aparler/RosettaCodeData
1
0
Fork 0
Code Issues 12 Pull requests 3 Projects Releases Packages Wiki Activity Actions

A-M baby

Browse source
This commit is contained in:
Ingy döt Net 2013-04-10 21:29:02 -07:00
parent 764da6cbbb
commit db842d013d
19005 changed files with 197040 additions and 7 deletions
Download patch file Download diff file Expand all files Collapse all files

65
Task/Knapsack-problem-0-1/0DESCRIPTION Normal file
View file

@ -0,0 +1,65 @@
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:
{| style="text-align: left; width: 80%;" border="4" cellpadding="2" cellspacing="2"
|+ Table of potential knapsack items
|- style="background-color: rgb(255, 204, 255);"
! 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
|- style="background-color: rgb(255, 204, 255);"
| 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.
'''Which items does the tourist carry in his knapsack so that their total weight does not exceed 400 dag [4 kg], and their total value is maximised?'''
[dag = decagram = 10 grams]
;See also:
* [[Knapsack problem/Unbounded]]
* [[Knapsack problem/Bounded]]

4
Task/Knapsack-problem-0-1/1META.yaml Normal file
View file

@ -0,0 +1,4 @@
---
category:
- Memoization
note: Classic CS problems and programs

13
Task/Knapsack-problem-0-1/APL/knapsack-problem-0-1.apl Normal file
View file

@ -0,0 +1,13 @@
∇ ret←NapSack;sum;b;list;total
[1] total←400
[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] list←list[⍒3⊃¨list]
[4]
[5] ret←⍬
[6] :while 0≠⍴list
[7] ret←ret,(b←total>sum←+\2⊃¨list)/list
[8] list←1↓(~b)/list
[9] total←total-sum←¯1↑(total>sum)/sum
[10] :end
[11] ret←⊃ret,⊂'TOTALS:' (+/2⊃¨ret)(+/3⊃¨ret)
∇

109
Task/Knapsack-problem-0-1/Ada/knapsack-problem-0-1.ada Normal file
View file

@ -0,0 +1,109 @@
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;

65
Task/Knapsack-problem-0-1/BBC-BASIC/knapsack-problem-0-1.bbc Normal file
View file

@ -0,0 +1,65 @@
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%

66
Task/Knapsack-problem-0-1/Bracmat/knapsack-problem-0-1-1.bracmat Normal file
View file

@ -0,0 +1,66 @@
(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;

13
Task/Knapsack-problem-0-1/Bracmat/knapsack-problem-0-1-2.bracmat Normal file
View file

@ -0,0 +1,13 @@
1030
. map
compass
water
sandwich
glucose
banana
suntan cream
waterproof trousers
waterproof overclothes
note-case
sunglasses
socks

98
Task/Knapsack-problem-0-1/C++/knapsack-problem-0-1.cpp Normal file
View file

@ -0,0 +1,98 @@
#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 ] ;
}

77
Task/Knapsack-problem-0-1/C/knapsack-problem-0-1.c Normal file
View file

@ -0,0 +1,77 @@
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
typedef struct {
const char * name;
int weight, value;
} item_t;
item_t 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},
{"suntancream", 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 n_items (sizeof(item)/sizeof(item_t))
typedef struct {
uint32_t bits; /* 32 bits, can solve up to 32 items */
int value;
} solution;
void optimal(int weight, int idx, solution *s)
{
solution v1, v2;
if (idx < 0) {
s->bits = s->value = 0;
return;
}
if (weight < item[idx].weight)
return optimal(weight, idx - 1, s);
optimal(weight, idx - 1, &v1);
optimal(weight - item[idx].weight, idx - 1, &v2);
v2.value += item[idx].value;
v2.bits |= (1 << idx);
*s = (v1.value >= v2.value) ? v1 : v2;
}
int main()
{
int i = 0, w = 0;
solution s = {0, 0};
optimal(400, n_items - 1, &s);
for (i = 0; i < n_items; i++) {
if (s.bits & (1 << i)) {
printf("%s\n", item[i].name);
w += item[i].weight;
}
}
printf("Total value: %d; weight: %d\n", s.value, w);
return 0;
}

27
Task/Knapsack-problem-0-1/Clojure/knapsack-problem-0-1-1.clj Normal file
View file

@ -0,0 +1,27 @@
(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))))

17
Task/Knapsack-problem-0-1/Clojure/knapsack-problem-0-1-2.clj Normal file
View file

@ -0,0 +1,17 @@
(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))

7
Task/Knapsack-problem-0-1/Clojure/knapsack-problem-0-1-3.clj Normal file
View file

@ -0,0 +1,7 @@
(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))))

30
Task/Knapsack-problem-0-1/Common-Lisp/knapsack-problem-0-1.lisp Normal file
View file

@ -0,0 +1,30 @@
;;; 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))))

60
Task/Knapsack-problem-0-1/D/knapsack-problem-0-1.d Normal file
View file

@ -0,0 +1,60 @@
import std.stdio, std.algorithm, std.typecons, std.array;
struct Item {
string name;
int weight, value;
}
Item[] knapsack01DinamicProg(in Item[] items, in int limit)
pure nothrow {
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);
Item[] 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() {
enum int limit = 400;
immutable Item[] 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}];
auto bagged = knapsack01DinamicProg(items, limit);
writeln("Items to pack:");
bagged.map!q{ a.name }().array().sort().join("\n").writeln();
const t = reduce!q{ a[] += [b.weight, b.value][] }([0, 0], bagged);
const tot_wv = (t[0] <= limit) ? t : [0, 0];
writefln("\nFor a total weight of %d and a total value of %d",
tot_wv[0], tot_wv[1]);
}

104
Task/Knapsack-problem-0-1/Dart/knapsack-problem-0-1.dart Normal file
View file

@ -0,0 +1,104 @@
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");
}

34
Task/Knapsack-problem-0-1/Emacs-Lisp/knapsack-problem-0-1-1.l Normal file
View file

@ -0,0 +1,34 @@
(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)))

47
Task/Knapsack-problem-0-1/Emacs-Lisp/knapsack-problem-0-1-2.l Normal file
View file

@ -0,0 +1,47 @@
(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)

26
Task/Knapsack-problem-0-1/Euler-Math-Toolbox/knapsack-problem-0-1.euler Normal file
View file

@ -0,0 +1,26 @@
>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

77
Task/Knapsack-problem-0-1/Factor/knapsack-problem-0-1.factor Normal file
View file

@ -0,0 +1,77 @@
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 ;

55
Task/Knapsack-problem-0-1/Go/knapsack-problem-0-1.go Normal file
View file

@ -0,0 +1,55 @@
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},
}
func main() {
items, w, v := m(len(wants)-1, 400)
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
}

9
Task/Knapsack-problem-0-1/Groovy/knapsack-problem-0-1-1.groovy Normal file
View file

@ -0,0 +1,9 @@
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)
}

11
Task/Knapsack-problem-0-1/Groovy/knapsack-problem-0-1-2.groovy Normal file
View file

@ -0,0 +1,11 @@
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]
}

37
Task/Knapsack-problem-0-1/Groovy/knapsack-problem-0-1-3.groovy Normal file
View file

@ -0,0 +1,37 @@
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)
}
}

17
Task/Knapsack-problem-0-1/Haskell/knapsack-problem-0-1-1.hs Normal file
View file

@ -0,0 +1,17 @@
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

15
Task/Knapsack-problem-0-1/Haskell/knapsack-problem-0-1-2.hs Normal file
View file

@ -0,0 +1,15 @@
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

7
Task/Knapsack-problem-0-1/Haskell/knapsack-problem-0-1-3.hs Normal file
View file

@ -0,0 +1,7 @@
-- snipped the items list; same as above
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

76
Task/Knapsack-problem-0-1/Icon/knapsack-problem-0-1.icon Normal file
View file

@ -0,0 +1,76 @@
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

28
Task/Knapsack-problem-0-1/J/knapsack-problem-0-1-1.j Normal file
View file

@ -0,0 +1,28 @@
'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

15
Task/Knapsack-problem-0-1/J/knapsack-problem-0-1-2.j Normal file
View file

@ -0,0 +1,15 @@
+/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

84
Task/Knapsack-problem-0-1/Java/knapsack-problem-0-1-1.java Normal file
View file

@ -0,0 +1,84 @@
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

154
Task/Knapsack-problem-0-1/Java/knapsack-problem-0-1-2.java Normal file
View file

@ -0,0 +1,154 @@
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

71
Task/Knapsack-problem-0-1/Java/knapsack-problem-0-1-3.java Normal file
View file

@ -0,0 +1,71 @@
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

50
Task/Knapsack-problem-0-1/LSL/knapsack-problem-0-1.lsl Normal file
View file

@ -0,0 +1,50 @@
string sNOTECARD = "Knapsack_Problem_0_1_Data.txt";
integer iMAX_WEIGHT = 400;
integer iSTRIDE = 4;
list lList = [];
default {
integer iNotecardLine = 0;
state_entry() {
llOwnerSay("Reading '"+sNOTECARD+"'");
llGetNotecardLine(sNOTECARD, iNotecardLine);
}
dataserver(key kRequestId, string sData) {
if(sData==EOF) {
//llOwnerSay("EOF");
lList = llListSort(lList, iSTRIDE, FALSE);
integer iTotalWeight = 0;
integer iTotalValue = 0;
list lKnapsack = [];
integer x = 0;
while(x*iSTRIDE<llGetListLength(lList)) {
float fValueWeight = (float)llList2String(lList, x*iSTRIDE);
string sItem = (string)llList2String(lList, x*iSTRIDE+1);
integer iWeight = (integer)llList2String(lList, x*iSTRIDE+2);
integer iValue = (integer)llList2String(lList, x*iSTRIDE+3);
if(iTotalWeight+iWeight<iMAX_WEIGHT) {
iTotalWeight += iWeight;
iTotalValue += iValue;
lKnapsack += [sItem, iWeight, iValue, fValueWeight];
}
x++;
}
for(x=0 ; x*iSTRIDE<llGetListLength(lKnapsack) ; x++) {
llOwnerSay((string)x+": "+llList2String(lList, x*iSTRIDE+1)+", "+llList2String(lList, x*iSTRIDE+2)+", "+llList2String(lList, x*iSTRIDE+3));
}
llOwnerSay("iTotalWeight="+(string)iTotalWeight);
llOwnerSay("iTotalValue="+(string)iTotalValue);
} else {
//llOwnerSay((string)iNotecardLine+": "+sData);
if(llStringTrim(sData, STRING_TRIM)!="") {
list lParsed = llParseString2List(sData, [","], []);
string sItem = llStringTrim(llList2String(lParsed, 0), STRING_TRIM);
integer iWeight = (integer)llStringTrim(llList2String(lParsed, 1), STRING_TRIM);
integer iValue = (integer)llStringTrim(llList2String(lParsed, 2), STRING_TRIM);
float fValueWeight = (1.0*iValue)/iWeight;
lList += [fValueWeight, sItem, iWeight, iValue];
}
llGetNotecardLine(sNOTECARD, ++iNotecardLine);
}
}
}

25
Task/Knapsack-problem-0-1/Mathematica/knapsack-problem-0-1.mathematica Normal file
View file

@ -0,0 +1,25 @@
#[[Flatten@
Position[LinearProgramming[-#[[;; , 3]], -{#[[;; , 2]]}, -{400},
{0, 1} & /@ #, Integers], 1], 1]] &@
{{"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}}

46
Task/Knapsack-problem-0-1/Mathprog/knapsack-problem-0-1.mathprog Normal file
View file

@ -0,0 +1,46 @@
/*Knapsack
This model finds the integer optimal packing of a knapsack
Nigel_Galloway
January 9th., 2012
*/
set Items;
param weight{t in Items};
param value{t in Items};
var take{t in Items}, binary;
knap_weight : sum{t in Items} take[t] * weight[t] <= 400;
maximize knap_value: sum{t in Items} take[t] * value[t];
data;
param : Items : weight 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
suntancream 11 70
camera 32 30
T-shirt 24 15
trousers 48 10
umbrella 73 40
w-trousers 42 70
w-overclothes 43 75
note-case 22 80
sunglasses 7 20
towel 18 12
socks 4 50
book 30 10
;
end;

101
Task/Knapsack-problem-0-1/PHP/knapsack-problem-0-1-1.php Normal file
View file

@ -0,0 +1,101 @@
#########################################################
# 0-1 Knapsack Problem Solve with memoization optimize and index returns
# $w = weight of item
# $v = value of item
# $i = index
# $aW = Available Weight
# $m = Memo items array
# PHP Translation from Python, Memoization,
# and index return functionality added by Brian Berneker
#
#It works uncorrectly! For examle if $aw=4. Max value is true, but no "Array Indices" and its parameters are displayed
#
#########################################################
function knapSolveFast2($w,$v,$i,$aW,&$m) {
global $numcalls;
$numcalls ++;
// echo "Called with i=$i, aW=$aW<br>";
// Return memo if we have one
if (isset($m[$i][$aW])) {
return array( $m[$i][$aW], $m['picked'][$i][$aW] );
} else {
// At end of decision branch
if ($i == 0) {
if ($w[$i] <= $aW) { // Will this item fit?
$m[$i][$aW] = $v[$i]; // Memo this item
$m['picked'][$i][$aW] = array($i); // and the picked item
return array($v[$i],array($i)); // Return the value of this item and add it to the picked list
} else {
// Won't fit
$m[$i][$aW] = 0; // Memo zero
$m['picked'][$i][$aW] = array(); // and a blank array entry...
return array(0,array()); // Return nothing
}
}
// Not at end of decision branch..
// Get the result of the next branch (without this one)
list ($without_i,$without_PI) = knapSolveFast2($w, $v, $i-1, $aW,$m,$pickedItems);
if ($w[$i] > $aW) { // Does it return too many?
$m[$i][$aW] = $without_i; // Memo without including this one
$m['picked'][$i][$aW] = array(); // and a blank array entry...
return array($without_i,array()); // and return it
} else {
// Get the result of the next branch (WITH this one picked, so available weight is reduced)
list ($with_i,$with_PI) = knapSolveFast2($w, $v, ($i-1), ($aW - $w[$i]),$m,$pickedItems);
$with_i += $v[$i]; // ..and add the value of this one..
// Get the greater of WITH or WITHOUT
if ($with_i > $without_i) {
$res = $with_i;
$picked = $with_PI;
array_push($picked,$i);
} else {
$res = $without_i;
$picked = $without_PI;
}
$m[$i][$aW] = $res; // Store it in the memo
$m['picked'][$i][$aW] = $picked; // and store the picked item
return array ($res,$picked); // and then return it
}
}
}
$items4 = array("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");
$w4 = array(9,13,153,50,15,68,27,39,23,52,11,32,24,48,73,42,43,22,7,18,4,30);
$v4 = array(150,35,200,160,60,45,60,40,30,10,70,30,15,10,40,70,75,80,20,12,50,10);
## Initialize
$numcalls = 0; $m = array(); $pickedItems = array();
## Solve
list ($m4,$pickedItems) = knapSolveFast2($w4, $v4, sizeof($v4) -1, 400,$m,$pickedItems);
# Display Result
echo "<b>Items:</b><br>".join(", ",$items4)."<br>";
echo "<b>Max Value Found:</b><br>$m4 (in $numcalls calls)<br>";
echo "<b>Array Indices:</b><br>".join(",",$pickedItems)."<br>";
echo "<b>Chosen Items:</b><br>";
echo "<table border cellspacing=0>";
echo "<tr><td>Item</td><td>Value</td><td>Weight</td></tr>";
foreach($pickedItems as $key) {
$totalVal += $v4[$key];
$totalWt += $w4[$key];
echo "<tr><td>".$items4[$key]."</td><td>".$v4[$key]."</td><td>".$w4[$key]."</td></tr>";
}
echo "<tr><td align=right><b>Totals</b></td><td>$totalVal</td><td>$totalWt</td></tr>";
echo "</table><hr>";

94
Task/Knapsack-problem-0-1/PHP/knapsack-problem-0-1-2.php Normal file
View file

@ -0,0 +1,94 @@
#########################################################
# 0-1 Knapsack Problem Solve
# $w = weight of item
# $v = value of item
# $i = index
# $aW = Available Weight
# PHP Translation by Brian Berneker
#########################################################
function knapSolve($w,$v,$i,$aW) {
global $numcalls;
$numcalls ++;
// echo "Called with i=$i, aW=$aW<br>";
if ($i == 0) {
if ($w[$i] <= $aW) {
return $v[$i];
} else {
return 0;
}
}
$without_i = knapSolve($w, $v, $i-1, $aW);
if ($w[$i] > $aW) {
return $without_i;
} else {
$with_i = $v[$i] + knapSolve($w, $v, ($i-1), ($aW - $w[$i]));
return max($with_i, $without_i);
}
}
#########################################################
# 0-1 Knapsack Problem Solve (with "memo"-ization optimization)
# $w = weight of item
# $v = value of item
# $i = index
# $aW = Available Weight
# $m = 'memo' array
# PHP Translation by Brian Berneker
#########################################################
function knapSolveFast($w,$v,$i,$aW,&$m) { // Note: We use &$m because the function writes to the $m array
global $numcalls;
$numcalls ++;
// echo "Called with i=$i, aW=$aW<br>";
// Return memo if we have one
if (isset($m[$i][$aW])) {
return $m[$i][$aW];
} else {
if ($i == 0) {
if ($w[$i] <= $aW) {
$m[$i][$aW] = $v[$i]; // save memo
return $v[$i];
} else {
$m[$i][$aW] = 0; // save memo
return 0;
}
}
$without_i = knapSolveFast($w, $v, $i-1, $aW,$m);
if ($w[$i] > $aW) {
$m[$i][$aW] = $without_i; // save memo
return $without_i;
} else {
$with_i = $v[$i] + knapSolveFast($w, $v, ($i-1), ($aW - $w[$i]),$m);
$res = max($with_i, $without_i);
$m[$i][$aW] = $res; // save memo
return $res;
}
}
}
$w3 = array(1, 1, 1, 2, 2, 2, 4, 4, 4, 44, 96, 96, 96);
$v3 = array(1, 1, 1, 2, 2, 2, 4, 4, 4, 44, 96, 96, 96);
$numcalls = 0;
$m = array();
$m3 = knapSolveFast($w3, $v3, sizeof($v3) -1, 54,$m);
print_r($w3); echo "<br>FAST: ";
echo "<b>Max: $m3</b> ($numcalls calls)<br><br>";
$numcalls = 0;
$m = array();
$m3 = knapSolve($w3, $v3, sizeof($v3) -1, 54 );
print_r($w3); echo "<br>";
echo "<b>Max: $m3</b> ($numcalls calls)<br><br>";

65
Task/Knapsack-problem-0-1/Perl/knapsack-problem-0-1.pl Normal file
View file

@ -0,0 +1,65 @@
my $raw = <<'TABLE';
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
suntancream 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
TABLE
my (@name, @weight, @value);
for (split "\n", $raw) {
for ([ split /\t+/ ]) {
push @name, $_->[0];
push @weight, $_->[1];
push @value, $_->[2];
}
}
my $max_weight = 400;
my @p = (map([[0, []], map undef, 0 .. $max_weight], 0 .. $#name),
[ map([0, []], 0 .. $max_weight + 1)]);
sub optimal {
my ($i, $w) = @_;
if (!defined $p[$i][$w]) {
if ($weight[$i] > $w) {
$p[$i][$w] = optimal($i - 1, $w)
} else {
my $x = optimal($i - 1, $w);
my $y = optimal($i - 1, $w - $weight[$i]);
if ($x->[0] > $y->[0] + $value[$i]) {
$p[$i][$w] = $x
} else {
$p[$i][$w] = [ $y->[0] + $value[$i],
[ @{$y->[1]}, $name[$i] ]]
}
}
}
return $p[$i][$w]
}
my $sol = optimal($#name, $max_weight);
print "$sol->[0]: @{$sol->[1]}\n";
# prints:
# 1030: map compass water sandwich glucose banana suntancream waterproof trousers
# waterproof overclothes note-case sunglasses socks

27
Task/Knapsack-problem-0-1/PicoLisp/knapsack-problem-0-1.l Normal file
View file

@ -0,0 +1,27 @@
(de *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) )
# Dynamic programming solution
(de knapsack (Lst W)
(when Lst
(cache '*KnapCache (pack (length Lst) ":" W)
(let X (knapsack (cdr Lst) W)
(if (ge0 (- W (cadar Lst)))
(let Y (cons (car Lst) (knapsack (cdr Lst) @))
(if (> (sum caddr X) (sum caddr Y)) X Y) )
X ) ) ) ) )
(let K (knapsack *Items 400)
(for I K
(apply tab I (3 -24 6 6) NIL) )
(tab (27 6 6) NIL (sum cadr K) (sum caddr K)) )

70
Task/Knapsack-problem-0-1/Prolog/knapsack-problem-0-1-1.pro Normal file
View file

@ -0,0 +1,70 @@
:- use_module(library(clpfd)).
knapsack :-
L = [
item(map, 9, 150),
item(compass, 13, 35),
item(water, 153, 200),
item(sandwich, 50, 160),
item(glucose, 15, 60),
item(tin, 68, 45),
item(banana, 27, 60),
item(apple, 39, 40),
item(cheese, 23, 30),
item(beer, 52, 10),
item('suntan cream', 11, 70),
item(camera, 32, 30),
item('t-shirt', 24, 15),
item(trousers, 48, 10),
item(umbrella, 73, 40),
item('waterproof trousers', 42, 70),
item('waterproof overclothes', 43, 75),
item('note-case',22, 80),
item(sunglasses, 7, 20),
item(towel, 18, 12),
item(socks, 4, 50),
item(book, 30, 10 )],
length(L, N),
length(R, N),
R ins 0..1,
maplist(arg(2), L, LW),
maplist(arg(3), L, LV),
scalar_product(LW, R, #=<, 400),
scalar_product(LV, R, #=, VM),
labeling([max(VM)], R),
scalar_product(LW, R, #=, WM),
%% affichage des résultats
compute_lenword(L, 0, Len),
sformat(A1, '~~w~~t~~~w|', [Len]),
sformat(A2, '~~t~~w~~~w|', [4]),
sformat(A3, '~~t~~w~~~w|', [5]),
print_results(A1,A2,A3, L, R, WM, VM).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% to show the results in a good way
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
compute_lenword([], N, N).
compute_lenword([item(Name, _, _)|T], N, NF):-
atom_length(Name, L),
( L > N -> N1 = L; N1 = N),
compute_lenword(T, N1, NF).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
print_results(A1,A2,A3, [], [], WM, WR) :-
sformat(W1, A1, [' ']),
sformat(W2, A2, [WM]),
sformat(W3, A3, [WR]),
format('~w~w~w~n', [W1,W2,W3]).
print_results(A1,A2,A3, [_H|T], [0|TR], WM, VM) :-
print_results(A1,A2,A3, T, TR, WM, VM).
print_results(A1, A2, A3, [item(Name, W, V)|T], [1|TR], WM, VM) :-
sformat(W1, A1, [Name]),
sformat(W2, A2, [W]),
sformat(W3, A3, [V]),
format('~w~w~w~n', [W1,W2,W3]),
print_results(A1, A2, A3, T, TR, WM, VM).

78
Task/Knapsack-problem-0-1/Prolog/knapsack-problem-0-1-2.pro Normal file
View file

@ -0,0 +1,78 @@
:- use_module(library(simplex)).
knapsack :-
L = [
(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 )],
gen_state(S0),
length(L, N),
numlist(1, N, LN),
time(( create_constraint_N(LN, S0, S1),
maplist(create_constraint_WV, LN, L, LW, LV),
constraint(LW =< 400, S1, S2),
maximize(LV, S2, S3)
)),
compute_lenword(L, 0, Len),
sformat(A1, '~~w~~t~~~w|', [Len]),
sformat(A2, '~~t~~w~~~w|', [4]),
sformat(A3, '~~t~~w~~~w|', [5]),
print_results(S3, A1,A2,A3, L, LN, 0, 0).
create_constraint_N([], S, S).
create_constraint_N([HN|TN], S1, SF) :-
constraint(integral(x(HN)), S1, S2),
constraint([x(HN)] =< 1, S2, S3),
constraint([x(HN)] >= 0, S3, S4),
create_constraint_N(TN, S4, SF).
create_constraint_WV(N, (_, W, V), W * x(N), V * x(N)).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
compute_lenword([], N, N).
compute_lenword([(Name, _, _)|T], N, NF):-
atom_length(Name, L),
( L > N -> N1 = L; N1 = N),
compute_lenword(T, N1, NF).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
print_results(_S, A1, A2, A3, [], [], WM, VM) :-
sformat(W1, A1, [' ']),
sformat(W2, A2, [WM]),
sformat(W3, A3, [VM]),
format('~w~w~w~n', [W1,W2,W3]).
print_results(S, A1, A2, A3, [(Name, W, V)|T], [N|TN], W1, V1) :-
variable_value(S, x(N), X),
( X = 0 -> W1 = W2, V1 = V2
; sformat(S1, A1, [Name]),
sformat(S2, A2, [W]),
sformat(S3, A3, [V]),
format('~w~w~w~n', [S1,S2,S3]),
W2 is W1 + W,
V2 is V1 + V),
print_results(S, A1, A2, A3, T, TN, W2, V2).

31
Task/Knapsack-problem-0-1/Python/knapsack-problem-0-1-1.py Normal file
View file

@ -0,0 +1,31 @@
from itertools import combinations
def anycomb(items):
' return combinations of any length from the items '
return ( comb
for r in range(1, len(items)+1)
for comb in combinations(items, r)
)
def totalvalue(comb):
' Totalise a particular combination of items'
totwt = totval = 0
for item, wt, val in comb:
totwt += wt
totval += val
return (totval, -totwt) if totwt <= 400 else (0, 0)
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),
)
bagged = max( anycomb(items), key=totalvalue) # max val or min wt if values equal
print("Bagged the following items\n " +
'\n '.join(sorted(item for item,_,_ in bagged)))
val, wt = totalvalue(bagged)
print("for a total value of %i and a total weight of %i" % (val, -wt))

53
Task/Knapsack-problem-0-1/Python/knapsack-problem-0-1-2.py Normal file
View file

@ -0,0 +1,53 @@
try:
xrange
except:
xrange = range
def totalvalue(comb):
' Totalise a particular combination of items'
totwt = totval = 0
for item, wt, val in comb:
totwt += wt
totval += val
return (totval, -totwt) if totwt <= 400 else (0, 0)
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),
)
def knapsack01_dp(items, limit):
table = [[0 for w in range(limit + 1)] for j in xrange(len(items) + 1)]
for j in xrange(1, len(items) + 1):
item, wt, val = items[j-1]
for w in xrange(1, limit + 1):
if wt > w:
table[j][w] = table[j-1][w]
else:
table[j][w] = max(table[j-1][w],
table[j-1][w-wt] + val)
result = []
w = limit
for j in range(len(items), 0, -1):
was_added = table[j][w] != table[j-1][w]
if was_added:
item, wt, val = items[j-1]
result.append(items[j-1])
w -= wt
return result
bagged = knapsack01_dp(items, 400)
print("Bagged the following items\n " +
'\n '.join(sorted(item for item,_,_ in bagged)))
val, wt = totalvalue(bagged)
print("for a total value of %i and a total weight of %i" % (val, -wt))

171
Task/Knapsack-problem-0-1/REXX/knapsack-problem-0-1.rexx Normal file
View file

@ -0,0 +1,171 @@
/*REXX pgm solves a knapsack problem (22 items with weight restriction).*/
@.=
@.1 = 'map 9 150'
@.2 = 'compass 13 35'
@.3 = 'water 153 200'
@.4 = 'sandwich 50 160'
@.5 = 'glucose 15 60'
@.6 = 'tin 68 45'
@.7 = 'banana 27 60'
@.8 = 'apple 39 40'
@.9 = 'cheese 23 30'
@.10 = 'beer 52 10'
@.11 = 'suntan_cream 11 70'
@.12 = 'camera 32 30'
@.13 = 'T-shirt 24 15'
@.14 = 'trousers 48 10'
@.15 = 'umbrella 73 40'
@.16 = 'waterproof_trousers 42 70'
@.17 = 'waterproof_overclothes 43 75'
@.18 = 'note-case 22 80'
@.19 = 'sunglasses 7 20'
@.20 = 'towel 18 12'
@.21 = 'socks 4 50'
@.22 = 'book 30 10'
maxWeight=400 /*the maximum weight for knapsack*/
say; say 'maximum weight allowed for a knapsack:' comma(maxWeight); say
maxL=length('item') /*maximum width for table names. */
maxL=length('knapsack items') /*maximum width for table names. */
maxW=length('weight') /* " " " " weights*/
maxV=length('value') /* " " " " values.*/
maxQ=length('pieces') /* " " " " quant. */
highQ=0 /*max quantity specified (if any)*/
items=0; i.=; w.=0; v.=0; q.=0; Tw=0; Tv=0; Tq=0 /*initialize stuff.*/
/*────────────────────────────────sort the choices by decreasing weight.*/
/*this minimizes # combinations. */
do j=1 while @.j\=='' /*process each choice and sort. */
_=@.j; _wt=word(_,2) /*choose first item (arbitrary). */
_wt=word(_,2)
do k=j+1 while @.k\=='' /*find a possible heavier item. */
?wt=word(@.k,2)
if ?wt>_wt then do; _=@.k; @.k=@.j; @.j=_; _wt=?wt; end
end /*k*/
end /*j*/
obj=j-1 /*adjust for the DO loop index. */
/*────────────────────────────────build list of choices.────────────────*/
do j=1 for obj /*build a list of choices. */
_=space(@.j) /*remove superfluous blanks. */
parse var _ item w v q . /*parse original choice for table*/
if w>maxWeight then iterate /*if the weight > maximum, ignore*/
Tw=Tw+w; Tv=Tv+v; Tq=Tq+1 /*add totals up (for alignment). */
maxL=max(maxL,length(item)) /*find maximum width for item. */
if q=='' then q=1
highQ=max(highQ,q)
items=items+1 /*bump the item counter. */
i.items=item; w.items=w; v.items=v; q.items=q
do k=2 to q; items=items+1 /*bump the item counter. */
i.items=item; w.items=w; v.items=v; q.items=q
Tw=Tw+w; Tv=Tv+v; Tq=Tq+1
end /*k*/
end /*j*/
maxW=max(maxW,length(comma(Tw))) /*find maximum width for weight. */
maxV=max(maxV,length(comma(Tv))) /* " " " " value. */
maxQ=max(maxQ,length(comma(Tq))) /* " " " " quantity*/
maxL=maxL+maxL%4+4 /*extend width of name for table.*/
/*────────────────────────────────show the list of choices.─────────────*/
call hdr 'item'; do j=1 for obj /*show all choices, nice format. */
parse var @.j item weight value q .
if highq==1 then q=
else if q=='' then q=1
call show item,weight,value,q
end /*j*/
say; say 'number of items:' items; say
/*─────────────────────────────────────examine the possible choices. */
h=items; ho=h+1; m=maxWeight; $=0; call sim22
/*─────────────────────────────────────show the best choice (weight,val)*/
do h-1; ?=strip(strip(?),"L",0); end
bestC=?; bestW=0; bestV=$; highQ=0; totP=words(bestC)
call hdr 'best choice'
do j=1 to totP /*J is modified within DO loop. */
_=word(bestC,j); _w=w._; _v=v._; q=1
if _==0 then iterate
do k=j+1 to totP
__=word(bestC,k); if i._\==i.__ then leave
j=j+1; w._=w._+_w; v._=v._+_v; q=q+1
end /*k*/
call show i._,w._,v._,q; bestW=bestw+w._
end /*j*/
call hdr2; say
call show 'best weight' ,bestW /*show a nicely formatted winnerW*/
call show 'best value' ,,bestV /*show a nicely formatted winnerV*/
call show 'knapsack items',,,totP /*show a nicely formatted pieces.*/
exit /*stick a fork in it, we're done.*/
/*────────────────────────────────COMMA subroutine──────────────────────*/
comma: procedure; parse arg _,c,p,t;arg ,cu;c=word(c ",",1)
if cu=='BLANK' then c=' ';o=word(p 3,1);p=abs(o);t=word(t 999999999,1)
if \datatype(p,'W')|\datatype(t,'W')|p==0|arg()>4 then return _;n=_'.9'
#=123456789;k=0;if o<0 then do;b=verify(_,' ');if b==0 then return _
e=length(_)-verify(reverse(_),' ')+1;end;else do;b=verify(n,#,"M")
e=verify(n,#'0',,verify(n,#"0.",'M'))-p-1;end
do j=e to b by -p while k<t;_=insert(c,_,j);k=k+1;end;return _
/*────────────────────────────────HDR subroutine────────────────────────*/
hdr: parse arg _item_,_; if highq\==1 then _=center('pieces',maxq)
call show center( _item_ ,maxL),,
center('weight',maxW),,
center('value' ,maxV),,
center(_ ,maxQ)
call hdr2
return
/*────────────────────────────────HDR2 subroutine───────────────────────*/
hdr2: _=maxQ; if highq==1 then _=0; call show copies('=' ,maxL),,
copies('=' ,maxW),,
copies('=' ,maxV),,
copies('=' ,_ )
return
/*────────────────────────────────J? subroutine─────────────────────────*/
j?: parse arg _,?; $=value('V'_); do j=1 for _; ?=? value('J'j); end; return
/*────────────────────────────────SHOW subroutine───────────────────────*/
show: parse arg _item,_weight,_value,_quant
say translate(left(_item,maxL,'─'),,'_'),
right(comma(_weight),maxW),
right(comma(_value ),maxV),
right(comma(_quant ),maxQ)
return
/*────────────────────────────────SIM22 subroutine──────────────────────*/
sim22: do j1=0 for h+1; w1=w.j1;v1=v.j1;if v1>$ then call j? 1
do j2=j1+(j1\==0) to h
if w.j2+w1>m then iterate j1;w2=w1+w.j2;v2=v1+v.j2;if v2>$ then call j? 2
do j3=j2+(j2\==0) to h
if w.j3+w2>m then iterate j2;w3=w2+w.j3;v3=v2+v.j3;if v3>$ then call j? 3
do j4=j3+(j3\==0) to h
if w.j4+w3>m then iterate j3;w4=w3+w.j4;v4=v3+v.j4;if v4>$ then call j? 4
do j5=j4+(j4\==0) to h
if w.j5+w4>m then iterate j4;w5=w4+w.j5;v5=v4+v.j5;if v5>$ then call j? 5
do j6=j5+(j5\==0) to h
if w.j6+w5>m then iterate j5;w6=w5+w.j6;v6=v5+v.j6;if v6>$ then call j? 6
do j7=j6+(j6\==0) to h
if w.j7+w6>m then iterate j6;w7=w6+w.j7;v7=v6+v.j7;if v7>$ then call j? 7
do j8=j7+(j7\==0) to h
if w.j8+w7>m then iterate j7;w8=w7+w.j8;v8=v7+v.j8;if v8>$ then call j? 8
do j9=j8+(j8\==0) to h
if w.j9+w8>m then iterate j8;w9=w8+w.j9;v9=v8+v.j9;if v9>$ then call j? 9
do j10=j9+(j9\==0) to h
if w.j10+w9>m then iterate j9;w10=w9+w.j10;v10=v9+v.j10;if v10>$ then call j? 10
do j11=j10+(j10\==0) to h
if w.j11+w10>m then iterate j10;w11=w10+w.j11;v11=v10+v.j11;if v11>$ then call j? 11
do j12=j11+(j11\==0) to h
if w.j12+w11>m then iterate j11;w12=w11+w.j12;v12=v11+v.j12;if v12>$ then call j? 12
do j13=j12+(j12\==0) to h
if w.j13+w12>m then iterate j12;w13=w12+w.j13;v13=v12+v.j13;if v13>$ then call j? 13
do j14=j13+(j13\==0) to h
if w.j14+w13>m then iterate j13;w14=w13+w.j14;v14=v13+v.j14;if v14>$ then call j? 14
do j15=j14+(j14\==0) to h
if w.j15+w14>m then iterate j14;w15=w14+w.j15;v15=v14+v.j15;if v15>$ then call j? 15
do j16=j15+(j15\==0) to h
if w.j16+w15>m then iterate j15;w16=w15+w.j16;v16=v15+v.j16;if v16>$ then call j? 16
do j17=j16+(j16\==0) to h
if w.j17+w16>m then iterate j16;w17=w16+w.j17;v17=v16+v.j17;if v17>$ then call j? 17
do j18=j17+(j17\==0) to h
if w.j18+w17>m then iterate j17;w18=w17+w.j18;v18=v17+v.j18;if v18>$ then call j? 18
do j19=j18+(j18\==0) to h
if w.j19+w18>m then iterate j18;w19=w18+w.j19;v19=v18+v.j19;if v19>$ then call j? 19
do j20=j19+(j19\==0) to h
if w.j20+w19>m then iterate j19;w20=w19+w.j20;v20=v19+v.j20;if v20>$ then call j? 20
do j21=j20+(j20\==0) to h
if w.j21+w20>m then iterate j20;w21=w20+w.j21;v21=v20+v.j21;if v21>$ then call j? 21
do j22=j21+(j21\==0) to h
if w.j22+w21>m then iterate j21;w22=w21+w.j22;v22=v21+v.j22;if v22>$ then call j? 22
end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end;end
return

57
Task/Knapsack-problem-0-1/Ruby/knapsack-problem-0-1-1.rb Normal file
View file

@ -0,0 +1,57 @@
KnapsackItem = Struct.new(:name, :weight, :value)
potential_items = [
KnapsackItem.new('map', 9, 150), KnapsackItem.new('compass', 13, 35),
KnapsackItem.new('water', 153, 200), KnapsackItem.new('sandwich', 50, 160),
KnapsackItem.new('glucose', 15, 60), KnapsackItem.new('tin', 68, 45),
KnapsackItem.new('banana', 27, 60), KnapsackItem.new('apple', 39, 40),
KnapsackItem.new('cheese', 23, 30), KnapsackItem.new('beer', 52, 10),
KnapsackItem.new('suntan cream', 11, 70), KnapsackItem.new('camera', 32, 30),
KnapsackItem.new('t-shirt', 24, 15), KnapsackItem.new('trousers', 48, 10),
KnapsackItem.new('umbrella', 73, 40), KnapsackItem.new('waterproof trousers', 42, 70),
KnapsackItem.new('waterproof overclothes', 43, 75), KnapsackItem.new('note-case', 22, 80),
KnapsackItem.new('sunglasses', 7, 20), KnapsackItem.new('towel', 18, 12),
KnapsackItem.new('socks', 4, 50), KnapsackItem.new('book', 30, 10),
]
knapsack_capacity = 400
class Array
# do something for each element of the array's power set
def power_set
yield [] if block_given?
self.inject([[]]) do |ps, elem|
r = []
ps.each do |i|
r << i
new_subset = i + [elem]
yield new_subset if block_given?
r << new_subset
end
r
end
end
end
maxval = 0
solutions = []
potential_items.power_set do |subset|
weight = subset.inject(0) {|w, elem| w += elem.weight}
next if weight > knapsack_capacity
value = subset.inject(0) {|v, elem| v += elem.value}
if value == maxval
solutions << subset
elsif value > maxval
maxval = value
solutions = [subset]
end
end
puts "value: #{maxval}"
solutions.each do |set|
items = []
wt = 0
set.each {|elem| wt += elem.weight; items << elem.name}
puts "weight: #{wt}"
puts "items: #{items.sort.join(',')}"
end

84
Task/Knapsack-problem-0-1/Ruby/knapsack-problem-0-1-2.rb Normal file
View file

@ -0,0 +1,84 @@
KnapsackItem = Struct.new(:name, :cost, :value)
KnapsackProblem = Struct.new(:items, :max_cost)
def dynamic_programming_knapsack(problem)
num_items = problem.items.size
items = problem.items
max_cost = problem.max_cost
cost_matrix = zeros(num_items, max_cost+1)
num_items.times do |i|
(max_cost + 1).times do |j|
if(items[i].cost > j)
cost_matrix[i][j] = cost_matrix[i-1][j]
else
cost_matrix[i][j] = [cost_matrix[i-1][j], items[i].value + cost_matrix[i-1][j-items[i].cost]].max
end
end
end
cost_matrix
end
def get_used_items(problem, cost_matrix)
i = cost_matrix.size - 1
currentCost = cost_matrix[0].size - 1
marked = Array.new(cost_matrix.size, 0)
while(i >= 0 && currentCost >= 0)
if(i == 0 && cost_matrix[i][currentCost] > 0 ) || (cost_matrix[i][currentCost] != cost_matrix[i-1][currentCost])
marked[i] = 1
currentCost -= problem.items[i].cost
end
i -= 1
end
marked
end
def get_list_of_used_items_names(problem, cost_matrix)
items = problem.items
used_items = get_used_items(problem, cost_matrix)
result = []
used_items.each_with_index do |item,i|
if item > 0
result << items[i].name
end
end
result.sort.join(', ')
end
def zeros(rows, cols)
Array.new(rows) do |row|
Array.new(cols, 0)
end
end
if $0 == __FILE__
items = [
KnapsackItem.new('map' , 9 , 150) , KnapsackItem.new('compass' , 13 , 35) ,
KnapsackItem.new('water' , 153 , 200) , KnapsackItem.new('sandwich' , 50 , 160) ,
KnapsackItem.new('glucose' , 15 , 60) , KnapsackItem.new('tin' , 68 , 45) ,
KnapsackItem.new('banana' , 27 , 60) , KnapsackItem.new('apple' , 39 , 40) ,
KnapsackItem.new('cheese' , 23 , 30) , KnapsackItem.new('beer' , 52 , 10) ,
KnapsackItem.new('suntan cream' , 11 , 70) , KnapsackItem.new('camera' , 32 , 30) ,
KnapsackItem.new('t-shirt' , 24 , 15) , KnapsackItem.new('trousers' , 48 , 10) ,
KnapsackItem.new('umbrella' , 73 , 40) , KnapsackItem.new('waterproof trousers' , 42 , 70) ,
KnapsackItem.new('waterproof overclothes' , 43 , 75) , KnapsackItem.new('note-case' , 22 , 80) ,
KnapsackItem.new('sunglasses' , 7 , 20) , KnapsackItem.new('towel' , 18 , 12) ,
KnapsackItem.new('socks' , 4 , 50) , KnapsackItem.new('book' , 30 , 10)
]
problem = KnapsackProblem.new(items, 400)
cost_matrix = dynamic_programming_knapsack problem
puts
puts 'Dynamic Programming:'
puts
puts 'Found solution: ' + get_list_of_used_items_names(problem, cost_matrix)
puts 'With value: ' + cost_matrix.last.last.to_s
end

92
Task/Knapsack-problem-0-1/Scala/knapsack-problem-0-1.scala Normal file
View file

@ -0,0 +1,92 @@
object Knapsack extends App {
case class Item(name: String, weight: Int, value: Int)
val elapsed: (=> Unit) => Long = f => {val s = System.currentTimeMillis; f; (System.currentTimeMillis - s)/1000}
//===== brute force (caution: increase the heap!) ====================================
val ks01b: List[Item] => Unit = loi => {
val tw:Set[Item]=>Int=ps=>(ps:\0)((a,b)=>a.weight+b) //total weight
val tv:Set[Item]=>Int=ps=>(ps:\0)((a,b)=>a.value+b) //total value
val pis = (loi.toSet.subsets).toList.filterNot(_==Set())
val res = pis.map(ss=>Pair(ss,tw(ss)))
.filter(p=>p._2>350 && p._2<401).map(p=>Pair(p,tv(p._1)))
.sortWith((s,t)=>s._2.compareTo(t._2) < 0)
.last
println{val h = "packing list of items (brute force):"; h+"\n"+"="*h.size}
res._1._1.foreach{p=>print(" "+p.name+": weight="+p.weight+" value="+p.value+"\n")}
println("\n"+" resulting items: "+res._1._1.size+" of "+loi.size)
println(" total weight: "+res._1._2+", total value: "+res._2)
}
//===== dynamic programming ==========================================================
val ks01d: List[Item] => Unit = loi => {
val W = 400
val N = loi.size
val m = Array.ofDim[Int](N+1,W+1)
val plm = (List((for {w <- 0 to W} yield Set[Item]()).toArray)++(
for {
n <- 0 to N-1
colN = (for {w <- 0 to W} yield Set[Item](loi(n))).toArray
} yield colN)).toArray
1 to N foreach {n =>
0 to W foreach {w =>
def in = loi(n-1)
def wn = loi(n-1).weight
def vn = loi(n-1).value
if (w<wn) {
m(n)(w) = m(n-1)(w)
plm(n)(w) = plm(n-1)(w)
}
else {
if (m(n-1)(w)>=m(n-1)(w-wn)+vn) {
m(n)(w) = m(n-1)(w)
plm(n)(w) = plm(n-1)(w)
}
else {
m(n)(w) = m(n-1)(w-wn)+vn
plm(n)(w) = plm(n-1)(w-wn)+in
}
}
}
}
println{val h = "packing list of items (dynamic programming):"; h+"\n"+"="*h.size}
plm(N)(W).foreach{p=>print(" "+p.name+": weight="+p.weight+" value="+p.value+"\n")}
println("\n"+" resulting items: "+plm(N)(W).size+" of "+loi.size)
println(" total weight: "+(0/:plm(N)(W).map{item=>item.weight})(_+_)+", total value: "+m(N)(W))
}
val items = List(
Item("map", 9, 150)
,Item("compass", 13, 35)
,Item("water", 153, 200)
,Item("sandwich", 50, 160)
,Item("glucose", 15, 60)
,Item("tin", 68, 45)
,Item("banana", 27, 60)
,Item("apple", 39, 40)
,Item("cheese", 23, 30)
,Item("beer", 52, 10)
,Item("suntan cream", 11, 70)
,Item("camera", 32, 30)
,Item("t-shirt", 24, 15)
,Item("trousers", 48, 10)
,Item("umbrella", 73, 40)
,Item("waterproof trousers", 42, 70)
,Item("waterproof overclothes", 43, 75)
,Item("note-case", 22, 80)
,Item("sunglasses", 7, 20)
,Item("towel", 18, 12)
,Item("socks", 4, 50)
,Item("book", 30, 10)
)
List(ks01b, ks01d).foreach{f=>
val t = elapsed{f(items)}
println(" elapsed time: "+t+" sec"+"\n")
}
}

75
Task/Knapsack-problem-0-1/Tcl/knapsack-problem-0-1.tcl Normal file
View file

@ -0,0 +1,75 @@
# The list of items to consider, as list of lists
set 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}
}
# Simple extraction functions
proc names {chosen} {
set names {}
foreach item $chosen {lappend names [lindex $item 0]}
return $names
}
proc weight {chosen} {
set weight 0
foreach item $chosen {incr weight [lindex $item 1]}
return $weight
}
proc value {chosen} {
set value 0
foreach item $chosen {incr value [lindex $item 2]}
return $value
}
# Recursive function for searching over all possible choices of items
proc knapsackSearch {items {chosen {}}} {
# If we've gone over the weight limit, stop now
if {[weight $chosen] > 400} {
return
}
# If we've considered all of the items (i.e., leaf in search tree)
# then see if we've got a new best choice.
if {[llength $items] == 0} {
global best max
set v [value $chosen]
if {$v > $max} {
set max $v
set best $chosen
}
return
}
# Branch, so recurse for chosing the current item or not
set this [lindex $items 0]
set rest [lrange $items 1 end]
knapsackSearch $rest $chosen
knapsackSearch $rest [lappend chosen $this]
}
# Initialize a few global variables
set best {}
set max 0
# Do the brute-force search
knapsackSearch $items
# Pretty-print the results
puts "Best filling has weight of [expr {[weight $best]/100.0}]kg and score [value $best]"
puts "Best items:\n\t[join [lsort [names $best]] \n\t]"