protected override long RunPart2()
{
var congruences = this.ParsedInput.AvailableBusLines.Select(l => l.AsCongruence());
var intersection = Congruence.RelativelyPrimeIntersection(congruences);
return(intersection.Offset);
}
private static Congruence RelativelyPrimeIntersection(Congruence one, Congruence other)
{
// this only works if this.Modulo and other.Module are relatively prime
// since it is trivial to manually check this in the input
// I'll skip the rather bothersome step of checking it here
var modulo = one.Modulo * other.Modulo;
var offset = one.FirstIntersectingElement(other);
return(new Congruence(modulo, offset));
}
public long FirstIntersectingElement(Congruence other)
{
var value = other.Offset - this.Offset;
while (true)
{
if (value % other.Modulo == 0)
{
return(value - other.Offset);
}
else
{
value += this.Modulo;
}
}
}