Task: Zumkeller numbers




Go: package main

import "fmt"

func getDivisors(n int) []int {
    divs := []int{1, n}
    for i := 2; i*i <= n; i++ {
        if n%i == 0 {
            j := n / i
            divs = append(divs, i)
            if i != j {
                divs = append(divs, j)
            }
        }
    }
    return divs
}

func sum(divs []int) int {
    sum := 0
    for _, div := range divs {
        sum += div
    }
    return sum
}

func isPartSum(divs []int, sum int) bool {
    if sum == 0 {
        return true
    }
    le := len(divs)
    if le == 0 {
        return false
    }
    last := divs[le-1]
    divs = divs[0 : le-1]
    if last > sum {
        return isPartSum(divs, sum)
    }
    return isPartSum(divs, sum) || isPartSum(divs, sum-last)
}

func isZumkeller(n int) bool {
    divs := getDivisors(n)
    sum := sum(divs)
    
    if sum%2 == 1 {
        return false
    }
    
    if n%2 == 1 {
        abundance := sum - 2*n
        return abundance > 0 && abundance%2 == 0
    }
    
    return isPartSum(divs, sum/2)
}

func main() {
    fmt.Println("The first 220 Zumkeller numbers are:")
    for i, count := 2, 0; count < 220; i++ {
        if isZumkeller(i) {
            fmt.Printf("%3d ", i)
            count++
            if count%20 == 0 {
                fmt.Println()
            }
        }
    }
    fmt.Println("\nThe first 40 odd Zumkeller numbers are:")
    for i, count := 3, 0; count < 40; i += 2 {
        if isZumkeller(i) {
            fmt.Printf("%5d ", i)
            count++
            if count%10 == 0 {
                fmt.Println()
            }
        }
    }
    fmt.Println("\nThe first 40 odd Zumkeller numbers which don't end in 5 are:")
    for i, count := 3, 0; count < 40; i += 2 {
        if (i % 10 != 5) && isZumkeller(i) {
            fmt.Printf("%7d ", i)
            count++
            if count%8 == 0 {
                fmt.Println()
            }
        }
    }
    fmt.Println()
}


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;
    }

}