package dev.mikeburgess.euler.problems

import dev.mikeburgess.euler.common.properDivisors

/**
 * Problem 21
 *
 * Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly
 * into n).
 *
 * If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are
 * called amicable numbers.
 *
 * For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110;
 * therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
 *
 * Evaluate the sum of all the amicable numbers under 10000.
 */
class Problem021 : Problem {

    override fun solve(): Long {
        val sums = (1..9999).associateWith { it.properDivisors.sum() }
        return sums.filter { (a, b) -> a != b }
            .mapValues { (_, b) -> sums[b] }
            .filter { (a, b) -> a == b }
            .keys.sum().toLong()
    }
}
