public static void DemoBoundedKnapsack()
{
Util.Entering();
Dictionary <KnapsackItem, int> bounds = new Dictionary <KnapsackItem, int>
{
{ KnapsackItem.Small, 4 }, { KnapsackItem.Medium, 3 }, { KnapsackItem.Large, 1 }
};
Dictionary <KnapsackItem, int> weights = new Dictionary <KnapsackItem, int>
{
{ KnapsackItem.Small, 10 }, { KnapsackItem.Medium, 20 }, { KnapsackItem.Large, 30 }
};
Dictionary <KnapsackItem, int> worths = new Dictionary <KnapsackItem, int>
{
{ KnapsackItem.Small, 30 }, { KnapsackItem.Medium, 20 }, { KnapsackItem.Large, 10 }
};
int goal = 100;
Console.WriteLine("\tItems: {0:s}",
String.Join(", ", bounds.Keys.Select(e => e.ToString())));
Console.WriteLine("\tBounds: {0:s}",
String.Join(", ", bounds.Select(b => b.Key.ToString() + " => " + b.Value.ToString())));
Console.WriteLine("\tWeights: {0:s}",
String.Join(", ", weights.Select(b => b.Key.ToString() + " => " + b.Value.ToString())));
Console.WriteLine("\tWorths: {0:s}",
String.Join(", ", worths.Select(b => b.Key.ToString() + " => " + b.Value.ToString())));
HashSet <List <KnapsackItem> > solutions = BoundedKnapsack.GetAllBoundedKnapsackSolutions_BruteForce(bounds, weights, worths, goal);
Console.WriteLine(" Solutions:");
if (solutions.Count == 0)
{
Console.WriteLine("\tNone");
}
else
{
int maxWorth = solutions.Max(solution => solution.Select(x => worths[x]).Sum());
IEnumerable <List <KnapsackItem> > maxSolutions = solutions.Where(
solution => solution.Select(x => worths[x]).Sum() == maxWorth).Distinct(new ListOfKnapsackItems());
foreach (List <KnapsackItem> solution in maxSolutions)
{
Console.WriteLine("\tWorth={0:d} : {1:s}",
solution.Select(x => worths[x]).Sum(),
String.Join(", ", solution));
}
}
}
/// <summary>
/// Finds via exhaustive search all best solutions to the bounded knapsack problem with exact weight constraints.
/// </summary>
/// <param name="bounds">Dictionary: Keys=knapsack items, Values=max count of that item</param>
/// <param name="weights">Dictionary: Keys=knapsack items, Values=item weights</param>
/// <param name="worths">Dictionary: Keys=knapsack items, Values=worths (often called values)</param>
/// <returns>The set of all solutions</returns>
/// <remark>Potential optimization: Terminate if no solutions are possible
/// because the sum of all weights, including multiplicity, does not reach the goal.</remark>
public static HashSet <List <KnapsackItem> > GetAllBoundedKnapsackSolutions_BruteForce(
Dictionary <KnapsackItem, int> bounds,
Dictionary <KnapsackItem, int> weights,
Dictionary <KnapsackItem, int> worths,
int goal)
{
var result = new HashSet <List <KnapsackItem> >();
foreach (KnapsackItem item in bounds.Keys)
{
if (weights[item] > goal)
{
continue;
}
if (weights[item] == goal)
{
result.Add(new List <KnapsackItem> {
item
});
}
var itemHistogram2 = new Dictionary <KnapsackItem, int>(bounds);
if (itemHistogram2[item]-- == 0)
{
itemHistogram2.Remove(item);
}
HashSet <List <KnapsackItem> > subsolutions = BoundedKnapsack.GetAllBoundedKnapsackSolutions_BruteForce(
itemHistogram2, weights, worths, goal - weights[item]);
foreach (List <KnapsackItem> subsolution in subsolutions)
{
subsolution.Add(item);
subsolution.Sort();
result.Add(subsolution);
}
}
return(result);
}