/* calculate least common multiple
* http://www.math.com/school/subject1/lessons/S1U3L3DP.html
* basically, get the prime factors of each number in the set,
* and multiply them together. if a factor appears more than once,
* multiply it the max number of times it appears in a single factor
* example:
* find LCM of 3, 9, 21
* prime factors:
* 3: 3
* 9: 3 × 3
* 21: 3 × 7
* solution = 3 x 3 x 7 = 63
*/
public static int LCMOfRange(int lo, int hi)
{
int[] numbers = Enumerable.Range(lo, hi - lo + 1).ToArray();
long[] primes = OP.Primes(hi).ToArray();
Dictionary <int, int> factorsWithCounts = new Dictionary <int, int>(numbers.Length);
//TODO nonrepeatedFactors can be replaced by a running product (just use division instead of List.Remove())
foreach (int num in numbers)
{
//TODO THIS IS DAMN UGLY!!!
// REPLACE with single dictionary with counts. the 2-list thing is stupid
/*
* single dict, for each N do a simple key check for count=1,
*
*/
Dictionary <int, int> factors = OP.FactorToPrimes(num, primes).GroupBy(p => p).ToDictionary(k => (int)k.Key, v => v.Count());
foreach (var i in factors)
{
int factor = i.Key;
int count = i.Value;
if (factorsWithCounts.ContainsKey(factor))
{
if (count > factorsWithCounts[factor])
{
factorsWithCounts[factor] = count;
}
}
else
{
factorsWithCounts.Add(factor, count);
}
}
#if verbose
string foo = String.Format("Prime factor counts for {0}: {1}", num, String.Join(",", factors.Select(o => $"{o.Key} ({o.Value})")));
System.Diagnostics.Debug.WriteLine(foo);
#endif
}
#if verbose
string allFactorsDebug = Utilities.StringifyDict <int, int>(factorsWithCounts, "factorsWithCounts");
System.Diagnostics.Debug.WriteLine(allFactorsDebug);
#endif
int lcm = 1;
foreach (var kvp in factorsWithCounts)
{
lcm *= (int)kvp.Key.Pow(kvp.Value);
}
return(lcm);
}
public static long GetNthPrime(int n, int segmentSize = DEFAULT_SLICE_SIZE)
{
// http://www.thelowlyprogrammer.com/2012/08/primes-part-2-segmented-sieve.html
List <long> primes = new List <long>(n);
primes.AddRange(OP.Primes(segmentSize));
//do segmented sieve passes with ranges of DEFAULT_SLICE_SIZE length
//until our list of primes reaches N length.
int rangeStart = 1;
while (primes.Count() <= n)
{
rangeStart += segmentSize;
primes.AddRange(OP.RangeSieve(rangeStart, segmentSize, primes));
}
// remember to subtract 1 to get Nth from 0-based list
return(primes[n - 1]);
}
