public void TestCalculateProbabilityAtLeastOnePersonGetsTheirOwnHat(int numHats, double expectedProbabilitySomeoneDrawsOwnHat)
{
double epsilon = 0.0001;
var hatProblemSolver = new HatProblemSolver();
var actualProbabilitySomeoneDrawsOwnHat = hatProblemSolver.CalculateProbabilityAtLeastOnePersonGetsTheirOwnHat(numHats);
var permutationGenerator = new PermutationGenerator();
var permutations = permutationGenerator.GeneratePermutationsOfNObjects(numHats);
var actualProbabilitySolvedThroughPermutations =
(double)permutations.Where(p => p.ContainsAtLeastOneFixedPoint()).Count() / (double)permutations.Count();
Assert.LessOrEqual(Math.Abs(expectedProbabilitySomeoneDrawsOwnHat - actualProbabilitySomeoneDrawsOwnHat), epsilon);
Assert.LessOrEqual(Math.Abs(expectedProbabilitySomeoneDrawsOwnHat - actualProbabilitySolvedThroughPermutations), epsilon);
}
public void TestGeneratePermutations(int n)
{
var permutationGenerator = new PermutationGenerator();
var permutations = permutationGenerator.GeneratePermutationsOfNObjects(n);
int nFactorial = Enumerable.Range(1, n).Aggregate(1, (p, item) => p * item);
Assert.AreEqual(nFactorial, permutations.Count);
var maxScore = 0;
// note, this only works for n < 10
foreach (var permutation in permutations)
{
var score = int.Parse(permutation.GetPermutation().Aggregate("", (score, i) => $"{score}{i}"));
Assert.Greater(score, maxScore);
maxScore = score;
}
}