Add XOR-based swap algorithm for two numbers (#13018)

* Add XOR-based swap algorithm for two numbers

* updating DIRECTORY.md

* Include additional test case for xor_swap function

Add example for xor_swap with larger integers

---------

Co-authored-by: Balamurugan315 <balamuruganmsde@gmail.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: 3 people

DIRECTORY.md

@@ -106,6 +106,7 @@
   * [Rotate Bits](bit_manipulation/rotate_bits.py)
   * [Single Bit Manipulation Operations](bit_manipulation/single_bit_manipulation_operations.py)
   * [Swap All Odd And Even Bits](bit_manipulation/swap_all_odd_and_even_bits.py)
+  * [Xor Swap Two Integers](bit_manipulation/xor_swap_two_integers.py)
 
 ## [Blockchain](blockchain)
   * [Diophantine Equation](blockchain/diophantine_equation.py)

bit_manipulation/xor_swap_two_integers.py

@@ -0,0 +1,40 @@
+# Information on XOR swap: https://en.wikipedia.org/wiki/Bitwise_operation#XOR
+
+# Algorithm:
+# 1. Take two integers a and b.
+# 2. Apply XOR between a and b and store the result in a:
+#       a = a ^ b
+# 3. XOR the new value of a with b to get the original value of a and store it in b:
+#       b = a ^ b
+# 4. XOR the new value of a with the new value of b.
+#    This gives the original value of b, which we store in a:
+#       a = a ^ b
+# 5. Return the swapped values (a, b).
+# This method swaps two numbers without using a temporary variable.
+
+
+def xor_swap(a: int, b: int) -> tuple[int, int]:
+    """
+    Swap two integers using bitwise XOR operation and return the swapped values.
+
+    >>> xor_swap(5, 10)
+    (10, 5)
+    >>> xor_swap(0, 0)
+    (0, 0)
+    >>> xor_swap(-1, 1)
+    (1, -1)
+    >>> xor_swap(123, 456)
+    (456, 123)
+    >>> xor_swap(12345, 54321)
+    (54321, 12345)
+    """
+    a = a ^ b
+    b = a ^ b
+    a = a ^ b
+    return a, b
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()