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

   Knapsack problem/Bounded
   Knapsack problem/Unbounded
   Knapsack problem/Continuous
   A* search algorithm


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"};
}