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