/// <summary>
/// Solves the knapsack problem.
/// </summary>
/// <param name="maxWeight">The maximum weight.</param>
/// <param name="itemList">The item list.</param>
/// <param name="valueMatrix">The value matrix.</param>
/// <param name="keepMatrix">The keep matrix.</param>
/// <param name="itemCount">The item count.</param>
private static void SolveKnapsackProblem(
long maxWeight,
IList <IItem> itemList,
InfiniteTwoDimensionalSparseMatrix <long> valueMatrix,
InfiniteTwoDimensionalSparseMatrix <bool> keepMatrix,
int itemCount)
{
for (int currentFileIndex = 1; currentFileIndex <= itemCount; currentFileIndex++)
{
long weightAtPreviousIndex = itemList[currentFileIndex - 1].Weight;
long valueAtPreviousIndex = itemList[currentFileIndex - 1].Value;
for (int currentWeight = 0; currentWeight <= maxWeight; currentWeight++)
{
long newProspectiveValue = valueAtPreviousIndex + valueMatrix[currentFileIndex - 1, currentWeight - weightAtPreviousIndex];
long oldValue = valueMatrix[currentFileIndex - 1, currentWeight];
if (weightAtPreviousIndex <= currentWeight && newProspectiveValue > oldValue)
{
valueMatrix[currentFileIndex, currentWeight] = newProspectiveValue;
keepMatrix[currentFileIndex, currentWeight] = true;
}
else
{
valueMatrix[currentFileIndex, currentWeight] = oldValue;
}
}
}
}
/// <summary>
/// Solves the Knapsack problem
/// </summary>
/// <param name="items">The items to put into the knapsack</param>
/// <param name="maxWeight">The maximum weight the knapsack can hold</param>
/// <returns>
/// The items to put into the knapsack
/// </returns>
public IEnumerable <IItem> Solve(IEnumerable <IItem> items, long maxWeight)
{
if (items.Any() == false)
{
return(Enumerable.Empty <IItem>());
}
IList <IItem> itemList = items.ToList();
var valueMatrix = new InfiniteTwoDimensionalSparseMatrix <long>();
var keepMatrix = new InfiniteTwoDimensionalSparseMatrix <bool>();
int itemCount = itemList.Count;
SolveKnapsackProblem(maxWeight, itemList, valueMatrix, keepMatrix, itemCount);
return(Package(itemList, keepMatrix, maxWeight));
}
/// <summary>
/// Packages the specified item list.
/// </summary>
/// <param name="itemList">The item list.</param>
/// <param name="keepMatrix">The keep matrix.</param>
/// <param name="maxWeight">The maximum weight.</param>
/// <returns>The items packed up into a knapsack</returns>
private static IEnumerable <IItem> Package(
IList <IItem> itemList,
InfiniteTwoDimensionalSparseMatrix <bool> keepMatrix,
long maxWeight)
{
int itemCount = itemList.Count;
var knapsackItems = Enumerable.Empty <IItem>();
long upperBound = maxWeight;
for (int i = itemCount; i > 0; i--)
{
if (keepMatrix[i, upperBound])
{
IItem currentItem = itemList[i - 1];
knapsackItems = knapsackItems.Append(currentItem);
upperBound -= currentItem.Weight;
}
}
return(knapsackItems);
}
