Solutions

sheet1/F/main.cpp

@@ -0,0 +1,130 @@
+#include <iostream>
+#include "mayer_primes.h"
+#include <vector>
+#include <algorithm>
+#include "timing.h"
+using namespace std;
+
+unsigned int single_goldbach(unsigned int k)
+{
+    unsigned int decomp = 0;
+    unsigned int p,q;
+    vector<unsigned int> primes = get_primes(k);
+    for(unsigned i=0; i< primes.size(); i++)
+    {
+        p = primes.at(i);
+        if(p > k/2)
+        {
+            break;
+        }
+        
+        q = k-p;
+        vector<unsigned int>::iterator it = lower_bound(primes.begin(), primes.end(), q);
+        if (it != primes.end() && *it == q)
+        {
+            decomp++;
+        }
+
+    }
+
+    return decomp;
+}
+
+//one can call single_goldbach but this way it is faster cause you dont have to regenerate primes and search in list
+vector<unsigned int> count_goldbach(unsigned int n)
+{
+     vector<unsigned int> counts(n+1,0); 
+     unsigned int p,q;
+     vector<unsigned int> primes = get_primes(n);
+     for(unsigned int j=0; j<primes.size(); j++)
+     {
+         for(unsigned i=j; i< primes.size(); i++) //start a j elsewise double counting of pairs
+        {
+           p = primes.at(j);
+           q = primes.at(i);
+
+           if(p+q > n)
+           {
+            continue;
+           }
+           counts[p+q] += 1;
+
+        }
+     }
+     return counts;
+}
+
+vector<vector<vector<unsigned int>>> count_goldbach_all(unsigned int n)
+{
+     vector<vector<vector<unsigned int>>> counts(n+1,{{0,0}}); 
+     unsigned int p,q;
+     vector<unsigned int> primes = get_primes(n);
+     for(unsigned int j=0; j<primes.size(); j++)
+     {
+         for(unsigned i=j; i< primes.size(); i++)
+        {
+           p = primes.at(j);
+           q = primes.at(i);
+
+           if(p+q > n)
+           {
+            continue;
+           }
+           if (counts[p+q].at(0).at(0) == 0) //first pair found
+           {
+            counts[p+q]={{p,q}};
+           }
+           else{
+            counts[p+q].push_back({p,q});
+           }
+
+        }
+     }
+     return counts;
+}
+
+int main()
+{   
+
+    //2
+    cout << single_goldbach(694) << endl;
+
+    //3
+    vector<unsigned int> counts = count_goldbach(100000);
+    cout << (max_element(counts.begin(), counts.end()) - counts.begin()) << endl; 
+
+    //4
+    vector<unsigned int> nvalues = {10000, 100000, 400000, 1000000, 2000000, 10000000};
+    double time;
+    unsigned int n;
+    for(unsigned int i = 0; i< nvalues.size(); i++)
+    {
+        n = nvalues.at(i);
+        tic();
+        count_goldbach(n);
+        time = toc();
+        cout << "Time for n=" << n << ": " << time << endl;
+    }
+    /*Time for n=10000: 0.0006853
+    Time for n=100000: 0.0371858
+    Time for n=400000: 0.505129
+    Time for n=1000000: 2.85873
+    Time for n=2000000: 15.0026
+    Time for n=10000000: 549.658*/
+
+
+    //*)
+    unsigned int n2 = 694;
+    vector<vector<vector<unsigned int>>> counts2 = count_goldbach_all(n2);
+    for(unsigned int i=4; i<n2; i+=2)
+    {
+        cout << "Decomp for " << i << ":"<<endl;
+        for(unsigned int j=0; j<counts2.at(i).size(); j++)
+        {
+            //cout << counts2.at(i).at(j).at(0) << "+" << counts2.at(i).at(j).at(1) << "=" << i << endl;
+        }
+    }
+
+
+    return 0;
+}