Luhn algorithm

DIRECTORY.md

@@ -146,6 +146,7 @@
     * Number Theory
       * [Prime Numbers](https://github.com/TheAlgorithms/Python/blob/master/data_structures/hashing/number_theory/prime_numbers.py)
     * [Quadratic Probing](https://github.com/TheAlgorithms/Python/blob/master/data_structures/hashing/quadratic_probing.py)
+    * [Luhn's Algorithm](https://github.com/TheAlgorithms/Python/blob/master/data_structures/hashing/luhn.py)
   * Heap
     * [Binomial Heap](https://github.com/TheAlgorithms/Python/blob/master/data_structures/heap/binomial_heap.py)
     * [Heap](https://github.com/TheAlgorithms/Python/blob/master/data_structures/heap/heap.py)

hashes/luhn.py

@@ -0,0 +1,46 @@
+""" Luhn Algorithm """
+from typing import List
+
+
+def is_luhn(string: str) -> bool:
+    """
+    Perform Luhn validation on input string
+    Algorithm:
+    * Double every other digit starting from 2nd last digit.
+    * Subtract 9 if number is greater than 9.
+    * Sum the numbers
+    *
+    >>> test_cases = [79927398710, 79927398711, 79927398712, 79927398713,
+    ...     79927398714, 79927398715, 79927398716, 79927398717, 79927398718,
+    ...     79927398719]
+    >>> test_cases = list(map(str, test_cases))
+    >>> list(map(is_luhn, test_cases))
+    [False, False, False, True, False, False, False, False, False, False]
+    """
+    check_digit: int
+    _vector: List[str] = list(string)
+    __vector, check_digit = _vector[:-1], int(_vector[-1])
+    vector: List[int] = [*map(int, __vector)]
+
+    vector.reverse()
+    for idx, i in enumerate(vector):
+
+        if idx & 1 == 0:
+            doubled: int = vector[idx] * 2
+            if doubled > 9:
+                doubled -= 9
+
+            check_digit += doubled
+        else:
+            check_digit += i
+
+    if (check_digit) % 10 == 0:
+        return True
+    return False
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    assert is_luhn("79927398713")