public static OptimalType GetLeastTypeForAllSubcases(int numItems, int groupSize)
{
// This method returns the least type that will be able to handle all subcases without overflowing.
//
// n choose (n / 2) is the worst subcase that generates the most combinations.
// So, if numItems is twice or more groupSize, then there is no subcase that will increase the number of combos.
//
BigInteger numCombos;
OptimalType returnValue;
if (numItems >= groupSize + groupSize)
{
numCombos = Combination.GetNumCombos(numItems, groupSize);
}
else
{
numCombos = Combination.GetNumCombosBigInt(numItems, numItems / 2);
}
// If overflowed ulong, then only big int will work with all subtypes.
if (numCombos > ulong.MaxValue)
{
returnValue = OptimalType.BigInt;
}
else if (numCombos <= uint.MaxValue)
{
returnValue = OptimalType.UnsignedInt;
}
else
{
returnValue = OptimalType.UnsignedLong;
}
return(returnValue);
}
public uint GetNumCombos(int numItems = -1, int groupSize = -1)
{
// This method gets the total number of combos for numItems choose groupSize from Pascal's triangle.
// If Pascal's triangle has not been created, then an alternative method is called to get the # of combinations.
// If either numItems or groupSize < 0, then NumItems or GroupSize, respectively is used instead.
//
// Both numItems and groupSize are optional parameters that provide a way to efficiently calculate the number of
// combinations from Pascal's Triangle without having to re-create Pascal's Triangle for a different case. But,
// both numItems and groupSize must be <= to the original NumItems and GroupSize, respectively, that were used to create the instance.
// If either numItems or groupSize < 0, then NumItems or GroupSize, respectively, is used instead.
//
// Zero is returned if overflow occurred.
// The expected runtime of this algorithm is O(1) when Pascal's Triangle is used.
//
string s;
ulong numCombos = 0;
//
numItems = (numItems < 0) ? NumItems : numItems;
groupSize = (groupSize < 0) ? GroupSize : groupSize;
if ((numItems > NumItems) || (groupSize > GroupSize))
{
s = "BinCoeff:GetNumCombos: numItems > NumItems or groupSize > GroupSize. Neither is allowed.";
ApplicationException ae = new ApplicationException(s);
throw ae;
}
if ((numItems == 0) || (groupSize == 0))
{
s = "BinCoeff:GetNumCombos: numItems or groupSize equals zero. Neither is allowed.";
ApplicationException ae = new ApplicationException(s);
throw ae;
}
if ((groupSize == 1) || (numItems == groupSize + 1))
{
return((uint)numItems);
}
if (groupSize == numItems)
{
return(1);
}
// if Pascal's Triangle has not been created, then use an alternate method to obtain the number of combos.
if (PasTri == null)
{
numCombos = Combination.GetNumCombos(numItems, groupSize);
if (numCombos > uint.MaxValue)
{
return(0);
}
return((uint)numCombos);
}
uint n = (uint)numItems - 1;
int startIndex = GroupSize - groupSize;
uint[] indexArray = PasTri[startIndex];
int endIndex = indexArray.Length - 1;
if (groupSize == 2)
{
endIndex -= (NumItems - numItems);
if ((indexArray.Length > endIndex) && (uint.MaxValue - indexArray[endIndex] > numItems - 1))
{
numCombos = indexArray[endIndex] + (uint)numItems - 1;
}
}
else
{
if (numItems == NumItems)
{
uint[] indexArrayPrev = PasTri[startIndex + 1];
int endIndexPrev = indexArrayPrev.Length - 1;
if ((indexArray.Length > n) && (indexArrayPrev.Length > n) && (uint.MaxValue - indexArray[endIndex] > indexArrayPrev[endIndexPrev]))
{
numCombos = indexArray[endIndex] + indexArrayPrev[endIndexPrev];
}
}
else
{
endIndex = endIndex - (NumItems - numItems) + 1;
if (indexArray.Length > endIndex)
{
return(indexArray[endIndex]);
}
}
}
return((uint)numCombos);
}
public BigInteger GetNumCombos(int numItems = -1, int groupSize = -1)
{
// This method gets the total number of combos for numItems choose groupSize from Pascal's triangle.
// If Pascal's triangle has not been created, then an alternative method is called to get the # of combinations.
// If either numItems or groupSize < 0, then NumItems or GroupSize, respectively is used instead.
//
// Both numItems and groupSize are optional parameters that provide a way to efficiently calculate the number of
// combinations from Pascal's Triangle without having to re-create Pascal's Triangle for a different case. But,
// both numItems and groupSize must be <= to the original NumItems and GroupSize, respectively, that were used to create the instance.
// If either numItems or groupSize < 0, then NumItems or GroupSize, respectively, is used instead.
//
// Zero is returned if overflow occurred.
// The expected runtime of this algorithm is O(1) when Pascal's Triangle is used.
//
string s;
BigInteger numCombos = 0;
//
numItems = (numItems == -1) ? NumItems : numItems;
groupSize = (groupSize == -1) ? GroupSize : groupSize;
if ((numItems > NumItems) || (groupSize > GroupSize))
{
s = "BinCoeffBigInt:GetNumCombos: numItems > NumItems || groupSize > GroupSize. Neither is allowed. Create a new instance instead.";
ApplicationException ae = new ApplicationException(s);
throw ae;
}
if ((numItems == 0) || (groupSize == 0))
{
s = "BinCoeffBigInt:GetNumCombos: numItems or groupSize equals zero. Neither is allowed.";
ApplicationException ae = new ApplicationException(s);
throw ae;
}
if ((groupSize == 1) || (numItems == groupSize + 1))
{
return(numItems);
}
if (groupSize == numItems)
{
return(1);
}
// There are times when Pascal's triangle may not have been legitimately created. For example 5 choose 5.
// If this method is called, for example, with 5 choose 3 after being created with a 5 choose 5 case, then this is handled here.
if (PasTri == null)
{
numCombos = Combination.GetNumCombos(numItems, groupSize);
return(numCombos);
}
uint n = (uint)numItems - 1;
int startIndex = GroupSize - groupSize;
BigInteger[] indexArray = PasTri[startIndex];
int endIndex = indexArray.Length - 1;
if (groupSize == 2)
{
if (numItems != NumItems)
{
endIndex -= (NumItems - numItems);
}
numCombos = indexArray[endIndex] + (uint)numItems - 1;
}
else
{
if (numItems == NumItems)
{
BigInteger[] indexArrayPrev = PasTri[startIndex + 1];
int endIndexPrev = indexArrayPrev.Length - 1;
numCombos = indexArray[endIndex] + indexArrayPrev[endIndexPrev];
}
else
{
endIndex = endIndex - (NumItems - numItems) + 1;
return(indexArray[endIndex]);
}
}
return(numCombos);
}
