/*                        __    __  __  __    __  ___
 *                       \  \  /  /    \  \  /  /  __/
 *                        \  \/  /  /\  \  \/  /  /
 *                         \____/__/  \__\____/__/.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.Stream;
import io.vavr.Tuple2;
import org.junit.Test;

import java.math.BigDecimal;

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

public class Euler57Test {

    /**
     * <strong>Problem 57: Square root convergents</strong>
     * <p>
     * It is possible to show that the square root of two can be expressed as an infinite continued fraction.
     * <p>
     * √ 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...
     * <p>
     * By expanding this for the first four iterations, we get:
     * <ul>
     * <li>1 + 1/2 = 3/2 = 1.5</li>
     * <li>1 + 1/(2 + 1/2) = 7/5 = 1.4</li>
     * <li>1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...</li>
     * <li>1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...</li>
     * </ul>
     * The next three expansions are 99/70, 239/169, and 577/408, but the eighth expansion, 1393/985,
     * is the first example where the number of digits in the numerator exceeds the number of digits in the denominator.
     * <p>
     * In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?
     * <p>
     * See also <a href="https://projecteuler.net/problem=57">projecteuler.net problem 57</a>.
     */
    @Test
    public void shouldSolveProblem57() {
        assertThat(cnt()).isEqualTo(153);
    }

    private static int cnt() {
        return fractions()
                .take(1000)
                .filter(f -> f._1.toPlainString().length() > f._2.toPlainString().length())
                .length();
    }

    private static Stream<Tuple2<BigDecimal, BigDecimal>> fractions() {
        return Stream.iterate(Tuple.of(BigDecimal.ONE, BigDecimal.ONE), Euler57Test::it);
    }

    /**
     * a/b -> 1 + 1/(1 + a/b) = (a + 2b)/(a + b)
     */
    private static Tuple2<BigDecimal, BigDecimal> it(Tuple2<BigDecimal, BigDecimal> val) {
        return Tuple.of(val._1.add(val._2.add(val._2)), val._1.add(val._2));
    }
}