add numbers different signs algorithm.

DIRECTORY.md

@@ -50,6 +50,7 @@
   * [Index Of Rightmost Set Bit](bit_manipulation/index_of_rightmost_set_bit.py)
   * [Is Even](bit_manipulation/is_even.py)
   * [Is Power Of Two](bit_manipulation/is_power_of_two.py)
+  * [Numbers Different Signs](bit_manipulation/numbers_different_signs.py)
   * [Reverse Bits](bit_manipulation/reverse_bits.py)
   * [Single Bit Manipulation Operations](bit_manipulation/single_bit_manipulation_operations.py)
 
@@ -561,6 +562,7 @@
   * [Greedy Coin Change](maths/greedy_coin_change.py)
   * [Hamming Numbers](maths/hamming_numbers.py)
   * [Hardy Ramanujanalgo](maths/hardy_ramanujanalgo.py)
+  * [Hexagonal Number](maths/hexagonal_number.py)
   * [Integration By Simpson Approx](maths/integration_by_simpson_approx.py)
   * [Is Ip V4 Address Valid](maths/is_ip_v4_address_valid.py)
   * [Is Square Free](maths/is_square_free.py)

bit_manipulation/numbers_different_signs.py

@@ -0,0 +1,37 @@
+"""
+Author  : Alexander Pantyukhin
+Date    : November 30, 2022
+
+Task:
+Given two int numbers. Return True these numbers have opposite signs
+or False otherwise.
+
+Implementation notes: Use bit manipulation.
+Use XOR for two numbers.
+"""
+
+def different_signs(a: int, b: int) -> bool:
+    """
+    Return True if numbers have opposite signs False otherwise.
+
+    >>> different_signs(1, -1)
+    True
+    >>> different_signs(1, 1)
+    False
+    >>> different_signs(1000000000000000000000000000, -1000000000000000000000000000)
+    True
+    >>> different_signs(-1000000000000000000000000000, 1000000000000000000000000000)
+    True
+    >>> different_signs(50, 278)
+    False
+    >>> different_signs(0, 2)
+    False
+    >>> different_signs(2, 0)
+    False
+    """
+    return a ^ b < 0
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()