Create euler87.cpp

C++-Version mit optimiertem Sieb.

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;
+}