public override object CalculateResult()
{
return new Range(1, 100, true)
.SelectMany(n => new Range(1, n, true)
.Where(r =>
{
var numerators = new Range(n - r + 1, n, true).Select(x => (long)x).ToArray();
var denominators = new Range(2, r, true).Select(x => (long)x).ToArray();
for (int i = 0; i < numerators.Length; i++)
{
long numerator = numerators[i];
if (numerator > 1)
{
for (int j = 0; j < denominators.Length; j++)
{
long denominator = denominators[j];
if (denominator > 1)
{
long divisor = MathUtilities.GreatestCommonDivisor(numerator, denominator);
numerator /= divisor;
denominator /= divisor;
denominators[j] = denominator;
}
}
numerators[i] = numerator;
}
}
if (denominators.Any(d => d != 1))
{
throw new InvalidOperationException();
}
long value = 1;
for (int i = 0; i < numerators.Length; i++)
{
value *= numerators[i];
if (value > 1000000)
{
return true;
}
}
return false;
}))
.Count();
}
/// <summary>
/// Scans the tickets associated with the specified notes.
/// </summary>
/// <param name="notes">The notes containing the ticket information.</param>
/// <returns>
/// The ticket scanning error rate and your parsed ticket.
/// </returns>
public static (int ErrorRate, IDictionary <string, int> Ticket) ScanTickets(IList <string> notes)
{
int indexOfFirstTicket = notes.IndexOf("your ticket:") + 1;
int indexOfSecondTicket = notes.IndexOf("nearby tickets:") + 1;
var rules = new Dictionary <string, ICollection <Range> >(indexOfFirstTicket - 2);
// Parse the rules
foreach (string line in notes.Take(indexOfFirstTicket - 2))
{
(string name, string instruction) = line.Bifurcate(':');
string[] split = instruction.Split(" or ", StringSplitOptions.RemoveEmptyEntries | StringSplitOptions.TrimEntries);
var ranges = new Range[split.Length];
for (int i = 0; i < split.Length; i++)
{
(int start, int end) = split[i].AsNumberPair <int>('-');
ranges[i] = new(start, end);
}
rules[name] = ranges;
}
var allTickets = new IList <int> [notes.Count - indexOfSecondTicket + 1];
allTickets[0] = notes[indexOfFirstTicket]
.AsNumbers <int>()
.ToArray();
// Parse the nearby tickets
for (int i = indexOfSecondTicket; i < notes.Count; i++)
{
allTickets[i - indexOfSecondTicket + 1] = notes[i]
.AsNumbers <int>()
.ToArray();
}
int invalidValues = 0;
var validTickets = new List <IList <int> >();
// Find the valid tickets
for (int i = 1; i < allTickets.Length; i++)
{
var ticket = allTickets[i];
bool isValid = true;
for (int j = 0; j < ticket.Count && isValid; j++)
{
int value = ticket[j];
foreach (ICollection <Range> ranges in rules.Values)
{
isValid = ranges.Any((p) => InRange(value, p));
if (isValid)
{
break;
}
}
if (!isValid)
{
invalidValues += value;
}
}
if (isValid)
{
validTickets.Add(ticket);
}
}
// Store indexes where each field could be located
var possibleIndexes = new Dictionary <string, List <int> >(rules.Keys.Count);
var allIndexes = Enumerable.Range(0, allTickets[0].Count).ToList();
foreach (string key in rules.Keys)
{
possibleIndexes[key] = new List <int>(allIndexes);
}
var indexes = new Dictionary <int, string>();
while (possibleIndexes.Values.Any((p) => p.Count > 1))
{
// For any fields where the index is known, remove it from all the other possibilities
foreach (var index in possibleIndexes.Where((p) => p.Value.Count == 1))
{
int foundIndex = index.Value[0];
indexes[foundIndex] = index.Key;
foreach (List <int> other in possibleIndexes.Values.Where((p) => p.Count > 1))
{
other.Remove(foundIndex);
}
}
// No need to iterate through the rules for fields we know the index for
foreach (var rule in rules.Where((p) => possibleIndexes[p.Key].Count > 1))
{
// Check if all the values for this index fit the current rule
for (int index = 0; index < possibleIndexes.Count; index++)
{
bool areAllValid = true;
for (int j = 0; j < validTickets.Count; j++)
{
IList <int> ticket = validTickets[j];
int value = ticket[index];
bool isInRange = rule.Value.Any((p) => InRange(value, p));
if (!isInRange)
{
// This index cannot be the field associated with this rule
areAllValid = false;
break;
}
}
if (!areAllValid)
{
// This index cannot be for the field associated with this rule
possibleIndexes[rule.Key].Remove(index);
}
}
}
}
// Build up the ticket from the indexes found
var yourTicket = new Dictionary <string, int>(indexes.Count);
foreach (var index in indexes)
{
yourTicket[index.Value] = allTickets[0][index.Key];
}
return(invalidValues, yourTicket);
