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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Zumkeller-numbers/C-sharp/zumkeller-numbers.cs Normal file
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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 is odd can't be split into two partitions with equal sums
if (sum % 2 == 1) {
return false;
}
// if n is odd use 'abundant odd number' optimization
if (n % 2 == 1) {
var abundance = sum - 2 * n;
return abundance > 0 && abundance % 2 == 0;
}
// if n and sum are both even check if there's a partition which totals sum / 2
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();
}
}
}
}
}
}