feat : new bit manipulation algo Single element in an array (#5689)

* feat : new algo uniquesubseqcount

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCount.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCountTest.java

* Update UniqueSubsequencesCount.java

* feat : new bitmanipulation algo

---------

Co-authored-by: Alex Klymenko <alexanderklmn@gmail.com>

src/main/java/com/thealgorithms/bitmanipulation/SingleElement.java

@@ -0,0 +1,39 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * Utility class to find the single non-duplicate element from an array
+ * where all other elements appear twice.
+ * <p>
+ * The algorithm runs in O(n) time complexity and O(1) space complexity
+ * using bitwise XOR.
+ * </p>
+ *
+ * @author <a href="http://github.com/tuhinm2002">Tuhin M</a>
+ */
+public final class SingleElement {
+
+    /**
+     * Private constructor to prevent instantiation of this utility class.
+     * Throws an UnsupportedOperationException if attempted.
+     */
+    private SingleElement() {
+        throw new UnsupportedOperationException("Utility Class");
+    }
+
+    /**
+     * Finds the single non-duplicate element in an array where every other
+     * element appears exactly twice. Uses bitwise XOR to achieve O(n) time
+     * complexity and O(1) space complexity.
+     *
+     * @param arr the input array containing integers where every element
+     *            except one appears exactly twice
+     * @return the single non-duplicate element
+     */
+    public static int findSingleElement(int[] arr) {
+        int ele = 0;
+        for (int i = 0; i < arr.length; i++) {
+            ele ^= arr[i];
+        }
+        return ele;
+    }
+}