Task: Zumkeller numbers





Java: import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

public class ZumkellerNumbers {

    public static void main(String[] args) {
        int n = 1;
        System.out.printf("First 220 Zumkeller numbers:%n");
        for ( int count = 1 ; count <= 220 ; n += 1 ) {
            if ( isZumkeller(n) ) {
                System.out.printf("%3d  ", n);
                if ( count % 20 == 0 ) {
                    System.out.printf("%n");
                }
                count++;
            }
        }
        
        n = 1;
        System.out.printf("%nFirst 40 odd Zumkeller numbers:%n");
        for ( int count = 1 ; count <= 40 ; n += 2 ) {
            if ( isZumkeller(n) ) {
                System.out.printf("%6d", n);
                if ( count % 10 == 0 ) {
                    System.out.printf("%n");
                }
                count++;
            }
        }
        
        n = 1;
        System.out.printf("%nFirst 40 odd Zumkeller numbers that do not end in a 5:%n");
        for ( int count = 1 ; count <= 40 ; n += 2 ) {
            if ( n % 5 != 0 && isZumkeller(n) ) {
                System.out.printf("%8d", n);
                if ( count % 10 == 0 ) {
                    System.out.printf("%n");
                }
                count++;
            }
        }

    }
    
    private static boolean isZumkeller(int n) {
        
        if ( n % 18 == 6 || n % 18 == 12 ) {
            return true;
        }
        
        List<Integer> divisors = getDivisors(n);        
        int divisorSum = divisors.stream().mapToInt(i -> i.intValue()).sum();
        
        
        if ( divisorSum % 2 == 1 ) {
            return false;
        }
        
        
        int abundance = divisorSum - 2 * n;
        if ( n % 2 == 1 && abundance > 0 && abundance % 2 == 0 ) {
            return true;
        }
        
        Collections.sort(divisors);
        int j = divisors.size() - 1;
        int sum = divisorSum/2;
        
        
        if ( divisors.get(j) > sum ) {
            return false;
        }
        
        return canPartition(j, divisors, sum, new int[2]);
    }
    
    private static boolean canPartition(int j, List<Integer> divisors, int sum, int[] buckets) {
        if ( j < 0 ) {
            return true;
        }
        for ( int i = 0 ; i < 2 ; i++ ) {
            if ( buckets[i] + divisors.get(j) <= sum ) {
                buckets[i] += divisors.get(j);
                if ( canPartition(j-1, divisors, sum, buckets) ) {
                    return true;
                }
                buckets[i] -= divisors.get(j);
            }
            if( buckets[i] == 0 ) {
                break;
            }
        }
        return false;
    }
    
    private static final List<Integer> getDivisors(int number) {
        List<Integer> divisors = new ArrayList<Integer>();
        long sqrt = (long) Math.sqrt(number);
        for ( int i = 1 ; i <= sqrt ; i++ ) {
            if ( number % i == 0 ) {
                divisors.add(i);
                int div = number / i;
                if ( div != i ) {
                    divisors.add(div);
                }
            }
        }
        return divisors;
    }

}




VB: Module Module1
    Function GetDivisors(n As Integer) As List(Of Integer)
        Dim divs As New List(Of Integer) From {
            1, n
        }
        Dim i = 2
        While i * i <= n
            If n Mod i = 0 Then
                Dim j = n \ i
                divs.Add(i)
                If i <> j Then
                    divs.Add(j)
                End If
            End If
            i += 1
        End While
        Return divs
    End Function

    Function IsPartSum(divs As List(Of Integer), sum As Integer) As Boolean
        If sum = 0 Then
            Return True
        End If
        Dim le = divs.Count
        If le = 0 Then
            Return False
        End If
        Dim last = divs(le - 1)
        Dim newDivs As New List(Of Integer)
        For i = 1 To le - 1
            newDivs.Add(divs(i - 1))
        Next
        If last > sum Then
            Return IsPartSum(newDivs, sum)
        End If
        Return IsPartSum(newDivs, sum) OrElse IsPartSum(newDivs, sum - last)
    End Function

    Function IsZumkeller(n As Integer) As Boolean
        Dim divs = GetDivisors(n)
        Dim sum = divs.Sum()
        REM if sum is odd can
        If sum Mod 2 = 1 Then
            Return False
        End If
        REM if n is odd use 
        If n Mod 2 = 1 Then
            Dim abundance = sum - 2 * n
            Return abundance > 0 AndAlso abundance Mod 2 = 0
        End If
        REM if n and sum are both even check if there
        Return IsPartSum(divs, sum \ 2)
    End Function

    Sub Main()
        Console.WriteLine("The first 220 Zumkeller numbers are:")
        Dim i = 2
        Dim count = 0
        While count < 220
            If IsZumkeller(i) Then
                Console.Write("{0,3} ", i)
                count += 1
                If count Mod 20 = 0 Then
                    Console.WriteLine()
                End If
            End If
            i += 1
        End While
        Console.WriteLine()

        Console.WriteLine("The first 40 odd Zumkeller numbers are:")
        i = 3
        count = 0
        While count < 40
            If IsZumkeller(i) Then
                Console.Write("{0,5} ", i)
                count += 1
                If count Mod 10 = 0 Then
                    Console.WriteLine()
                End If
            End If
            i += 2
        End While
        Console.WriteLine()

        Console.WriteLine("The first 40 odd Zumkeller numbers which don
        i = 3
        count = 0
        While count < 40
            If i Mod 10 <> 5 AndAlso IsZumkeller(i) Then
                Console.Write("{0,7} ", i)
                count += 1
                If count Mod 8 = 0 Then
                    Console.WriteLine()
                End If
            End If
            i += 2
        End While
    End Sub
End Module