/*                        __    __  __  __    __  ___
 *                       \  \  /  /    \  \  /  /  __/
 *                        \  \/  /  /\  \  \/  /  /
 *                         \____/__/  \__\____/__/.ɪᴏ
 * ᶜᵒᵖʸʳᶦᵍʰᵗ ᵇʸ ᵛᵃᵛʳ ⁻ ˡᶦᶜᵉⁿˢᵉᵈ ᵘⁿᵈᵉʳ ᵗʰᵉ ᵃᵖᵃᶜʰᵉ ˡᶦᶜᵉⁿˢᵉ ᵛᵉʳˢᶦᵒⁿ ᵗʷᵒ ᵈᵒᵗ ᶻᵉʳᵒ
 */
package io.vavr.collection.euler;

import io.vavr.Tuple;
import io.vavr.collection.CharSeq;
import io.vavr.collection.List;
import io.vavr.collection.Stream;
import org.junit.Test;

import static org.assertj.core.api.Assertions.assertThat;

/**
 * <strong>Problem 30: Digit fifth powers</strong>
 * <p>
 * Surprisingly there are only three numbers that can be written as the sum of
 * fourth powers of their digits:
 * <pre>
 * 1634 = 1^4 + 6^4 + 3^4 + 4^4
 * 8208 = 8^4 + 2^4 + 0^4 + 8^4
 * 9474 = 9^4 + 4^4 + 7^4 + 4^4
 * </pre>
 *
 * As 1 = 1^4 is not a sum it is not included.
 * <p>
 * The sum of these numbers is 1634 + 8208 + 9474 = 19316.
 * <p>
 * Find the sum of all the numbers that can be written as the sum of fifth
 * powers of their digits.
 * <p>
 * See also
 * <a href="https://projecteuler.net/problem=30">projecteuler.net problem 30
 * </a>.
 */
public class Euler30Test {

    @Test
    public void shouldSolveProblem26() {
        assertThat(sumOfAllTheNumbersThatCanBeWrittenAsTheSumOfPowersOfTheirDigits(4)).isEqualTo(19316);
        assertThat(sumOfAllTheNumbersThatCanBeWrittenAsTheSumOfPowersOfTheirDigits(5)).isEqualTo(443_839);
    }

    private static long sumOfAllTheNumbersThatCanBeWrittenAsTheSumOfPowersOfTheirDigits(int powers) {
        return List.rangeClosed(10, maximalSumForPowers(powers))
                .filter(i -> sumOfPowersOfDigits(powers, i) == i)
                .sum().longValue();
    }

    private static long maximalSumForPowers(int powers) {
        return Stream.from(1)
                .map(i -> Tuple.of((long) Math.pow(10, i) - 1, List.fill(i, () -> Math.pow(9, powers)).sum().longValue()))
                .find(t -> t._1 > t._2)
                .map(t -> t._1).get();
    }

    private static long sumOfPowersOfDigits(int powers, long num) {
        return CharSeq.of(Long.toString(num))
                .map(c -> Character.digit(c, 10))
                .map(d -> (long) Math.pow(d, powers))
                .sum().longValue();
    }
}
