contests/projecteuler/060/main.cpp

/*
The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property.

Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime.
*/

#include <iostream>
#include <chrono>
#include <vector>
#include <unordered_set>
#include <cmath>

using namespace std;

vector<unsigned int> sieve(int n){
    if(n < 2) return vector<unsigned int>();

    vector<bool> ns(n, true);

    for(int i = 2; i <= sqrt(n); ++i){
        if(ns[i]){
            int j = pow(i, 2);

            while(j < n){
                ns[j] = false;
                j += i;
            }
        }
    }

    vector<unsigned int> primes;

    for(size_t i = 2; i < ns.size(); ++i){
        if(ns[i]) primes.push_back(i);
    }

    return primes;
}

// Wheel factorization primality test
bool isPrime(const unsigned long long n){
    if(n % 2 == 0 || n % 3 == 0 || n % 5 == 0){
        return n == 2 || n == 3 || n == 5;
    }

    const unsigned int delta[] = {6, 4, 2, 4, 2, 4, 6, 2};
    unsigned long long i = 7;
    int pos = 1;

    while(i*i <= n){
        if(n % i == 0){
            return false;
        }
        i += delta[pos];
        pos = (pos + 1) & 7;
    }
    return n > 1;
}

int intLength(const unsigned long long n){
    return trunc(log10(n)) + 1;
}

unsigned long long combine(const unsigned long long n, const unsigned long long m){
    unsigned long long res = n;
    int mLength = intLength(m);

    res *= pow(10, mLength);
    res += m;

    return res;
}

bool match(unsigned long long n, unsigned long long m){
    return isPrime(combine(n, m)) && isPrime(combine(m, n));
}



// Assume that the size of all unordered sets is equal, otherwise this doesn't work
// WARNING: this is not an efficient function and it might even be bugged
vector<unordered_set<unsigned int>> aPriori(const vector<unordered_set<unsigned int>> & primePairs, const unordered_set<unsigned int> & primes){
    if(primePairs.empty()) return vector<unordered_set<unsigned int>>();

    int setSize = primePairs[0].size();
    vector<unordered_set<unsigned int>> result;

    for(size_t i = 0; i < primePairs.size(); ++i){
        for(size_t j = min(i + 1, primePairs.size() - 1); j < primePairs.size(); ++j){
            unordered_set<unsigned int> combinationSet(primePairs[i]);

            for(int k : primePairs[j]){
                combinationSet.insert(k);
            }

            if(combinationSet.size() == setSize + 1){
                bool allPrimes = true;

                for(auto it = combinationSet.begin(); it != combinationSet.end(); ++it){
                    for(auto jt = combinationSet.begin(); jt != combinationSet.end(); ++jt){
                        if(it != jt){
                            int p1 = combine(*it, *jt), p2 = combine(*jt, *it);

                            if(primes.find(p1) == primes.end() || primes.find(p2) == primes.end()){
                                allPrimes = false;
                                break;
                            }
                        }
                    }
                }

                if(allPrimes) result.push_back(combinationSet);
            }
        }
    }

    return result;
}

int main(){
    std::cout << "Hello this is Patrick" << endl;
    auto start = chrono::high_resolution_clock::now();

    auto primeVector = sieve(10000);
    // unordered_set<unsigned int> primes(primeVector.begin(), primeVector.end());
    bool foundSum = false;

    for(auto it = primeVector.begin(); it != primeVector.end(); ++it){
        if(foundSum) break;

        vector<int> candidateDoubles(it + 1, primeVector.end());

        for(auto jt = candidateDoubles.begin(); jt != candidateDoubles.end(); ++jt){
            if(foundSum) break;

            if(match(*it, *jt)){
                vector<int> candidateTriples(jt + 1, candidateDoubles.end());

                for(auto kt = candidateTriples.begin(); kt != candidateTriples.end(); ++kt){
                    if(foundSum) break;

                    if(match(*it, *kt) && match(*jt, *kt)){
                        vector<int> candidateQuartets(kt + 1, candidateTriples.end());

                        for(auto lt = candidateQuartets.begin(); lt != candidateQuartets.end(); ++lt){
                            if(foundSum) break;

                            if(match(*it, *lt) && match(*jt, *lt) && match(*kt, *lt)){
                                vector<int> candidateQuintets(lt + 1, candidateQuartets.end());

                                for(auto mt = candidateQuintets.begin(); mt != candidateQuintets.end(); ++mt){
                                    if(match(*it, *mt) && match(*jt, *mt) && match(*kt, *mt) && match(*lt, *mt)){
                                        std::cout << *it << " " << *jt << " " << *kt << " " << *lt << " " << *mt << " equals: " << *it + *jt + *kt + *lt + *mt << endl;

                                        foundSum = true;
                                        break;
                                    }
                                }

                                // For checking the result of four
                                // cout << *it << " " << *jt << " " << *kt << " " << *lt << endl;
                            }
                        }
                    }
                }
            }
        }
    }

    auto duration = chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - start);
    std::cout << (float)duration.count()/1000 << endl;

    return 0;
}