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project-euler/87/euler87.cpp

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// C++-Lösung auf der Basis der C-Variante von Jörg Sommer
// Beinhaltet verbessertes Primzahlsieb
#include <cmath>
#include <cstdlib>
#include <vector>
#include <iostream>
#include <algorithm>
/**
prime: Vektor zum Speichern der Primzahlen
limit: Obere Grenze des Bereichs in dem berechnet wird
Implementiert eine optimierte Version des Sieb des Eratosthenes.
Prüft nicht, ob die Grenze kleiner als 5 ist.
*/
static void sieve(std::vector<unsigned>& prime, unsigned const limit) {
prime.push_back(2u);
prime.push_back(3u);
for (unsigned num = 5; num <= limit; num += 2) {
unsigned sqrtnum = (unsigned) std::sqrt(num);
bool isPrime = true;
for (auto primeIt = ++prime.begin(); primeIt != prime.end() && *primeIt <= sqrtnum; ++primeIt) {
if (num % *primeIt == 0) {
isPrime = false;
break;
}
}
if (isPrime) {
prime.push_back(num);
}
}
}
int main(void) {
constexpr unsigned LIMIT = 50000000;
constexpr unsigned PRIMELIMIT = (unsigned) std::sqrt(LIMIT);
std::vector<unsigned> primes;
primes.reserve(PRIMELIMIT / std::log(PRIMELIMIT)); // schätze Primzahldichte
sieve(primes, PRIMELIMIT);
std::cout << "Es wurden " << primes.size() << " Primzahlen gefunden" << std::endl;
std::vector<unsigned> numbers;
for (auto p4 = primes.begin(); p4 != primes.end(); ++p4) {
unsigned pow4 = *p4 * *p4;
pow4 *= pow4;
if (pow4 >= LIMIT)
break;
for (auto p3 = primes.begin(); p3 != primes.end(); ++p3) {
unsigned sum = pow4 + *p3 * *p3 * *p3;
if (sum >= LIMIT)
break;
for (auto p2 = primes.begin(); p2 != primes.end(); ++p2) {
unsigned pow2 = *p2 * *p2;
unsigned sum2 = sum + pow2;
if (sum2 >= LIMIT) {
break;
}
numbers.push_back(sum2);
}
}
}
//Zähle vorkommende Elemente
unsigned count = 1;
std::sort(numbers.begin(), numbers.end());
for (auto n = ++numbers.begin(); n != numbers.end(); ++n) {
if (*(n - 1) != *n) {
++count;
}
}
std::cout << "Ergebnis: " << count << std::endl;
return EXIT_SUCCESS;
}