public static long Problem15(int n, int m, Dictionary <string, long> Memo)
{
if (Memo == null)
{
Memo = new Dictionary <string, long>();
}
if (m == 1 || n == 1)
{
return(1);
}
string Key = $"{m},{n}";
if (Memo.ContainsKey(Key))
{
return(Memo[Key]);
}
else
{
long Result = Problem15(m - 1, n, Memo) + Problem15(m, n - 1, Memo);
Memo[Key] = Result;
return(Result);
}
}
private List <WordEquivalencyClassComposition> Recursive(
WordEquivalencyClassComposition currentWord,
string anagramCharPool,
IList <WordEquivalencyClass> equivalencyClasses,
Memo memo,
int level)
{
var newCandidates = new List <WordEquivalencyClassComposition>();
foreach (var equivalencyClass in equivalencyClasses)
{
var newPartialPhraseComposition = new WordEquivalencyClassComposition(currentWord,
new WordEquivalencyClass(equivalencyClass.CharPool, equivalencyClass.Words));
var remainder = anagramCharPool.SubtractChars(newPartialPhraseComposition.CharPool.Alphabetize());
// not a fit
if (remainder == null)
{
newPartialPhraseComposition.IsDeadend = true;
if (!memo.ContainsKey(newPartialPhraseComposition.CharPool))
{
memo.AddDeadEnd(newPartialPhraseComposition);
}
continue;
}
// a fit
if (remainder.Length == 0)
{
newPartialPhraseComposition.IsDeadend = false;
memo.AddSolution(newPartialPhraseComposition);
newCandidates.Add(newPartialPhraseComposition);
continue;
}
// inconclusive
if (remainder.Length > 0)
{
newPartialPhraseComposition.IsDeadend = false;
// check new word against memo
if (memo.ContainsKey(newPartialPhraseComposition.CharPool))
{
//we have been here before...
var val = memo[newPartialPhraseComposition.CharPool];
if (val == null)
{
//its a dead end!
continue;
}
else
{
if (val.IsDeadend == false)
{
memo.GenerateAndAddFullSolution_FromIncomplete(newPartialPhraseComposition);
continue;
}
else
{
throw new ArgumentException("I should not be here again!");
}
}
}
var countBeforeRecursion = memo.SolutionCount;
var candidates = Recursive(newPartialPhraseComposition, anagramCharPool, equivalencyClasses, memo, level + 1);
var countAfterRecursion = memo.SolutionCount;
if (countBeforeRecursion == countAfterRecursion)
{
newPartialPhraseComposition.IsDeadend = true;
memo.AddDeadEnd(newPartialPhraseComposition);
}
else
{
newPartialPhraseComposition.IsDeadend = false;
memo.AddSolvable(newPartialPhraseComposition);
newCandidates.AddRange(candidates);
}
continue;
}
}
return(newCandidates);
}