//Binary decision between doubling and adding the next sequential power of 3
//Starts from 1, first power of 3 added is 3^1 = 3
public static IEnumerable <long> EnumerateTwoThreeDecisionSequenceResults(int max) //capToMaximum = true
{
if (max > int.MaxValue)
{
throw new ArgumentOutOfRangeException(
nameof(max),
max,
nameof(max) + " is greater than int.MaxValue, so not all summed paths would be possible to return."
);
}
if (max < 1)
{
throw new ArgumentOutOfRangeException(nameof(max), max, "Cannot be less than 1.");
}
var decisionTracker = new TwoThreeDecisionTracker(max: max);
//Console.WriteLine("#A : " + decisionTracker.Current + " " + decisionTracker.ToString());
decisionTracker.DoubleRepeatedlyUpToMax();
while (decisionTracker.TryAddNextPowerOf3())
{
//Console.WriteLine("#A2: " + decisionTracker.Current + " " + decisionTracker.ToString());
}
//Console.WriteLine("#B : " + decisionTracker.Current + " " + decisionTracker.ToString());
yield return(decisionTracker.Current); //Reached maximum length of this branch; yield the branch's result
while (!decisionTracker.IsAtRoot) //Starts at root but we did an initial repeated doubling; when we get back to the root we're done
{
//Console.WriteLine("#C : " + decisionTracker.Current + " " + decisionTracker.ToString());
if (decisionTracker.BacktrackAndCheckIfWasDoublingOp())
{
//Console.WriteLine("#D : " + decisionTracker.Current + " " + decisionTracker.ToString());
if (decisionTracker.TryAddNextPowerOf3())
{
//Console.WriteLine("#E : " + decisionTracker.Current + " " + decisionTracker.ToString());
decisionTracker.DoubleRepeatedlyUpToMax();
while (decisionTracker.TryAddNextPowerOf3())
{
//Console.WriteLine("#E2: " + decisionTracker.Current + " " + decisionTracker.ToString());
}
//Console.WriteLine("#F : " + decisionTracker.Current + " " + decisionTracker.ToString());
yield return(decisionTracker.Current); //Reached maximum length of this branch; yield the branch's result
}
else
{
//Console.WriteLine("#G : " + decisionTracker.Current + " " + decisionTracker.ToString());
//Adding the next power of 3 makes it too big; loop around to backtrack again
//But first, yield the current branch as we've now explored all sub-branches (see below)
yield return(decisionTracker.Current);
continue;
}
}
else
{
//Console.WriteLine("#H : " + decisionTracker.Current + " " + decisionTracker.ToString());
//Explored all sub-branches of the current branch; yield the current branch
//When we first go into the branch, we're doubling repeatedly so can't yield at every step,
//but here we can't do anything repeatedly, so for efficiency do the yielding here.
yield return(decisionTracker.Current);
}
}
}
//Returns an array that, for each position corresponding to a result found, contains the exponents
//used on the highest power of 3 involved each time that result was reached, all encoded as binary flags.
public static LongChunkedArray <int> GetExpansionRegister(int max)
{
if (max > int.MaxValue)
{
throw new ArgumentOutOfRangeException(
nameof(max),
max,
nameof(max) + " is greater than int.MaxValue, so not all summed paths would be possible to return."
);
}
if (max < 1)
{
throw new ArgumentOutOfRangeException(nameof(max), max, "Cannot be less than 1.");
}
var decisionTracker = new TwoThreeDecisionTracker(max: max);
var expansionRegister = new LongChunkedArray <int>(max + 1, 16777216);
// ^ For each position corresponding to a result found, contains exponent that was used on the
//last power of 3 added to get to that result. This is encoded as a binary flag, so that if a
//given result is reached multiple times using different powers of 3, all of the powers can be
//recorded without needing additional storage.
// //If that result has been reached multiple times,
// //contains the one that was reached most recently.
// // //contains the one that's closest to 3/4 * log3(10,000). This is a rough estimate for the
// // //exponent that is likely to be repeated the most, saving the most steps.
//Console.WriteLine("#A : " + decisionTracker.Current + " " + decisionTracker.ToString());
decisionTracker.DoubleRepeatedlyUpToMax();
while (decisionTracker.TryAddNextPowerOf3())
{
//Console.WriteLine("#A2: " + decisionTracker.Current + " " + decisionTracker.ToString());
}
//Console.WriteLine("#B : " + decisionTracker.Current + " " + decisionTracker.ToString());
//Console.WriteLine(decisionTracker.LastAddedThreeExponent + " " + decisionTracker.Current);
//yield return decisionTracker.Current;
//Reached maximum length of this branch; yield the branch's result
expansionRegister[decisionTracker.Current] |= 1 << decisionTracker.LastAddedThreeExponent;
while (!decisionTracker.IsAtRoot) //Starts at root but we did an initial repeated doubling; when we get back to the root we're done
{
//Console.WriteLine("#C : " + decisionTracker.Current + " " + decisionTracker.ToString());
if (decisionTracker.BacktrackAndCheckIfWasDoublingOp())
{
if ((expansionRegister[decisionTracker.Current] & (1 << decisionTracker.LastAddedThreeExponent)) > 0)
{
continue; //Already done this branch
}
//Console.WriteLine("#D : " + decisionTracker.Current + " " + decisionTracker.ToString());
if (decisionTracker.TryAddNextPowerOf3())
{
if ((expansionRegister[decisionTracker.Current] & (1 << decisionTracker.LastAddedThreeExponent)) > 0)
{
continue; //Already done this branch
}
//Console.WriteLine("#E : " + decisionTracker.Current + " " + decisionTracker.ToString());
decisionTracker.DoubleRepeatedlyUpToMax();
if ((expansionRegister[decisionTracker.Current] & (1 << decisionTracker.LastAddedThreeExponent)) > 0)
{
continue; //Already done this branch
}
while (decisionTracker.TryAddNextPowerOf3())
{
if ((expansionRegister[decisionTracker.Current] & (1 << decisionTracker.LastAddedThreeExponent)) > 0)
{
continue; //Already done this branch
}
//Console.WriteLine("#E2: " + decisionTracker.Current + " " + decisionTracker.ToString());
}
//Console.WriteLine("#F : " + decisionTracker.Current + " " + decisionTracker.ToString());
//Console.WriteLine(decisionTracker.LastAddedThreeExponent + " " + decisionTracker.Current);
//yield return decisionTracker.Current;
//Reached maximum length of this branch; yield the branch's result
expansionRegister[decisionTracker.Current] |= 1 << decisionTracker.LastAddedThreeExponent;
}
else
{
//Console.WriteLine("#G : " + decisionTracker.Current + " " + decisionTracker.ToString());
//Console.WriteLine(decisionTracker.LastAddedThreeExponent + " " + decisionTracker.Current);
//yield return decisionTracker.Current;
//Adding the next power of 3 makes it too big; loop around to backtrack again
//But first, yield the current branch as we've now explored all sub-branches (see below)
expansionRegister[decisionTracker.Current] |= 1 << decisionTracker.LastAddedThreeExponent;
continue;
}
}
else
{
//Console.WriteLine("#H : " + decisionTracker.Current + " " + decisionTracker.ToString());
//Console.WriteLine(decisionTracker.LastAddedThreeExponent + " " + decisionTracker.Current);
//yield return decisionTracker.Current;
//Explored all sub-branches of the current branch; yield the current branch
//When we first go into the branch, we're doubling repeatedly so can't yield at every step,
//but here we can't do anything repeatedly, so for efficiency do the yielding here.
expansionRegister[decisionTracker.Current] |= 1 << decisionTracker.LastAddedThreeExponent;
}
}
return(expansionRegister);
}
