Add Binary Parity Pattern Algorithm

DIRECTORY.md

@@ -37,6 +37,7 @@
   * [Binary Twos Complement](bit_manipulation/binary_twos_complement.py)
   * [Binary Xor Operator](bit_manipulation/binary_xor_operator.py)
   * [Bitwise Addition Recursive](bit_manipulation/bitwise_addition_recursive.py)
+  * [Binary Parity Pattern](bit_manipulation/binary_parity_pattern.py)
   * [Count 1S Brian Kernighan Method](bit_manipulation/count_1s_brian_kernighan_method.py)
   * [Count Number Of One Bits](bit_manipulation/count_number_of_one_bits.py)
   * [Excess 3 Code](bit_manipulation/excess_3_code.py)

bit_manipulation/binary_parity_pattern.py

@@ -0,0 +1,47 @@
+"""
+binary_parity_pattern.py
+========================
+
+Generates a binary parity pattern based on the cumulative sum of bits
+in the binary representation of an integer.
+
+Reference:
+https://en.wikipedia.org/wiki/Parity_(mathematics)
+"""
+
+
+def binary_parity_pattern(number: int) -> str:
+    """
+    Return a binary parity pattern string for a given integer.
+
+    >>> binary_parity_pattern(13)
+    '0b1001'
+    >>> binary_parity_pattern(7)
+    '0b101'
+    >>> binary_parity_pattern(4)
+    '0b111'
+    >>> binary_parity_pattern(0)
+    '0b0'
+    """
+    if number < 0:
+        raise ValueError("Number must be non-negative")
+
+    if number == 0:
+        return "0b0"
+
+    binary_str = bin(number)[2:]
+    cum_sum = 0
+    pattern = []
+
+    for bit in binary_str:
+        cum_sum += int(bit)
+        pattern.append(str(cum_sum % 2))
+
+    result = "".join(pattern).lstrip("0")
+    return "0b" + (result if result else "0")
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()