Add solution for FrobeniusCoinProblem task

Author: andrei-punko

src/main/java/by/andd3dfx/numeric/FrobeniusCoinProblem.java

@@ -0,0 +1,37 @@
+package by.andd3dfx.numeric;
+
+import by.andd3dfx.dynamic.ChangeWithMinNumberOfCoins;
+
+/**
+ * See <a href="https://en.wikipedia.org/wiki/Coin_problem">article</a> in wiki
+ * <p>
+ * Find the largest monetary amount that cannot be obtained using only coins of specified denominations.
+ */
+public class FrobeniusCoinProblem {
+
+    public static int find(int[] nominals) {
+        var capAmount = determineStartingValueEnhanced(nominals);
+        for (var amount = capAmount; amount >= 1; amount--) {
+            if (ChangeWithMinNumberOfCoins.determine_usingMemoization(nominals, amount) == -1) {
+                return amount;
+            }
+        }
+        return 1;
+    }
+
+    /**
+     * Method wasn't deleted for demo purposes
+     */
+    private static int determineStartingValuePrimitive(int[] nominals) {
+        var result = 1;
+        for (int nominal : nominals) {
+            result *= nominal;
+        }
+        System.out.println(result);
+        return result;
+    }
+
+    private static int determineStartingValueEnhanced(int[] nominals) {
+        return LeastCommonMultiple.find(nominals);
+    }
+}

src/test/java/by/andd3dfx/numeric/FrobeniusCoinProblemTest.java

@@ -0,0 +1,19 @@
+package by.andd3dfx.numeric;
+
+import org.junit.Test;
+
+import static org.assertj.core.api.Assertions.assertThat;
+
+public class FrobeniusCoinProblemTest {
+
+    @Test
+    public void testFind() {
+        // Formula g = a1*a2-a1-a2 works only for relatively prime numbers a1, a2
+        assertThat(FrobeniusCoinProblem.find(new int[]{2, 5})).isEqualTo(2 * 5 - 2 - 5);
+        assertThat(FrobeniusCoinProblem.find(new int[]{3, 7})).isEqualTo(3 * 7 - 3 - 7);
+        assertThat(FrobeniusCoinProblem.find(new int[]{6, 7})).isEqualTo(6 * 7 - 6 - 7);
+
+        // McNuggets problem
+        assertThat(FrobeniusCoinProblem.find(new int[]{6, 9, 20})).isEqualTo(43);
+    }
+}