Added HappyNumber algorithm in maths section (#6571)

* Added HappyNumber algorithm in maths section * Fix Checkstyle: remove trailing spaces in HappyNumber * Fix formatting: remove trailing spaces and apply clang-format * Update HappyNumberTest.java * Removed old HappyNumbersSeq.java as replaced by new HappyNumber.java

Author: ruturajjadhav07

src/main/java/com/thealgorithms/maths/HappyNumber.java

@@ -0,0 +1,57 @@
+package com.thealgorithms.maths;
+
+/**
+ * A Happy Number is defined as a number which eventually reaches 1 when replaced
+ * by the sum of the squares of each digit.
+ * If it falls into a cycle that does not include 1, then it is not a happy number.
+
+ * Example:
+ * 19 → 1² + 9² = 82
+ * 82 → 8² + 2² = 68
+ * 68 → 6² + 8² = 100
+ * 100 → 1² + 0² + 0² = 1 → Happy Number!
+ */
+public final class HappyNumber {
+
+ private HappyNumber() {
+ }
+
+ /**
+ * Checks whether the given number is a Happy Number.
+ * Uses Floyd’s Cycle Detection algorithm (tortoise and hare method)
+ * to detect loops efficiently.
+ *
+ * @param n The number to check
+ * @return true if n is a Happy Number, false otherwise
+ */
+ public static boolean isHappy(int n) {
+ int slow = n;
+ int fast = n;
+
+ do {
+ slow = sumOfSquares(slow); // move 1 step
+ fast = sumOfSquares(sumOfSquares(fast)); // move 2 steps
+ } while (slow != fast);
+
+ return slow == 1; // If cycle ends in 1 → Happy number
+ }
+
+ /**
+ * Calculates the sum of squares of the digits of a number.
+ *
+ * Example:
+ * num = 82 → 8² + 2² = 64 + 4 = 68
+ *
+ * @param num The number to calculate sum of squares of digits
+ * @return The sum of squares of the digits
+ */
+ private static int sumOfSquares(int num) {
+ int sum = 0;
+ while (num > 0) {
+ int digit = num % 10;
+ sum += digit * digit;
+ num /= 10;
+ }
+ return sum;
+ }
+}

src/main/java/com/thealgorithms/others/HappyNumbersSeq.java

@@ -0,0 +1,32 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+public class HappyNumberTest {
+
+ @Test
+ void testHappyNumbers() {
+ // Known happy numbers
+ assertTrue(HappyNumber.isHappy(1));
+ assertTrue(HappyNumber.isHappy(7));
+ assertTrue(HappyNumber.isHappy(19));
+ assertTrue(HappyNumber.isHappy(100));
+ }
+
+ @Test
+ void testUnhappyNumbers() {
+ // Known unhappy numbers
+ assertFalse(HappyNumber.isHappy(2));
+ assertFalse(HappyNumber.isHappy(4));
+ assertFalse(HappyNumber.isHappy(20));
+ }
+
+ @Test
+ void testLargeNumber() {
+ // Just to check behavior with larger input
+ assertTrue(HappyNumber.isHappy(1000000)); // reduces to 1 eventually
+ }
+}