public static LCG GetShuffleFunction(
BigInteger deckSize,
IList <ShuffleInstruction> shuffleInstructions)
{
// Combine all shuffle instructions into one LCG
var result = LCG.GetIdentity(deckSize);
var dealIntoNewStack = GetShuffleFunctionDealIntoNewStack(deckSize);
foreach (var shuffleInstruction in shuffleInstructions)
{
if (ShuffleTechnique.DealIntoNewStack.Equals(shuffleInstruction.Technique))
{
result = LCG.Compose(result, dealIntoNewStack);
}
else if (ShuffleTechnique.CutNCards.Equals(shuffleInstruction.Technique))
{
var cutNCards = GetShuffleFunctionCutNCards(shuffleInstruction.ShuffleParameter, deckSize);
result = LCG.Compose(result, cutNCards);
}
else if (ShuffleTechnique.DealWithIncrementN.Equals(shuffleInstruction.Technique))
{
var dealWithIncrementN = GetShuffleFunctionDealWithIncrementN(shuffleInstruction.ShuffleParameter, deckSize);
result = LCG.Compose(result, dealWithIncrementN);
}
}
return(result);
}
public static BigInteger ShuffleCard(
BigInteger startCardIndex,
BigInteger deckSize,
BigInteger numberOfShuffles,
IList <ShuffleInstruction> shuffleInstructions,
bool runBackwards)
{
var shuffleFunction = GetShuffleFunction(deckSize, shuffleInstructions);
// Compose the shuffle function into itself once for each shuffle pass
shuffleFunction = ExponentiationHelper.GetExponentiationByPowers(
x: shuffleFunction,
exponent: numberOfShuffles,
MultiplyFunction: LCG.Compose,
identity: LCG.GetIdentity(deckSize));
// If we are running backwards, then use the inverse of the
// shuffle function
if (runBackwards)
{
shuffleFunction = shuffleFunction.GetInverse();
}
var endCardIndex = shuffleFunction.Evaluate(startCardIndex);
return(endCardIndex);
}
public void GetExponentiationByPowersLCFTest()
{
var testData = new List <Tuple <LCG, BigInteger, Func <LCG, LCG, LCG>, LCG> >()
{
// f(f(f(x))) where f(x) = 2*x + 3 (mod 5)
// f(f(f(x))) = f(f(2x + 3))
// = f(2*(2x + 3) + 3)
// = f(4x + 6 + 3)
// = f(4x + 9)
// = 2*(4x + 9) + 3
// = 8x + 18 + 3
// = 8x + 21 (mod 5)
Tuple.Create(
new LCG(2, 3, 5),
(BigInteger)0,
(Func <LCG, LCG, LCG>)LCG.Compose,
LCG.GetIdentity(5)),
Tuple.Create(
new LCG(2, 3, 5),
(BigInteger)1,
(Func <LCG, LCG, LCG>)LCG.Compose,
new LCG(2, 3, 5)),
Tuple.Create(
new LCG(2, 3, 5),
(BigInteger)3,
(Func <LCG, LCG, LCG>)LCG.Compose,
new LCG(8, 21, 5)),
};
foreach (var testExample in testData)
{
var result = ExponentiationHelper.GetExponentiationByPowers <LCG>(
x: testExample.Item1,
exponent: testExample.Item2,
MultiplyFunction: testExample.Item3,
identity: LCG.GetIdentity(testExample.Item1.M));
Assert.Equal(testExample.Item4, result);
}
}
