/// <summary>
/// Computes each unique set of values of length <paramref name="boxSize"/> that can be
/// formed from the given values.
/// </summary>
/// <param name="values">
/// All the possible values for the magic square. Each value must be unique. Values must
/// have length `boxSize*boxSize`.
/// </param>
/// <param name="allPossibleValues">
/// The
/// </param>
public static HashSet <BitVector> ComputeSets(ReadOnlySpan <int> values, int boxSize, BitVector allPossibleValues)
{
if (values.Length != boxSize * boxSize)
{
throw new ArgumentException(
$"{nameof(boxSize)} ({boxSize}) must be the exact square root of the length of {nameof(values)} ({values.Length}).");
}
if (allPossibleValues.ComputeCount() != values.Length)
{
throw new ArgumentException($"Expected {nameof(allPossibleValues)} to have the same length as {nameof(values)}.");
}
int magicSum = _ComputeSum(values, boxSize);
var sets = new HashSet <BitVector>();
for (int i = 0; i < values.Length; ++i)
{
int possibleValue = values[i];
var set = new BitVector();
set.SetBit(possibleValue);
BitVector possibleValues = allPossibleValues;
possibleValues.UnsetBit(possibleValue);
sets = new(sets.Union(_ComputeMagicSetsForRemainder(boxSize - 1, magicSum - possibleValue, possibleValues, set)));
}
return(sets);
}
private static HashSet <BitVector> _ComputeMagicSetsForRemainder(int remainingSize, int remainder, BitVector possibleValues, BitVector partialSet)
{
var result = new HashSet <BitVector>();
if (remainingSize == 0)
{
if (remainder == 0)
{
result.Add(partialSet);
}
return(result);
}
Span <int> setBits = stackalloc int[BitVector.NumBits];
int numSetBits = possibleValues.PopulateSetBits(setBits);
foreach (var possibleValue in setBits.Slice(0, numSetBits))
{
if (remainder - possibleValue >= 0)
{
BitVector set = partialSet;
set.SetBit(possibleValue);
BitVector reducedPossibleValues = possibleValues;
reducedPossibleValues.UnsetBit(possibleValue);
result = new(result.Union(_ComputeMagicSetsForRemainder(remainingSize - 1, remainder - possibleValue, reducedPossibleValues, set)));
}
}
return(result);
}