Task: Knapsack problem_0-1


C++: #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 ;
   
   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 ; 
   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 ) {
   
   
   
   
   
   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 { 
		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 ] ;
}










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
      
      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;