Dateien nach „BSP_1_F“ hochladen

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Georg Thomas Mandl 2025-10-22 23:12:23 +02:00
commit 40e2b29d95
5 changed files with 212 additions and 0 deletions

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BSP_1_F/bsp_1_f.cbp Normal file
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<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
<CodeBlocks_project_file>
<FileVersion major="1" minor="6" />
<Project>
<Option title="bsp_1_f" />
<Option pch_mode="2" />
<Option compiler="gcc" />
<Build>
<Target title="Debug">
<Option output="bin/Debug/bsp_1_f" prefix_auto="1" extension_auto="1" />
<Option object_output="obj/Debug/" />
<Option type="1" />
<Option compiler="gcc" />
<Compiler>
<Add option="-g" />
</Compiler>
</Target>
<Target title="Release">
<Option output="bin/Release/bsp_1_f" prefix_auto="1" extension_auto="1" />
<Option object_output="obj/Release/" />
<Option type="1" />
<Option compiler="gcc" />
<Compiler>
<Add option="-O2" />
</Compiler>
<Linker>
<Add option="-s" />
</Linker>
</Target>
</Build>
<Compiler>
<Add option="-Wall" />
<Add option="-fexceptions" />
</Compiler>
<Unit filename="bsp_1_f.cpp" />
<Unit filename="bsp_1_f.h" />
<Unit filename="main.cpp" />
<Unit filename="mayer_primes.h" />
<Extensions>
<lib_finder disable_auto="1" />
</Extensions>
</Project>
</CodeBlocks_project_file>

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BSP_1_F/bsp_1_f.cpp Normal file
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#include "bsp_1_f.h"
#include "mayer_primes.h"
#include "algorithm"
#include <iostream>
using namespace std;
int single_goldbach(const int &k)
{
vector<int> primes = get_primes(k);
int amount = 0;
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
{
for(size_t j = it; j<primes.size(); ++j)
{
if(primes[it] + primes[j] == k)
{
amount += 1;
}
}
}
return amount;
}
vector<int> count_goldbach(const int &n)
{
vector<int> count_vec((n-4)/2+1,0);
vector<int> primes = get_primes(n);
for(size_t k=0; k < primes.size() && primes[k]<=n/2; ++k)
{
for(size_t i=k; i<primes.size(); ++i)
{
int sum = primes[k] + primes[i];
if(sum<=n)
{
count_vec[(sum-4)/2] += 1;
}
}
}
return count_vec;
}

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BSP_1_F/bsp_1_f.h Normal file
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#ifndef BSP_1_F_H_INCLUDED
#define BSP_1_F_H_INCLUDED
#include <vector>
/** \brief Zaehlt fuer eine gegebene Zahl @k die Anzahl der moeglichen Zerlegungen als Summe zweier Primzahlen
*
* \param[in] k fuer diese Zahl wird die Anzahl der Zerlegungen berechnet
* \return Anzahl der Zerlegungen
*
*/
int single_goldbach(const int &k);
/** \brief Zaehlt die Anzahl der Dekomposition für alle geraden Zahlen in [4,n]
*
* \param[in] n obere Intervallgrenze (in diesem Bereich werden die Dekompositionen berechnet
* \return Vektor mit den Anzahl der Dekompositionen (ad Adressierung: x[0] = (n=4), x[1] = (n=6), x[2] = (n=8), Umrechnung *2 + 4
*
*/
std::vector<int> count_goldbach(const int &n);
#endif // BSP_1_F_H_INCLUDED

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BSP_1_F/main.cpp Normal file
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#include "bsp_1_f.h"
#include "mayer_primes.h"
#include <iostream>
#include <algorithm>
#include <chrono>
// BSP 1_F
using namespace std;
int main()
{
// Auswertung für n=100000 bzw herausfinden der Zahl, welche die meisten Dekompositionen hat
vector<int> v = count_goldbach(1e5);
auto ip = max_element(v.begin(), v.end());
cout << "Zahl zwischen [4,1e5] mit meisten Zerlegungen" << endl;
cout << "Zahl k " << distance(v.begin(), ip)*2+4 << " mit " << *ip << " Zerlegungen" << endl;
cout << "Zeitmessungen" << endl;
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
for(size_t k=0; k<nvec.size(); ++k)
{
auto timestart = chrono::system_clock::now();
vector<int> vall = count_goldbach(nvec[k]);
auto timeend = chrono::system_clock::now();
auto time = chrono::duration_cast<chrono::milliseconds>(timeend - timestart);
cout << "n = " << nvec[k] << " time: " << time.count() << " ms" << endl << endl;
}
// cout << single_goldbach(694) << endl;
// cout << count_goldbach(10000)[690/2] << endl;
return 0;
}

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BSP_1_F/mayer_primes.h Normal file
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#pragma once
#include <cstring> //memset
#include <vector>
//using namespace std;
/** \brief Determines all prime numbers in interval [2, @p max].
*
* The sieve of Eratosthenes is used.
*
* The implementation originates from <a href="http://code.activestate.com/recipes/576559-fast-prime-generator/">Florian Mayer</a>.
*
* \param[in] max end of interval for the prime number search.
* \return vector of prime numbers @f$2,3,5, ..., p<=max @f$.
*
* \copyright
* Copyright (c) 2008 Florian Mayer (adapted by Gundolf Haase 2018)
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
* INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
template <class T>
std::vector<T> get_primes(T max)
{
std::vector<T> primes;
char *sieve;
sieve = new char[max / 8 + 1];
// Fill sieve with 1
memset(sieve, 0xFF, (max / 8 + 1) * sizeof(char));
for (T x = 2; x <= max; x++)
{
if (sieve[x / 8] & (0x01 << (x % 8))) {
primes.push_back(x);
// Is prime. Mark multiplicates.
for (T j = 2 * x; j <= max; j += x)
{
sieve[j / 8] &= ~(0x01 << (j % 8));
}
}
}
delete[] sieve;
return primes;
}
//---------------------------------------------------------------
//int main() // by Florian Mayer
//{g++ -O3 -std=c++14 -fopenmp main.cpp && ./a.out
// vector<unsigned long> primes;
// primes = get_primes(10000000);
// // return 0;
// // Print out result.
// vector<unsigned long>::iterator it;
// for(it=primes.begin(); it < primes.end(); it++)
// cout << *it << " ";
//
// cout << endl;
// return 0;
//}