Dateien nach „BSP_1_F“ hochladen
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43
BSP_1_F/bsp_1_f.cbp
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43
BSP_1_F/bsp_1_f.cbp
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<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
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<CodeBlocks_project_file>
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<FileVersion major="1" minor="6" />
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<Project>
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<Option title="bsp_1_f" />
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<Option pch_mode="2" />
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<Option compiler="gcc" />
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<Build>
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<Target title="Debug">
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<Option output="bin/Debug/bsp_1_f" prefix_auto="1" extension_auto="1" />
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<Option object_output="obj/Debug/" />
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<Option type="1" />
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<Option compiler="gcc" />
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<Compiler>
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<Add option="-g" />
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</Compiler>
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</Target>
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<Target title="Release">
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<Option output="bin/Release/bsp_1_f" prefix_auto="1" extension_auto="1" />
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<Option object_output="obj/Release/" />
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<Option type="1" />
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<Option compiler="gcc" />
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<Compiler>
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<Add option="-O2" />
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</Compiler>
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<Linker>
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<Add option="-s" />
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</Linker>
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</Target>
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</Build>
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<Compiler>
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<Add option="-Wall" />
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<Add option="-fexceptions" />
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</Compiler>
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<Unit filename="bsp_1_f.cpp" />
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<Unit filename="bsp_1_f.h" />
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<Unit filename="main.cpp" />
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<Unit filename="mayer_primes.h" />
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<Extensions>
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<lib_finder disable_auto="1" />
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</Extensions>
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</Project>
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</CodeBlocks_project_file>
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44
BSP_1_F/bsp_1_f.cpp
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BSP_1_F/bsp_1_f.cpp
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#include "bsp_1_f.h"
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#include "mayer_primes.h"
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#include "algorithm"
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#include <iostream>
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using namespace std;
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int single_goldbach(const int &k)
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{
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vector<int> primes = get_primes(k);
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int amount = 0;
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for(size_t it = 0; primes[it]<=k/2.0; ++it) //für Primzahl größer als k/2 haben wir bereits Zerlegung gezählt: 3+7 = 7+3
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{
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for(size_t j = it; j<primes.size(); ++j)
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{
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if(primes[it] + primes[j] == k)
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{
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amount += 1;
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}
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}
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}
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return amount;
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}
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vector<int> count_goldbach(const int &n)
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{
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vector<int> count_vec((n-4)/2+1,0);
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vector<int> primes = get_primes(n);
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for(size_t k=0; k < primes.size() && primes[k]<=n/2; ++k)
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{
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for(size_t i=k; i<primes.size(); ++i)
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{
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int sum = primes[k] + primes[i];
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if(sum<=n)
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{
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count_vec[(sum-4)/2] += 1;
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}
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}
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}
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return count_vec;
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}
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21
BSP_1_F/bsp_1_f.h
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BSP_1_F/bsp_1_f.h
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#ifndef BSP_1_F_H_INCLUDED
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#define BSP_1_F_H_INCLUDED
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#include <vector>
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/** \brief Zaehlt fuer eine gegebene Zahl @k die Anzahl der moeglichen Zerlegungen als Summe zweier Primzahlen
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*
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* \param[in] k fuer diese Zahl wird die Anzahl der Zerlegungen berechnet
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* \return Anzahl der Zerlegungen
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*
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*/
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int single_goldbach(const int &k);
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/** \brief Zaehlt die Anzahl der Dekomposition für alle geraden Zahlen in [4,n]
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*
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* \param[in] n obere Intervallgrenze (in diesem Bereich werden die Dekompositionen berechnet
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* \return Vektor mit den Anzahl der Dekompositionen (ad Adressierung: x[0] = (n=4), x[1] = (n=6), x[2] = (n=8), Umrechnung *2 + 4
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*
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*/
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std::vector<int> count_goldbach(const int &n);
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#endif // BSP_1_F_H_INCLUDED
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31
BSP_1_F/main.cpp
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31
BSP_1_F/main.cpp
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#include "bsp_1_f.h"
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#include "mayer_primes.h"
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#include <iostream>
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#include <algorithm>
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#include <chrono>
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// BSP 1_F
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using namespace std;
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int main()
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{
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// Auswertung für n=100000 bzw herausfinden der Zahl, welche die meisten Dekompositionen hat
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vector<int> v = count_goldbach(1e5);
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auto ip = max_element(v.begin(), v.end());
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cout << "Zahl zwischen [4,1e5] mit meisten Zerlegungen" << endl;
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cout << "Zahl k " << distance(v.begin(), ip)*2+4 << " mit " << *ip << " Zerlegungen" << endl;
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cout << "Zeitmessungen" << endl;
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vector<int> nvec{static_cast<int>(1e4), static_cast<int>(1e5), static_cast<int>(4*1e5), static_cast<int>(1e6), static_cast<int>(2*1e6)}; // Vektor für n
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for(size_t k=0; k<nvec.size(); ++k)
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{
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auto timestart = chrono::system_clock::now();
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vector<int> vall = count_goldbach(nvec[k]);
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auto timeend = chrono::system_clock::now();
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auto time = chrono::duration_cast<chrono::milliseconds>(timeend - timestart);
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cout << "n = " << nvec[k] << " time: " << time.count() << " ms" << endl << endl;
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}
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// cout << single_goldbach(694) << endl;
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// cout << count_goldbach(10000)[690/2] << endl;
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return 0;
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}
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73
BSP_1_F/mayer_primes.h
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BSP_1_F/mayer_primes.h
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#pragma once
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#include <cstring> //memset
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#include <vector>
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//using namespace std;
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/** \brief Determines all prime numbers in interval [2, @p max].
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*
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* The sieve of Eratosthenes is used.
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*
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* The implementation originates from <a href="http://code.activestate.com/recipes/576559-fast-prime-generator/">Florian Mayer</a>.
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*
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* \param[in] max end of interval for the prime number search.
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* \return vector of prime numbers @f$2,3,5, ..., p<=max @f$.
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*
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* \copyright
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* Copyright (c) 2008 Florian Mayer (adapted by Gundolf Haase 2018)
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
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* INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*
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*/
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template <class T>
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std::vector<T> get_primes(T max)
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{
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std::vector<T> primes;
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char *sieve;
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sieve = new char[max / 8 + 1];
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// Fill sieve with 1
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memset(sieve, 0xFF, (max / 8 + 1) * sizeof(char));
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for (T x = 2; x <= max; x++)
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{
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if (sieve[x / 8] & (0x01 << (x % 8))) {
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primes.push_back(x);
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// Is prime. Mark multiplicates.
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for (T j = 2 * x; j <= max; j += x)
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{
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sieve[j / 8] &= ~(0x01 << (j % 8));
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}
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}
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}
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delete[] sieve;
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return primes;
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}
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//---------------------------------------------------------------
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//int main() // by Florian Mayer
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//{g++ -O3 -std=c++14 -fopenmp main.cpp && ./a.out
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// vector<unsigned long> primes;
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// primes = get_primes(10000000);
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// // return 0;
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// // Print out result.
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// vector<unsigned long>::iterator it;
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// for(it=primes.begin(); it < primes.end(); it++)
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// cout << *it << " ";
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//
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// cout << endl;
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// return 0;
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//}
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