solution for problem 44 (#2685)

Author: smthelusive

src/test/java/io/vavr/collection/euler/Euler44Test.java

@@ -0,0 +1,65 @@
+/* ____  ______________  ________________________  __________
+ * \   \/   /      \   \/   /   __/   /      \   \/   /      \
+ *  \______/___/\___\______/___/_____/___/\___\______/___/\___\
+ *
+ * Copyright 2021 Vavr, https://vavr.io
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package io.vavr.collection.euler;
+
+import io.vavr.API;
+import io.vavr.concurrent.Future;
+import org.junit.Test;
+
+import java.util.concurrent.TimeUnit;
+
+import static org.assertj.core.api.Assertions.assertThat;
+
+public class Euler44Test {
+
+    /**
+     * <strong>Problem 44 Pentagon numbers</strong>
+     * <p>
+     * Pentagonal numbers are generated by the formula, P<sub><i>n</i></sub>=<i>n</i>(3<i>n</i>−1)/2.
+     * The first ten pentagonal numbers are: </p>
+     * <p>
+     *     1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
+     * </p>
+     * <p>
+     * It can be seen that P<sub>4</sub> + P<sub>7</sub> = 22 + 70 = 92 = P<sub>8</sub>.
+     * However, their difference, 70 − 22 = 48, is not pentagonal.
+     * </p>
+     * <p>
+     * Find the pair of pentagonal numbers, P<sub><i>j</i></sub> and P<sub><i>k</i></sub>,
+     * for which their sum and difference are pentagonal and D = |P<sub><i>k</i></sub> - P<sub><i>j</i></sub>|
+     * is minimised; what is the value of D?
+     * <p>
+     * See also <a href="https://projecteuler.net/problem=44">projecteuler.net
+     * problem 44</a>.
+     */
+    @Test
+    public void shouldSolveProblem44() {
+        final Future<Long> computation = API.Future(this::minimalPentagonalDiff)
+                .await(2, TimeUnit.SECONDS);
+        assertThat(computation.getOrElse(-1L)).isEqualTo(5482660);
+    }
+
+    private Long minimalPentagonalDiff() {
+        return Utils.pentagonal().flatMap(sumPentagonal ->
+                Utils.pentagonal().takeWhile(pentagonal -> sumPentagonal.compareTo(pentagonal) > 0)
+                        .filter(pj -> Utils.isPentagonal(sumPentagonal - pj) &&
+                                Utils.isPentagonal(sumPentagonal - 2 * pj))
+                        .map(pj -> sumPentagonal - 2 * pj)).head();
+    }
+}

src/test/java/io/vavr/collection/euler/Utils.java

@@ -20,6 +20,7 @@
 
 import io.vavr.API;
 import io.vavr.Function1;
+import io.vavr.Tuple;
 import io.vavr.collection.Iterator;
 import io.vavr.collection.Stream;
 
@@ -30,7 +31,6 @@
 import java.util.Scanner;
 
 import static io.vavr.API.$;
-import static io.vavr.API.Case;
 
 final class Utils {
 
@@ -115,4 +115,15 @@ static boolean isPalindrome(String val) {
     static boolean isPalindrome(int val) {
         return isPalindrome(Long.toString(val));
     }
+
+    static Stream<Long> pentagonal() {
+        return Stream.of(Tuple.of(1L, 1)).appendSelf(self ->
+                self.map(t ->
+                        Tuple.of((t._2 + 1) * (3L * (t._2 + 1) - 1) / 2, t._2 + 1)))
+                .map(t -> t._1);
+    }
+
+    static boolean isPentagonal(long number) {
+        return ((1 + Math.sqrt(1 + 24 * number)) / 6) % 1 == 0;
+    }
 }