/// <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)
{
IList<IItem> itemList = items.ToList();
var smallerSolutionList = new OneDimensionalSparseArray<long>();
var intermediateSolution = new OneDimensionalSparseArray<long>();
var memoList = new OneDimensionalSparseArray<long>();
var keepMatrix = new TwoDimensionalSparseMatrix<bool>();
SolveUnboundedKnapsack(maxWeight, itemList, ref smallerSolutionList, ref intermediateSolution, ref memoList, ref keepMatrix);
return Package(itemList, keepMatrix, maxWeight);
}
/// <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 TwoDimensionalSparseMatrix<long>();
var keepMatrix = new TwoDimensionalSparseMatrix<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,
TwoDimensionalSparseMatrix<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;
}
/// <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,
TwoDimensionalSparseMatrix<long> valueMatrix,
TwoDimensionalSparseMatrix<bool> keepMatrix,
int itemCount)
{
for (var currentFileIndex = 1; currentFileIndex <= itemCount; currentFileIndex++)
{
var weightAtPreviousIndex = itemList[currentFileIndex - 1].Weight;
var valueAtPreviousIndex = itemList[currentFileIndex - 1].Value;
for (var currentWeight = 0; currentWeight <= maxWeight; currentWeight++)
{
var newProspectiveValue = valueAtPreviousIndex + valueMatrix[currentFileIndex - 1, currentWeight - weightAtPreviousIndex];
var oldValue = valueMatrix[currentFileIndex - 1, currentWeight];
if (weightAtPreviousIndex <= currentWeight && newProspectiveValue > oldValue)
{
valueMatrix[currentFileIndex, currentWeight] = newProspectiveValue;
keepMatrix[currentFileIndex, currentWeight] = true;
}
else
{
valueMatrix[currentFileIndex, currentWeight] = oldValue;
}
}
}
}
/// <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,
TwoDimensionalSparseMatrix<bool> keepMatrix,
long maxWeight)
{
int itemCount = itemList.Count;
var knapsackItems = Enumerable.Empty<IItem>();
long currentWeightToCheck = maxWeight;
while(true)
{
bool foundItem = false;
for (int itemIndex = 0; itemIndex < itemList.Count; itemIndex++)
{
if(keepMatrix[itemIndex, currentWeightToCheck])
{
IItem itemToTake = itemList[itemIndex];
knapsackItems = knapsackItems.Append(itemToTake);
currentWeightToCheck -= itemToTake.Weight;
foundItem = true;
break;
}
}
if (foundItem == false)
{
break;
}
}
return knapsackItems;
}
/// <summary>
/// Solves the unbounded knapsack.
/// </summary>
/// <param name="maxWeight">The maximum weight.</param>
/// <param name="itemList">The item list.</param>
/// <param name="smallerSolutionList">The smaller solution list.</param>
/// <param name="intermediateSolutionList">The intermediate solution list.</param>
/// <param name="memoList">The memo list.</param>
/// <param name="keepMatrix">The keep matrix.</param>
private static void SolveUnboundedKnapsack(
long maxWeight,
IList<IItem> itemList,
ref OneDimensionalSparseArray<long> smallerSolutionList,
ref OneDimensionalSparseArray<long> intermediateSolutionList,
ref OneDimensionalSparseArray<long> memoList,
ref TwoDimensionalSparseMatrix<bool> keepMatrix)
{
for (long weight = 1; weight <= maxWeight; weight++)
{
for (int itemIndex = 0; itemIndex < itemList.Count; itemIndex++)
{
IItem currentItem = itemList[itemIndex];
if (weight >= currentItem.Weight)
{
smallerSolutionList[itemIndex] = memoList[weight - currentItem.Weight];
}
else
{
smallerSolutionList[itemIndex] = 0;
}
}
for (int itemIndex = 0; itemIndex < itemList.Count; itemIndex++)
{
IItem currentItem = itemList[itemIndex];
if (weight >= currentItem.Weight)
{
intermediateSolutionList[itemIndex] = smallerSolutionList[itemIndex] + currentItem.Value;
}
else
{
intermediateSolutionList[itemIndex] = 0;
}
}
long fileIndexOfMaxValue = 0;
memoList[weight] = intermediateSolutionList[0];
for (int itemIndex = 1; itemIndex < itemList.Count; itemIndex++)
{
if (intermediateSolutionList[itemIndex] > memoList[weight])
{
memoList[weight] = intermediateSolutionList[itemIndex];
fileIndexOfMaxValue = itemIndex;
}
}
keepMatrix[fileIndexOfMaxValue, weight] = true;
}
}
