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CountSemiprimes.cs
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CountSemiprimes.cs
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
public class Solution
{
public static void Main(string[] args)
{
solution(26, new[] { 1, 4, 16 }, new[] { 26, 10, 20 });
}
public static int[] solution(int N, int[] P, int[] Q)
{
var sieveInput = Enumerable.Repeat(true, N + 1).ToArray();
var nSqrt = Math.Sqrt(N);
// perform sieve
sieveInput[0] = false; sieveInput[1] = false;
for (int i = 2; i < nSqrt; i++)
{
if (sieveInput[i])
{
int j = i * i;
while (j <= N)
{
sieveInput[j] = false;
j += i;
}
}
}
// get array of primes
var primes = new List<int>();
for (int i = 0; i < sieveInput.Length; i++)
{
if (sieveInput[i])
{
primes.Add(i);
}
}
// calculate semiprimes
var semiPrimes = new int[N + 1];
for (int i = 0; i <= nSqrt; i++)
{
for (int j = i; j < primes.Count(); j++)
{
var semiPrime = primes[i] * primes[j];
if (semiPrime > N)
{
break;
}
semiPrimes[semiPrime] = 1;
}
}
// calculate prefix sums
var semiPrimesCount = new int[N + 1];
for (int i = 1; i < semiPrimesCount.Length; i++)
{
semiPrimesCount[i] = semiPrimesCount[i - 1] + semiPrimes[i];
}
//obtain result
var result = new List<int>();
for (int i = 0; i < P.Length; i++)
{
result.Add(semiPrimesCount[Q[i]] - semiPrimesCount[P[i] - 1]);
}
return result.ToArray();
}
}