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

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;
+    }
+}