static long Solve(int n)
{
// finding the nth prime, reusing Problem 3's prime enumerable,
// which while not the most efficient prime finding algorithm, works reasonably
// well for finding only the prime number 10001
return(Sequences.Primes().Skip(n).First());
}
public string Solve()
{
return(Enumerable.Range(2, 999998)
.Select(n => new Tuple <long, long>(n, Sequences.Collatz(n).Count()))
.Aggregate(new Tuple <long, long>(0, 0), (prev, next) => next.Item2 > prev.Item2 ? next : prev)
.Item1.ToString());
}
public static HashSet <long> GetFactors(long n)
{
if (FactorsDictionary.ContainsKey(n))
{
return(FactorsDictionary[n]);
}
// initialize the factor list to the prime factors and 1 and n
var primeFactors = Sequences.GetPrimeFactors(n);
var factorSet = new HashSet <long>(primeFactors)
{
1, n
};
// divide by primes and recursively determine the factors to be aggregated
foreach (var prime in primeFactors)
{
var factor = n / prime;
if (factor <= 2 || factorSet.Contains(factor))
{
continue;
}
foreach (var subfactor in GetFactors(factor))
{
factorSet.Add(subfactor);
}
}
FactorsDictionary[n] = factorSet;
return(factorSet);
}
public string Solve()
{
var abundantSums = new HashSet <long>(Sequences.GetAbundantSums(28123).ToList());
var answer = Enumerable.Range(1, 28123).Where(n => !abundantSums.Contains(n)).Sum();
return(answer.ToString());
}
/// <summary>
/// Find the prime factors of a^b.
/// </summary>
public static IEnumerable <long> PowerFactors(int a, int b)
{
var baseFactors = Sequences.GetPrimeFactors(a);
var allFactors = Enumerable.Range(0, b).SelectMany(n => baseFactors);
return(from factor in allFactors orderby factor select factor);
}
public static IEnumerable <long> GetAbundantNumbers(long limit)
{
return
(Sequences.LongRange(1, limit)
.Select(n => new Tuple <long, HashSet <long> >(n, Problem012.GetFactors(n)))
.Where(t => t.Item1 < t.Item2.Sum() - t.Item1) // subtract t.Item1 to get only proper divisors
.Select(t => t.Item1));
}
public string Solve()
{
var words = GetWords();
var wordValues = words.Select(GetWordValue).ToArray();
var maxValue = wordValues.Max();
var triangleValues = new HashSet <long>(Sequences.TriangleNumbers().TakeWhile(x => x < maxValue));
return(wordValues.Count(x => triangleValues.Contains(x)).ToString());
}
private int BruteSolve()
{
var maxPerimeter = Sequences.PythagoreanTriplets()
.TakeWhile(x => x.Item1 + x.Item2 + x.Item3 < 1000)
.ToLookup(x => x.Item1 + x.Item2 + x.Item3)
.Aggregate(Tuple.Create(0, 0), (maxes, perimeters) =>
perimeters.Count() > maxes.Item1 ? Tuple.Create(perimeters.Count(), perimeters.Key) : maxes);
return(maxPerimeter.Item2);
}
public string Solve()
{
var count = Sequences
.LongRange(1, 100)
.Select(n => Sequences
.LongRange(2, 100)
.Count(r => nCr(n, r) > 1000000))
.Sum();
return(count.ToString());
}
public string Solve()
{
var answer = Sequences.LongRange(1, int.MaxValue)
.First(n =>
{
var count = new[] { n, n + 1, n + 2, n + 3 }
.TakeWhile(x => Sequences.GetPrimeFactors(x).Distinct().Count() == 4)
.Count();
return(count == 4);
});
return(answer.ToString());
}
static Tuple <int, int, int> SolveAbcAddTo1000()
{
foreach (var triplet in Sequences.PythagoreanTriplets())
{
var a = triplet.Item1;
var b = triplet.Item2;
var c = triplet.Item3;
if (a + b + c == 1000)
{
return(new Tuple <int, int, int>(a, b, c));
}
if (a + b + c > 2000)
{
break;
}
}
return(null);
}
public static long GetGreatestCommonFactor(long a, long b)
{
var aPrimeFactors = Sequences.GetPrimeFactors(a).GroupBy(x => x).ToDictionary(x => x.Key, x => x.Count());
var bPrimeFactors = Sequences.GetPrimeFactors(b).GroupBy(x => x).ToDictionary(x => x.Key, x => x.Count());
// collect the factors between the two, similar to Problem005,
// except this time pool the shared minimums
var minCount = new Dictionary <long, int>();
foreach (var factor in aPrimeFactors.Concat(bPrimeFactors))
{
if (aPrimeFactors.ContainsKey(factor.Key) && bPrimeFactors.ContainsKey(factor.Key))
{
minCount[factor.Key] = minCount.ContainsKey(factor.Key)
? Math.Min(minCount[factor.Key], factor.Value)
: factor.Value;
}
}
return(minCount.Aggregate <KeyValuePair <long, int>, long>(
1, (current, factor) => current * (long)Math.Pow(factor.Key, factor.Value)));
}
static long CommonFactorCountSolve()
{
// find the common factors between the numbers 1 to 20
var factorCounts = Sequences.LongRange(1, 20).Select(n => Sequences.GetPrimeFactors(n).GroupBy(x => x).ToDictionary(g => g.Key, g => g.Count()));
// collect the maximum factor counts for each of the numbers;
// for instance, 16 is 2^4, so the 2 factors of 20 (2*2*5)
// are not necessary as they are already accounted for
var maxCount = new Dictionary <long, int>();
foreach (var factor in factorCounts.SelectMany(factorCount => factorCount))
{
maxCount[factor.Key] = maxCount.ContainsKey(factor.Key)
? Math.Max(maxCount[factor.Key], factor.Value)
: factor.Value;
}
// compute the smallest number that is divisible by all numbers from 1 to 20,
// ie, the number with the minimum number of factors shared by those numbers
return(maxCount.Aggregate <KeyValuePair <long, int>, long>(
1, (current, factor) => current * (long)Math.Pow(factor.Key, factor.Value)
));
}
public string Solve()
{
return(Sequences.TriangleNumbers().First(t => GetFactors(t).Count > 500).ToString());
}
public string Solve()
{
var answer = Sequences.BigFibonacci().Enumerate().First(t => t.Item2 > BigInteger.Pow(10, 999));
return(answer.Item1.ToString());
}
static int Solve(int maxFibValue)
{
return(Sequences.Fibonacci().Where(x => x % 2 == 0).TakeWhile(x => (x < maxFibValue)).Sum());
}
public static BigInteger Factorial(this long n)
{
return(n <= 1 ? 1 : Sequences.LongRange(1, n).Aggregate(new BigInteger(1), (acc, x) => acc * x));
}
public string Solve()
{
return(Sequences.DateTimeRange("1901-01-01T12:00:00", "2000-12-31T12:00:00", 60 * 60 * 24)
.Count(n => n.Day == 1 && n.DayOfWeek == DayOfWeek.Sunday).ToString());
}