Add find_unique_number algorithm to bit manipulation (#12654)

* Add find_unique_number algorithm to bit manipulation

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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: parth-6945

Diff for: bit_manipulation/find_unique_number.py

@@ -0,0 +1,37 @@
+def find_unique_number(arr: list[int]) -> int:
+    """
+    Given a list of integers where every element appears twice except for one,
+    this function returns the element that appears only once using bitwise XOR.
+
+    >>> find_unique_number([1, 1, 2, 2, 3])
+    3
+    >>> find_unique_number([4, 5, 4, 6, 6])
+    5
+    >>> find_unique_number([7])
+    7
+    >>> find_unique_number([10, 20, 10])
+    20
+    >>> find_unique_number([])
+    Traceback (most recent call last):
+        ...
+    ValueError: input list must not be empty
+    >>> find_unique_number([1, 'a', 1])
+    Traceback (most recent call last):
+        ...
+    TypeError: all elements must be integers
+    """
+    if not arr:
+        raise ValueError("input list must not be empty")
+    if not all(isinstance(x, int) for x in arr):
+        raise TypeError("all elements must be integers")
+
+    result = 0
+    for num in arr:
+        result ^= num
+    return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()