private void Test13Choose5()
{
// This function tests out the binomial coefficien class for the 13 choose 5 case.
int n = 13;
int k = 5;
ulong numCombos = BinCoeffBase.GetCombosCount(n, k);
if (numCombos != 1287)
{
DisplayMsg("BinCoeffBase.GetNumCombos did not calculate the correct value for 13 choose 5 case.");
return;
}
// Create the BinCoeff object that will be used for all the tests for the 13 choose 5 case.
// The table is created when the 3rd argument of the constuctor is set to true.
BC = new BinCoeff <uint>(n, k, 0, true);
try
{
TestTableData();
VerifyPascalsTriangle();
VerifyTranslastion();
TestOutputIndexes();
}
catch (Exception e)
{
DisplayMsg($"The Test 13 choose 5 tests did not complete successfully - {e.Message}.");
return;
}
DisplayMsg("Test13Choose5: completed successfully.");
}
private uint BenchmarkBCRankAlt(int n, int k, out long ticks)
{
// This method benchmarks obtaining the rank for this n choose k case
// using the Combination.GetRank method.
//
uint rank;
GC.Collect();
// Get the combination for rank of 100 in kIndexes.
var bc = new BinCoeff <int>(n, k);
int[] kIndexes = new int[k];
bc.GetCombFromRank(bc.TotalCombos / 2, kIndexes);
Stopwatch sw = Stopwatch.StartNew();
rank = (uint)Combination.GetRank(kIndexes, out bool overflow, n, k);
// Some cases overflow. So, use big integer.
if (rank == 0)
{
rank = (uint)Combination.GetRankBigInt(kIndexes, n, k);
}
sw.Stop();
ticks = sw.ElapsedTicks;
return(rank);
}
private void BenchmarkConst(int n, int k, out long ticks)
{
// This method benchmarks the constructor for this n choose k case.
//
GC.Collect();
Stopwatch sw = Stopwatch.StartNew();
var bc = new BinCoeff <int>(n, k);
sw.Stop();
ticks = sw.ElapsedTicks;
}
private uint BenchmarkBCNumCombos2(int n, int k, out long ticks)
{
// This method benchmarks getting the number of combos for this n choose k case, including the constructor.
//
uint numCombos;
GC.Collect();
Stopwatch sw = Stopwatch.StartNew();
var bc = new BinCoeff <int>(n, k);
numCombos = bc.GetNumCombos();
sw.Stop();
ticks = sw.ElapsedTicks;
return(numCombos);
}
private int[] BenchmarkBCGetComboFromRank(int n, int k, out long ticks)
{
// This method benchmarks obtaining the rank for this n choose k case.
//
GC.Collect();
var bc = new BinCoeff <int>(n, k);
int[] kIndexes = new int[k];
uint rank = bc.TotalCombos / 2;
Stopwatch sw = Stopwatch.StartNew();
bc.GetCombFromRank(rank, kIndexes);
sw.Stop();
ticks = sw.ElapsedTicks;
return(kIndexes);
}
private uint BenchmarkBCRank(int n, int k, out long ticks)
{
// This method benchmarks obtaining the rank for this n choose k case.
//
uint rank;
GC.Collect();
var bc = new BinCoeff <int>(n, k);
int[] kIndexes = new int[k];
bc.GetCombFromRank(bc.TotalCombos / 2, kIndexes);
Stopwatch sw = Stopwatch.StartNew();
rank = bc.GetRank(true, kIndexes, out bool overflow);
sw.Stop();
ticks = sw.ElapsedTicks;
return(rank);
}
private void BenchmarkBinCoeffMultiple(int[] numElemArray, int[] numGroupArray)
{
// This method benchmarks the n choose k tests for many subcases & ranks, and compares the performance against the Combination class methods.
// The first benchmark compares the performance of single methods. This one attempts a more "real-life" analysis and calls GetRank and
// GetComboFromRank 1,000 times for all the subcases for each test case.
//
int numItems, groupSize, caseLoop;
int[] kIndexes = new int[26];
ulong rankSum = 1;
int kLoop;
bool overflow;
BinCoeff <int> bc;
long ticks, ticksAlt, ticksSum = 0, ticksSumAlt = 0;
uint numCombos, rank, startRank, endRank, rankCount = 1000, rankLoop;
double d;
Stopwatch sw;
// Benchmark all the specified n choose k test cases.
for (caseLoop = 0; caseLoop < numElemArray.Length; caseLoop++)
{
GC.Collect();
sw = Stopwatch.StartNew();
numItems = numElemArray[caseLoop];
groupSize = numGroupArray[caseLoop];
bc = new BinCoeff <int>(numItems, groupSize);
// Benchmark the subcases > 1,000 combinations.
for (kLoop = groupSize; kLoop > 3; kLoop--)
{
numCombos = bc.GetNumCombos(numItems, kLoop);
rankSum += numCombos;
startRank = (numCombos / 2) - (rankCount / 2);
endRank = startRank + rankCount;
for (rankLoop = startRank; rankLoop < endRank; rankLoop++)
{
bc.GetCombFromRank(rankLoop, kIndexes, numItems, kLoop);
rank = bc.GetRank(true, kIndexes, out overflow, kLoop);
rankSum += rank;
}
}
sw.Stop();
ticks = sw.ElapsedTicks;
sw = Stopwatch.StartNew();
// Benchmark the combination class using the same code as above.
for (kLoop = groupSize; kLoop > 3; kLoop--)
{
numCombos = (uint)Combination.GetNumCombos(numItems, kLoop);
rankSum += numCombos;
startRank = (numCombos / 2) - (rankCount / 2);
endRank = startRank + rankCount;
for (rankLoop = startRank; rankLoop < endRank; rankLoop++)
{
Combination.GetCombFromRank(rankLoop, kIndexes, numItems, kLoop);
rank = (uint)Combination.GetRank(kIndexes, out overflow, numItems, kLoop);
rankSum += rank;
}
}
sw.Stop();
ticksAlt = sw.ElapsedTicks;
// Display the results.
d = (double)ticksAlt / (double)ticks;
d = Math.Round(d, 2);
Console.WriteLine($"Multiple methods benchmark for {numItems} choose {groupSize} & subcases .vs. Combination class ratio = {d} to 1.");
ticksSum += ticks;
ticksSumAlt += ticksAlt;
}
d = (double)ticksSumAlt / (double)ticksSum;
d = Math.Round(d, 2);
Console.WriteLine($"Average for all n choose k cases & subcases .vs. Combination class ratio = {d} to 1.");
Console.WriteLine();
// Looking at the sum of the return values makes sure that the compiler does not optimize the code away.
if (rankSum == 0)
{
Console.WriteLine("Error - rankSum = 0?");
}
}
private void Test35Choose16()
{
// This function tests out the long binomial coefficien class for the case 35 choose 16.
// This produces one of the largest number of combinations that will fit within a uint:
// 4,059,928,950
//
int n = 35;
int k = 16;
string s;
bool overflow;
// Create the BinCoeff object that will be used for all the tests for the 50 choose 25 case.
var bc = new BinCoeff <uint>(n, k);
if (bc.TotalCombos != 4059928950)
{
s = $"Test35Choose16: Error calculating # of combos - {BC.TotalCombos}.";
DisplayMsg(s);
throw new ApplicationException(s);
}
int kLoop;
uint rank = 0, numCombos, numCombos2, highRank, rank2, rankLoop;
int[] kIndexes = new int[k];
// Try getting the first and last 5 combinations and ranks for this case.
try
{
// Test all subcases of 35 choose 16.
for (kLoop = k; kLoop > 0; kLoop--)
{
numCombos = bc.GetNumCombos(n, kLoop);
numCombos2 = (uint)BinCoeffBase.GetCombosCount(n, kLoop);
if (numCombos != numCombos2)
{
s = $"Test100Choose95SubCases: Error - {n} choose {k}: # of combos does not match.";
Console.WriteLine(s);
return;
}
// Test the lowest 10 ranks and the highest 10 ranks for each subcase test case.
for (rankLoop = 1; rankLoop < 10; rankLoop++)
{
bc.GetCombFromRank(rankLoop, kIndexes, n, kLoop);
rank = bc.GetRank(true, kIndexes, out overflow, kLoop);
if (rank != kLoop)
{
s = $"Test67Choose33: Either rank or combos was not calculated correctly. rank = {rank}, kloop = {kloop}";
DisplayMsg(s);
throw new ApplicationException(s);
}
highRank = numCombos - rankLoop;
rank2 = bc.GetRank(true, kIndexes, out overflow);
bc.GetCombFromRank(highRank, kIndexes, n, kLoop);
rank2 = bc.GetRank(true, kIndexes, out overflow);
if (highRank != rank2)
{
s = $"Test67Choose33: Either rank or combos was not calculated correctly. highRank = {highRank}, rank2 = {rank2}";
DisplayMsg(s);
throw new ApplicationException(s);
}
highRank--;
}
}
}
catch (Exception e)
{
DisplayMsg($"Test67Choose33: Exception = {e.Message}.");
return;
}
DisplayMsg("Test67Choose33: completed successfully.");
}
private TestResult TestIntSubCases(int n, int k)
{
// This method tests out the new int functionality of specifying a lower n choose k case without having to
// create a new version of Pascal's Triangle to handle it. n & k specifies the main n choose k case.
//
string s;
int nLoop, kLoop;
BinCoeff <int> bc = new BinCoeff <int>(n, k);
uint numCombos, numCombos2, rank, rankHigh, rank2, rankLoop;
int[] kIndexes = new int[k];
// If the # of combos overflowed, then don't try this case with uint.
if (bc.TotalCombos == 0)
{
return(TestResult.IntOverflow);
}
// Try getting the rank and combination for all subcases of n choose k.
for (kLoop = k; kLoop > 0; kLoop--)
{
for (nLoop = n; nLoop >= kLoop; nLoop--)
{
numCombos = bc.GetNumCombos(nLoop, kLoop);
// If GetNumCombos overflowed, then return that status.
if (numCombos == 0)
{
return(TestResult.IntOverflow);
}
numCombos2 = (uint)BinCoeffBase.GetCombosCount(nLoop, kLoop);
if (numCombos != numCombos2)
{
s = $"TestIntSubCases: Error - {n} choose {k}: # of combos does not match.";
Console.WriteLine(s);
return(TestResult.Failed);
}
uint comboCount = numCombos;
// Loop thru all the combinations for this n choose k case if # of combos <= 1000.
// Otherwise, just do the lowest ranked 500 and the highest ranked 500.
if (numCombos > 1000)
{
comboCount = 500;
}
// Loop thru the combinations for this n choose k case.
for (rankLoop = 0; rankLoop < comboCount; rankLoop++)
{
bc.GetCombFromRank(rankLoop, kIndexes, nLoop, kLoop);
rank = bc.GetRank(true, kIndexes, out bool overflow, kLoop);
if (rank != rankLoop)
{
s = $"TestIntSubCases: Error - {n} choose {k}: rank or combo is wrong.";
Console.WriteLine(s);
return(TestResult.Failed);
}
// If not doing all the combinations, then process the high ranks.
if (numCombos > comboCount)
{
rankHigh = numCombos - rankLoop - 1;
// Get the k-indexes for this combination.
bc.GetCombFromRank(rankHigh, kIndexes, nLoop, kLoop);
// Verify that the Kindexes returned can be used to retrieve the rank of the combination.
rank2 = bc.GetRank(true, kIndexes, out overflow, kLoop);
if (rank2 != rankHigh)
{
s = $"TestIntSubCases: Error - {n} choose {k}: GetRank or GetCombFromRank failed - {rank2} != rankHigh at {rankLoop}";
Console.WriteLine(s);
return(TestResult.Failed);
}
}
}
}
}
return(TestResult.Passed);
}
private bool TestRankCombo(int numItems, int groupSize)
{
// This method tests getting the rank and combination for the specified 32-bit int case.
// If the test failed, then false is returned. Otherwise true is returned.
string s;
int n = numItems, k = groupSize;
bool overflow;
// Create the bin coeff object required to get all the combos for this n choose k combination.
BinCoeff <int> bc = new BinCoeff <int>(n, k);
// The Kindexes array specifies the indexes for a combination.
int[] kIndexes = new int[k];
uint numCombos = bc.TotalCombos, rankLoop;
bc.GetCombFromRank(numCombos - 1, kIndexes);
uint numCombos2 = (uint)BinCoeffBase.GetRankAlt(kIndexes, n, k, out overflow) + 1;
if (overflow)
{
s = $"TestRankCombo: {n} choose {k}: # of combos overflowed with alt method.";
Console.WriteLine(s);
return(false);
}
if (numCombos != numCombos2)
{
s = $"TestRankCombo: {n} choose {k}: # of combos not the same with alternate method - {numCombos} .vs. {numCombos2}";
Console.WriteLine(s);
return(false);
}
uint rank2, rankHigh;
uint comboCount = numCombos;
// Loop thru all the combinations for this n choose k case if # of combos <= 1000.
// Otherwise, just do the lowest ranked 500 and the highest ranked 500.
if (numCombos > 1000)
{
comboCount = 500;
}
// Loop thru all the combinations for this n choose k case.
for (rankLoop = 1; rankLoop < comboCount; rankLoop++)
{
// Get the k-indexes for this combination.
bc.GetCombFromRank(rankLoop, kIndexes);
// Verify that the Kindexes returned can be used to retrieve the rank of the combination.
rank2 = bc.GetRank(true, kIndexes, out overflow);
if (rank2 != rankLoop)
{
s = $"TestRankCombo: {n} choose {k}: GetRank or GetCombFromRank failed - value of {rank2} != rank at {rankLoop}";
Console.WriteLine(s);
return(false);
}
// If not doing all the combinations, then process the high ranks.
if (numCombos > comboCount)
{
rankHigh = numCombos - rankLoop - 1;
// Get the k-indexes for this combination.
bc.GetCombFromRank(rankHigh, kIndexes);
// Verify that the Kindexes returned can be used to retrieve the rank of the combination.
rank2 = bc.GetRank(true, kIndexes, out overflow);
if (rank2 != rankHigh)
{
s = $"TestRankCombo: {n} choose {k}: GetRank or GetCombFromRank failed - value of {rank2} != rankHigh at {rankLoop}";
Console.WriteLine(s);
return(false);
}
}
}
s = $"TestRankCombo: {n} choose {k} completed successfully.";
Console.WriteLine(s);
return(true);
}
