'; 35 3
)

X=: +/ .*"1
plausible=: (] (] #~ 40 >: X) #:@i.@(2&^)@#)@:({."1)
best=: (plausible ([ {~  [ (i. >./)@:X {:"1@]) ]) values

Illustration:

   +/best#values
40 4
   best#names
sunscreen
GPS

Java

General dynamic solution after wikipedia.

package hu.pj.alg.test;

import hu.pj.alg.ZeroOneKnapsack;
import hu.pj.obj.Item;
import java.util.*;
import java.text.*;

public class ZeroOneKnapsackForTourists {

    public ZeroOneKnapsackForTourists() {
        ZeroOneKnapsack zok = new ZeroOneKnapsack(400); // 400 dkg = 400 dag = 4 kg

        // making the list of items that you want to bring
        zok.add("map", 9, 150);
        zok.add("compass", 13, 35);
        zok.add("water", 153, 200);
        zok.add("sandwich", 50, 160);
        zok.add("glucose", 15, 60);
        zok.add("tin", 68, 45);
        zok.add("banana", 27, 60);
        zok.add("apple", 39, 40);
        zok.add("cheese", 23, 30);
        zok.add("beer", 52, 10);
        zok.add("suntan cream", 11, 70);
        zok.add("camera", 32, 30);
        zok.add("t-shirt", 24, 15);
        zok.add("trousers", 48, 10);
        zok.add("umbrella", 73, 40);
        zok.add("waterproof trousers", 42, 70);
        zok.add("waterproof overclothes", 43, 75);
        zok.add("note-case", 22, 80);
        zok.add("sunglasses", 7, 20);
        zok.add("towel", 18, 12);
        zok.add("socks", 4, 50);
        zok.add("book", 30, 10);

        // calculate the solution:
        List<Item> itemList = zok.calcSolution();

        // write out the solution in the standard output
        if (zok.isCalculated()) {
            NumberFormat nf  = NumberFormat.getInstance();

            System.out.println(
                "Maximal weight           = " +
                nf.format(zok.getMaxWeight() / 100.0) + " kg"
            );
            System.out.println(
                "Total weight of solution = " +
                nf.format(zok.getSolutionWeight() / 100.0) + " kg"
            );
            System.out.println(
                "Total value              = " +
                zok.getProfit()
            );
            System.out.println();
            System.out.println(
                "You can carry the following materials " +
                "in the knapsack:"
            );
            for (Item item : itemList) {
                if (item.getInKnapsack() == 1) {
                    System.out.format(
                        "%1$-23s %2$-3s %3$-5s %4$-15s \n",
                        item.getName(),
                        item.getWeight(), "dag  ",
                        "(value = " + item.getValue() + ")"
                    );
                }
            }
        } else {
            System.out.println(
                "The problem is not solved. " +
                "Maybe you gave wrong data."
            );
        }

    }

    public static void main(String[] args) {
        new ZeroOneKnapsackForTourists();
    }

} // class
package hu.pj.alg;

import hu.pj.obj.Item;
import java.util.*;

public class ZeroOneKnapsack {

    protected List<Item> itemList  = new ArrayList<Item>();
    protected int maxWeight        = 0;
    protected int solutionWeight   = 0;
    protected int profit           = 0;
    protected boolean calculated   = false;

    public ZeroOneKnapsack() {}

    public ZeroOneKnapsack(int _maxWeight) {
        setMaxWeight(_maxWeight);
    }

    public ZeroOneKnapsack(List<Item> _itemList) {
        setItemList(_itemList);
    }

    public ZeroOneKnapsack(List<Item> _itemList, int _maxWeight) {
        setItemList(_itemList);
        setMaxWeight(_maxWeight);
    }

    // calculte the solution of 0-1 knapsack problem with dynamic method:
    public List<Item> calcSolution() {
        int n = itemList.size();

        setInitialStateForCalculation();
        if (n > 0  &&  maxWeight > 0) {
            List< List<Integer> > c = new ArrayList< List<Integer> >();
            List<Integer> curr = new ArrayList<Integer>();

            c.add(curr);
            for (int j = 0; j <= maxWeight; j++)
                curr.add(0);
            for (int i = 1; i <= n; i++) {
                List<Integer> prev = curr;
                c.add(curr = new ArrayList<Integer>());
                for (int j = 0; j <= maxWeight; j++) {
                    if (j > 0) {
                        int wH = itemList.get(i-1).getWeight();
                        curr.add(
                            (wH > j)
                            ?
                            prev.get(j)
                            :
                            Math.max(
                                prev.get(j),
                                itemList.get(i-1).getValue() + prev.get(j-wH)
                            )
                        );
                    } else {
                        curr.add(0);
                    }
                } // for (j...)
            } // for (i...)
            profit = curr.get(maxWeight);

            for (int i = n, j = maxWeight; i > 0  &&  j >= 0; i--) {
                int tempI   = c.get(i).get(j);
                int tempI_1 = c.get(i-1).get(j);
                if (
                    (i == 0  &&  tempI > 0)
                    ||
                    (i > 0  &&  tempI != tempI_1)
                )
                {
                    Item iH = itemList.get(i-1);
                    int  wH = iH.getWeight();
                    iH.setInKnapsack(1);
                    j -= wH;
                    solutionWeight += wH;
                }
            } // for()
            calculated = true;
        } // if()
        return itemList;
    }

    // add an item to the item list
    public void add(String name, int weight, int value) {
        if (name.equals(""))
            name = "" + (itemList.size() + 1);
        itemList.add(new Item(name, weight, value));
        setInitialStateForCalculation();
    }

    // add an item to the item list
    public void add(int weight, int value) {
        add("", weight, value); // the name will be "itemList.size() + 1"!
    }

    // remove an item from the item list
    public void remove(String name) {
        for (Iterator<Item> it = itemList.iterator(); it.hasNext(); ) {
            if (name.equals(it.next().getName())) {
                it.remove();
            }
        }
        setInitialStateForCalculation();
    }

    // remove all items from the item list
    public void removeAllItems() {
        itemList.clear();
        setInitialStateForCalculation();
    }

    public int getProfit() {
        if (!calculated)
            calcSolution();
        return profit;
    }

    public int getSolutionWeight() {return solutionWeight;}
    public boolean isCalculated() {return calculated;}
    public int getMaxWeight() {return maxWeight;}

    public void setMaxWeight(int _maxWeight) {
        maxWeight = Math.max(_maxWeight, 0);
    }

    public void setItemList(List<Item> _itemList) {
        if (_itemList != null) {
            itemList = _itemList;
            for (Item item : _itemList) {
                item.checkMembers();
            }
        }
    }

    // set the member with name "inKnapsack" by all items:
    private void setInKnapsackByAll(int inKnapsack) {
        for (Item item : itemList)
            if (inKnapsack > 0)
                item.setInKnapsack(1);
            else
                item.setInKnapsack(0);
    }

    // set the data members of class in the state of starting the calculation:
    protected void setInitialStateForCalculation() {
        setInKnapsackByAll(0);
        calculated     = false;
        profit         = 0;
        solutionWeight = 0;
    }

} // class
package hu.pj.obj;

public class Item {

    protected String name    = "";
    protected int weight     = 0;
    protected int value      = 0;
    protected int bounding   = 1; // the maximal limit of item's pieces
    protected int inKnapsack = 0; // the pieces of item in solution

    public Item() {}

    public Item(Item item) {
        setName(item.name);
        setWeight(item.weight);
        setValue(item.value);
        setBounding(item.bounding);
    }

    public Item(int _weight, int _value) {
        setWeight(_weight);
        setValue(_value);
    }

    public Item(int _weight, int _value, int _bounding) {
        setWeight(_weight);
        setValue(_value);
        setBounding(_bounding);
    }

    public Item(String _name, int _weight, int _value) {
        setName(_name);
        setWeight(_weight);
        setValue(_value);
    }

    public Item(String _name, int _weight, int _value, int _bounding) {
        setName(_name);
        setWeight(_weight);
        setValue(_value);
        setBounding(_bounding);
    }

    public void setName(String _name) {name = _name;}
    public void setWeight(int _weight) {weight = Math.max(_weight, 0);}
    public void setValue(int _value) {value = Math.max(_value, 0);}

    public void setInKnapsack(int _inKnapsack) {
        inKnapsack = Math.min(getBounding(), Math.max(_inKnapsack, 0));
    }

    public void setBounding(int _bounding) {
        bounding = Math.max(_bounding, 0);
        if (bounding == 0)
            inKnapsack = 0;
    }

    public void checkMembers() {
        setWeight(weight);
        setValue(value);
        setBounding(bounding);
        setInKnapsack(inKnapsack);
    }

    public String getName() {return name;}
    public int getWeight() {return weight;}
    public int getValue() {return value;}
    public int getInKnapsack() {return inKnapsack;}
    public int getBounding() {return bounding;}

} // class
Output:
Maximal weight           = 4 kg
Total weight of solution = 3,96 kg
Total value              = 1030

You can carry te following materials in the knapsack:
map                     9   dag   (value = 150)   
compass                 13  dag   (value = 35)    
water                   153 dag   (value = 200)   
sandwich                50  dag   (value = 160)   
glucose                 15  dag   (value = 60)    
banana                  27  dag   (value = 60)    
suntan cream            11  dag   (value = 70)    
waterproof trousers     42  dag   (value = 70)    
waterproof overclothes  43  dag   (value = 75)    
note-case               22  dag   (value = 80)    
sunglasses              7   dag   (value = 20)    
socks                   4   dag   (value = 50)    

JavaScript

Also available at gist.

/*global portviz:false, _:false */
/*
 * 0-1 knapsack solution, recursive, memoized, approximate.
 *
 * credits:
 *
 * the Go implementation here:
 *   http://rosettacode.org/mw/index.php?title=Knapsack_problem/0-1
 *
 * approximation details here:
 *   http://math.mit.edu/~goemans/18434S06/knapsack-katherine.pdf
 */
portviz.knapsack = {};
(function() {
  this.combiner = function(items, weightfn, valuefn) {
    // approximation guarantees result >= (1-e) * optimal
    var _epsilon = 0.01;
    var _p = _.max(_.map(items,valuefn));
    var _k = _epsilon * _p / items.length;
 
    var _memo = (function(){
      var _mem = {};
      var _key = function(i, w) {
        return i + '::' + w;
      };
      return {
        get: function(i, w) {
          return _mem[_key(i,w)];
        },
        put: function(i, w, r) {
          _mem[_key(i,w)]=r;
          return r;
        }
      };
    })();
 
    var _m = function(i, w) {
 
      i = Math.round(i);
      w = Math.round(w);
 
 
      if (i < 0 || w === 0) {
        // empty base case
        return {items: [], totalWeight: 0, totalValue: 0};
      }
 
      var mm = _memo.get(i,w);
      if (!_.isUndefined(mm)) {
        return mm;
      }
 
      var item = items[i];
      if (weightfn(item) > w) {
        //item does not fit, try the next item
        return _memo.put(i, w, _m(i-1, w));
      }
      // this item could fit.
      // are we better off excluding it?
      var excluded = _m(i-1, w);
      // or including it?
      var included = _m(i-1, w - weightfn(item));
      if (included.totalValue + Math.floor(valuefn(item)/_k) > excluded.totalValue) {
        // better off including it
        // make a copy of the list
        var i1 = included.items.slice();
        i1.push(item);
        return _memo.put(i, w,
          {items: i1,
           totalWeight: included.totalWeight + weightfn(item),
           totalValue: included.totalValue + Math.floor(valuefn(item)/_k)});
      }
      //better off excluding it
      return _memo.put(i,w, excluded);
    };
    return {
      /* one point */
      one: function(maxweight) {
        var scaled = _m(items.length - 1, maxweight);
        return {
          items: scaled.items,
          totalWeight: scaled.totalWeight,
          totalValue: scaled.totalValue * _k
        };
      },
      /* the entire EF */
      ef: function(maxweight, step) {
        return _.map(_.range(0, maxweight+1, step), function(weight) {
          var scaled = _m(items.length - 1, weight);
          return {
            items: scaled.items,
            totalWeight: scaled.totalWeight,
            totalValue: scaled.totalValue * _k
          };
        });
      }
    };
  };
}).apply(portviz.knapsack);

/*global portviz:false, _:false */
/*
 * after rosettacode.org/mw/index.php?title=Knapsack_problem/0-1
 */
var allwants = [
  {name:"map", weight:9, value: 150},
  {name:"compass", weight:13, value: 35},
  {name:"water", weight:153, value: 200},
  {name:"sandwich", weight: 50, value: 160},
  {name:"glucose", weight:15, value: 60},
  {name:"tin", weight:68, value: 45},
  {name:"banana", weight:27, value: 60},
  {name:"apple", weight:39, value: 40},
  {name:"cheese", weight:23, value: 30},
  {name:"beer", weight:52, value: 10},
  {name:"suntan cream", weight:11, value: 70},
  {name:"camera", weight:32, value: 30},
  {name:"T-shirt", weight:24, value: 15},
  {name:"trousers", weight:48, value: 10},
  {name:"umbrella", weight:73, value: 40},
  {name:"waterproof trousers", weight:42, value: 70},
  {name:"waterproof overclothes", weight:43, value: 75},
  {name:"note-case", weight:22, value: 80},
  {name:"sunglasses", weight:7, value: 20},
  {name:"towel", weight:18, value: 12},
  {name:"socks", weight:4, value: 50},
  {name:"book", weight:30, value: 10}
];
 
var near = function(actual, expected, tolerance) {
  if (expected === 0 && actual === 0) return true;
  if (expected === 0) {
    return Math.abs(expected - actual) / actual < tolerance;
  }
  return Math.abs(expected - actual) / expected < tolerance;
};
 
test("one knapsack", function() {
  var combiner =
    portviz.knapsack.combiner(allwants,
      function(x){return x.weight;},
      function(x){return x.value;});
  var oneport = combiner.one(400);
  ok(near(oneport.totalValue, 1030, 0.01), "correct total value");
  ok(near(oneport.totalValue, 1030, 0.01), "correct total value");
  equal(oneport.totalWeight, 396, "correct total weight");
});
 
test("fro