static int MultSymbolsFromPosToPos(int[] seq, int startPos, int endPos)
{
int mult = 1;
for (var i = startPos; i <= endPos; i++)
{
mult = Symb.Mult(mult, seq[i]);
}
return(mult);
}
static IEnumerable <int> FindAllKPos(int[] seq)
{
int mult = 1;
for (var i = seq.Length - 1; i >= 0; i--)
{
mult = Symb.Mult(seq[i], mult);
if (mult == Symb.k)
{
yield return(i);
}
}
}
static IEnumerable <int> FindAllIPos(int[] seq)
{
int mult = 1;
for (var i = 0; i < seq.Length; i++)
{
mult = Symb.Mult(mult, seq[i]);
if (mult == Symb.i)
{
yield return(i);
}
}
}
static string Solve(Tuple <long, int[]> d)
{
long r = d.Item1;
int[] seq = d.Item2;
if (r == 1)
{
var possibleIPos = FindAllIPos(seq).ToList();
var possibleKPos = FindAllKPos(seq).Reverse().ToList();
if (!possibleIPos.Any() || !possibleKPos.Any())
{
return("NO");
}
//possibleKPos.Reverse();
//possibleKPos = possibleKPos.Where(kp => kp > (possibleIPos[0] + 1)).ToList();
Dictionary <int, int> nextKPosMult = new Dictionary <int, int>();
for (var i = 1; i < possibleKPos.Count; i++)
{
var cur = possibleKPos[i];
var prev = possibleKPos[i - 1];
nextKPosMult.Add(cur, MultSymbolsFromPosToPos(seq, prev, cur - 1));
}
foreach (var pI in possibleIPos)
{
possibleKPos = possibleKPos.Where(pK => pK > (pI + 1)).ToList();
if (!possibleKPos.Any())
{
break;
}
int prevPK = possibleKPos[0];
int prevMult = MultSymbolsFromPosToPos(seq, pI + 1, prevPK - 1);
if (prevMult == Symb.j)
{
return("YES");
}
foreach (var pK in possibleKPos.Skip(1).ToList())
{
prevMult = Symb.Mult(prevMult, nextKPosMult[pK]);
if (prevMult == Symb.j)
{
return("YES");
}
}
}
return("NO");
}
else if (r > 1)
{
int cf = MultSymbolsFromPosToPos(seq, 0, seq.Length - 1);
//long newR = r % 4;
long newR = Math.Min((r % 4) + 16, r);
//for (var newR = (int)(r % 4); newR <= r && newR <= 100; newR += 4)
//{
for (var i = 0; i < newR; i++)
{
int cfpi = Symb.Power(cf, i);
for (var k = i; k < newR; k++)
{
int cfpk = Symb.Power(cf, (int)(newR - 1 - k));
int cfpj = Symb.Power(cf, k - i - 1);
if (Solve(new Tuple <long, int[]>(1, Merge(seq, cfpi, cfpk, cfpj, k == i))) == "YES")
{
return("YES");
}
}
}
//}
return("NO");
}
else
{
throw new NotImplementedException();
}
}