0-1 Knapsack algorithm

Question

Is the following 0-1 Knapsack problem solvable:

• \'float\' positive values and
• \'float\' weights (can be positive or negative)
• \'float\' capacity

Answer 1

Yeah, brute force it. This is an NP-Complete problem, but that shouldn't matter because you will have less than 10 items. Brute forcing won't be problematic.

        var size = 10;
        var capacity = 0;
        var permutations = 1024;
        var repeat = 10000;

        // Generate items
        float[] items = new float[size];
        float[] weights = new float[size];
        Random rand = new Random();
        for (int i = 0; i < size; i++)
        {
            items[i] = (float)rand.NextDouble();
            weights[i] = (float)rand.NextDouble();
            if (rand.Next(2) == 1)
            {
                weights[i] *= -1;
            }
        }

        // solution
        int bestPosition= -1;

        Stopwatch sw = new Stopwatch();            
        sw.Start();

        // for perf testing
        //for (int r = 0; r < repeat; r++)
        {
            var bestValue = 0d;

            // solve
            for (int i = 0; i < permutations; i++)
            {
                var total = 0d;
                var weight = 0d;
                for (int j = 0; j < size; j++)
                {
                    if (((i >> j) & 1) == 1)
                    {
                        total += items[j];
                        weight += weights[j];
                    }
                }

                if (weight <= capacity && total > bestValue)
                {
                    bestPosition = i;
                    bestValue = total;
                }
            }
        }
        sw.Stop();
        sw.Elapsed.ToString();