Task: Zumkeller numbers


C++: #include <iostream">
#include <cmath>
#include <vector>
#include <algorithm>
#include <iomanip>
#include <numeric>

using namespace std;


const uint* binary(uint n, uint length);



uint sum_subset_unrank_bin(const vector<uint>& d, uint r);

vector<uint> factors(uint x);

bool isPrime(uint number);

bool isZum(uint n);

ostream& operator<<(ostream& os, const vector<uint>& zumz) {
    for (uint i = 0; i < zumz.size(); i++) {
        if (i % 10 == 0)
            os << endl;
        os << setw(10) << zumz[i] << ' ';
    }
    return os;
}

int main() {
    cout << "First 220 Zumkeller numbers:" << endl;
    vector<uint> zumz;
    for (uint n = 2; zumz.size() < 220; n++)
        if (isZum(n))
            zumz.push_back(n);
    cout << zumz << endl << endl;

    cout << "First 40 odd Zumkeller numbers:" << endl;
    vector<uint> zumz2;
    for (uint n = 2; zumz2.size() < 40; n++)
        if (n % 2 && isZum(n))
            zumz2.push_back(n);
    cout << zumz2 << endl << endl;

    cout << "First 40 odd Zumkeller numbers not ending in 5:" << endl;
    vector<uint> zumz3;
    for (uint n = 2; zumz3.size() < 40; n++)
        if (n % 2 && (n % 10) !=  5 && isZum(n))
            zumz3.push_back(n);
    cout << zumz3 << endl << endl;

    return 0;
}


const uint* binary(uint n, uint length) {
    uint* bin = new uint[length];	    
    fill(bin, bin + length, 0);         
    
    for (uint i = 0; n > 0; i++) {
        uint rem = n % 2;
        n /= 2;
        if (rem)
            bin[length - 1 - i] = 1;
    }

    return bin;
}



uint sum_subset_unrank_bin(const vector<uint>& d, uint r) {
    vector<uint> subset;
    
    const uint* bits = binary(r, d.size() - 1);

    
    for (uint i = 0; i < d.size() - 1; i++)
        if (bits[i])
            subset.push_back(d[i]);

    delete[] bits;

    return accumulate(subset.begin(), subset.end(), 0u);
}

vector<uint> factors(uint x) {
    vector<uint> result;
    
    for (uint i = 1; i * i <= x; i++) {
        
        if (x % i == 0) {
            result.push_back(i);

            if (x / i != i)
                result.push_back(x / i);
        }
    }

    
    sort(result.begin(), result.end());
    return result;
}

bool isPrime(uint number) {
    if (number < 2) return false;
    if (number == 2) return true;
    if (number % 2 == 0) return false;
    for (uint i = 3; i * i <= number; i += 2)
        if (number % i == 0) return false;

    return true;
}

bool isZum(uint n) {
    
    if (isPrime(n))
        return false;

    
    const auto d = factors(n);
    uint s = accumulate(d.begin(), d.end(), 0u);

    
    if (s % 2 || s < 2 * n)
        return false;

    
    
    
    if (n % 2 || d.size() >= 24)
        return true;

    if (!(s % 2) && d[d.size() - 1] <= s / 2)
        for (uint x = 2; (uint) log2(x) < (d.size() - 1); x++) 
            if (sum_subset_unrank_bin(d, x) == s / 2)
                return true; 

    
    return false;
}


C#: using System;
using System.Collections.Generic;
using System.Linq;

namespace ZumkellerNumbers {
    class Program {
        static List<int> GetDivisors(int n) {
            List<int> divs = new List<int> {
                1, n
            };
            for (int i = 2; i * i <= n; i++) {
                if (n % i == 0) {
                    int j = n / i;
                    divs.Add(i);
                    if (i != j) {
                        divs.Add(j);
                    }
                }
            }
            return divs;
        }

        static bool IsPartSum(List<int> divs, int sum) {
            if (sum == 0) {
                return true;
            }
            var le = divs.Count;
            if (le == 0) {
                return false;
            }
            var last = divs[le - 1];
            List<int> newDivs = new List<int>();
            for (int i = 0; i < le - 1; i++) {
                newDivs.Add(divs[i]);
            }
            if (last > sum) {
                return IsPartSum(newDivs, sum);
            }
            return IsPartSum(newDivs, sum) || IsPartSum(newDivs, sum - last);
        }

        static bool IsZumkeller(int n) {
            var divs = GetDivisors(n);
            var sum = divs.Sum();
            
            if (sum % 2 == 1) {
                return false;
            }
            
            if (n % 2 == 1) {
                var abundance = sum - 2 * n;
                return abundance > 0 && abundance % 2 == 0;
            }
            
            return IsPartSum(divs, sum / 2);
        }

        static void Main() {
            Console.WriteLine("The first 220 Zumkeller numbers are:");
            int i = 2;
            for (int count = 0; count < 220; i++) {
                if (IsZumkeller(i)) {
                    Console.Write("{0,3} ", i);
                    count++;
                    if (count % 20 == 0) {
                        Console.WriteLine();
                    }
                }
            }

            Console.WriteLine("\nThe first 40 odd Zumkeller numbers are:");
            i = 3;
            for (int count = 0; count < 40; i += 2) {
                if (IsZumkeller(i)) {
                    Console.Write("{0,5} ", i);
                    count++;
                    if (count % 10 == 0) {
                        Console.WriteLine();
                    }
                }
            }

            Console.WriteLine("\nThe first 40 odd Zumkeller numbers which don't end in 5 are:");
            i = 3;
            for (int count = 0; count < 40; i += 2) {
                if (i % 10 != 5 && IsZumkeller(i)) {
                    Console.Write("{0,7} ", i);
                    count++;
                    if (count % 8 == 0) {
                        Console.WriteLine();
                    }
                }
            }
        }
    }
}