using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Algorithms.Numeric
{
    /// <summary>
    /// Amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of
    /// each is equal to the other number. That is, σ(a)=b+a and σ(b)=a+b, where σ(n) is equal to the sum of positive divisors of n (see also divisor function).
    /// See <a href="https://en.wikipedia.org/wiki/Amicable_numbers">here</a> for more info.
    /// </summary>
    public static class AmicableNumbersChecker
    {
        /// <summary>
        /// Checks if two numbers are amicable or not.
        /// </summary>
        /// <param name="x">First number to check.</param>
        /// <param name="y">Second number to check.</param>
        /// <returns>True if they are amicable numbers. False if not.</returns>
        public static bool AreAmicableNumbers(int x, int y)
        {
            return SumOfDivisors(x) == y && SumOfDivisors(y) == x;
        }

        private static int SumOfDivisors(int number)
        {
            var sum = 0; /* sum of its positive divisors */
            for (var i = 1; i < number; ++i)
            {
                if (number % i == 0)
                {
                    sum += i;
                }
            }

            return sum;
        }
    }
}