diff --git a/src/main/java/com/thealgorithms/maths/FriendlyNumber.java b/src/main/java/com/thealgorithms/maths/FriendlyNumber.java new file mode 100644 index 000000000000..a9aa249e982f --- /dev/null +++ b/src/main/java/com/thealgorithms/maths/FriendlyNumber.java @@ -0,0 +1,47 @@ +package com.thealgorithms.maths; + +/** + * Two numbers are Friendly if they share the same abundancy index, + * which is the ratio of the sum of divisors to the number itself. + * Example: 6 and 28 are friendly because sigma(6)/6 = 2 and sigma(28)/28 = 2 + * + * @see + * Wikipedia: Friendly Number + * + * author: Vraj Prajapati @Rosander0 + */ +public final class FriendlyNumber { + + private FriendlyNumber() { + // Utility class + } + + static int sumOfDivisors(final int number) { + int sum = 0; + for (int i = 1; i <= number; i++) { + if (number % i == 0) { + sum += i; + } + } + return sum; + } + + /** + * Checks whether two numbers are Friendly Numbers. + * Two numbers are friendly if they share the same abundancy index + * (sumOfDivisors / number), compared via cross multiplication to avoid + * floating point errors. + * + * @param a First number (must be positive) + * @param b Second number (must be positive) + * @return true if a and b are friendly numbers, false otherwise + */ + public static boolean areFriendly(final int a, final int b) { + if (a <= 0 || b <= 0) { + return false; + } + int sigmaA = sumOfDivisors(a); + int sigmaB = sumOfDivisors(b); + return sigmaA * b == sigmaB * a; + } +} diff --git a/src/test/java/com/thealgorithms/maths/FriendlyNumberTest.java b/src/test/java/com/thealgorithms/maths/FriendlyNumberTest.java new file mode 100644 index 000000000000..be5ddd7ee79e --- /dev/null +++ b/src/test/java/com/thealgorithms/maths/FriendlyNumberTest.java @@ -0,0 +1,33 @@ +package com.thealgorithms.maths; +// author: Vraj Prajapati @Rosander0 + +import static org.junit.jupiter.api.Assertions.assertFalse; +import static org.junit.jupiter.api.Assertions.assertTrue; + +import org.junit.jupiter.api.Test; + +public class FriendlyNumberTest { + + @Test + public void testFriendlyNumbers() { + // 6 and 28 are friendly (abundancy index = 2) + assertTrue(FriendlyNumber.areFriendly(6, 28)); + // Every number is friendly with itself + assertTrue(FriendlyNumber.areFriendly(6, 6)); + assertTrue(FriendlyNumber.areFriendly(1, 1)); + } + + @Test + public void testNonFriendlyNumbers() { + assertFalse(FriendlyNumber.areFriendly(6, 10)); + assertFalse(FriendlyNumber.areFriendly(10, 15)); + assertFalse(FriendlyNumber.areFriendly(4, 9)); + } + + @Test + public void testInvalidInputs() { + assertFalse(FriendlyNumber.areFriendly(0, 6)); + assertFalse(FriendlyNumber.areFriendly(-1, 6)); + assertFalse(FriendlyNumber.areFriendly(6, -1)); + } +}