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

This can be solved using Dynamic Programming. Below code can help you solve the 0/1 Knapsack problem using Dynamic Programming.

    internal class knapsackProblem
    {
    private int[] weight;
    private int[] profit;
    private int capacity;
    private int itemCount;
    private int[,] data;

    internal void GetMaxProfit()
    {
        ItemDetails();

        data = new int[itemCount, capacity + 1];

        for (int i = 1; i < itemCount; i++)
        {
            for (int j = 1; j < capacity + 1; j++)
            {
                int q = j - weight[i] >= 0 ? data[i - 1, j - weight[i]] + profit[i] : 0;

                if (data[i - 1, j] > q)
                {
                    data[i, j] = data[i - 1, j];
                }
                else
                {
                    data[i, j] = q;
                }
            }
        }

        Console.WriteLine($"\nMax profit can be made : {data[itemCount-1, capacity]}");
        IncludedItems();
    }

    private void ItemDetails()
    {
        Console.Write("\nEnter the count of items to be inserted : ");
        itemCount = Convert.ToInt32(Console.ReadLine()) + 1;
        Console.WriteLine();

        weight = new int[itemCount];
        profit = new int[itemCount];

        for (int i = 1; i < itemCount; i++)
        {
            Console.Write($"Enter weight of item {i} : ");
            weight[i] = Convert.ToInt32(Console.ReadLine());

            Console.Write($"Enter the profit on the item {i} : ");
            profit[i] = Convert.ToInt32(Console.ReadLine());

            Console.WriteLine();
        }

        Console.Write("\nEnter the capacity of the knapsack : ");
        capacity = Convert.ToInt32(Console.ReadLine());
    }

    private void IncludedItems()
    {
        int i = itemCount - 1;
        int j = capacity;

        while(i > 0)
        {
            if(data[i, j] == data[i - 1, j])
            {
                Console.WriteLine($"Item {i} : Not included");
                i--;
            }
            else
            {
                Console.WriteLine($"Item {i} : Included");
                j = j - weight[i];
                i--;
            }
        }
    }
}