public static long Solution()
{
long solution = 0;
for (long a = (long)Math.Ceiling(limit / 3.0); a < limit; a++)
{
for (long b = (long)Math.Ceiling((limit - a) / 2.0); b <= a; b++)
{
var c = limit - a - b;
var powerOfFive = UtilityFunctions.LargestPowerDividingFactorial(limit, 5)
- UtilityFunctions.LargestPowerDividingFactorial(a, 5)
- UtilityFunctions.LargestPowerDividingFactorial(b, 5)
- UtilityFunctions.LargestPowerDividingFactorial(c, 5);
var powerOfTwo = UtilityFunctions.LargestPowerDividingFactorial(limit, 2)
- UtilityFunctions.LargestPowerDividingFactorial(a, 2)
- UtilityFunctions.LargestPowerDividingFactorial(b, 2)
- UtilityFunctions.LargestPowerDividingFactorial(c, 2);
if (powerOfFive >= 12 && powerOfTwo >= 12)
{
solution += 6;
if (a == b || b == c)
{
solution -= 3;
if (a == b && b == c)
{
solution -= 2;
}
}
}
}
}
return(solution);
}
public static long Solution()
{
var stopwatch = new Stopwatch();
long solution = 0;
var primes = UtilityFunctions.Primes(limit);
var minima = new long[limit + 1];
minima[0] = 1;
foreach (var p in primes)
{
long primePower = p;
long exponent = 1;
while (primePower <= limit)
{
long upper = exponent;
long lower = 1;
while (upper - lower > 1)
{
long mid = (upper + lower) / 2;
if (UtilityFunctions.LargestPowerDividingFactorial(p * mid, p) < exponent)
{
lower = mid;
}
else
{
upper = mid;
}
}
minima[primePower] = (upper) * p;
stopwatch.Start();
for (long i = 1; i <= limit / primePower; i++)
{
minima[i * primePower] = Math.Max(minima[i], minima[primePower]);
}
stopwatch.Stop();
primePower *= p;
exponent += 1;
}
}
Console.WriteLine($"Populating table took {stopwatch.ElapsedMilliseconds}.");
for (long i = 1; i < limit; i++)
{
solution += minima[i + 1];
}
return(solution);
}