Added implementation for MSD radix sort algorithm based on binary representation (#4441)

* Added MSD radix sort algorithm

* Fixed typos

* Added doctests

* Added link to wikipedia

* Added doctest and improved code

sorts/msd_radix_sort.py

@@ -0,0 +1,80 @@
+"""
+Python implementation of the MSD radix sort algorithm.
+It used the binary representation of the integers to sort
+them.
+https://en.wikipedia.org/wiki/Radix_sort
+"""
+from typing import List
+
+
+def msd_radix_sort(list_of_ints: List[int]) -> List[int]:
+    """
+    Implementation of the MSD radix sort algorithm. Only works
+    with positive integers
+    :param list_of_ints: A list of integers
+    :return: Returns the sorted list
+    >>> msd_radix_sort([40, 12, 1, 100, 4])
+    [1, 4, 12, 40, 100]
+    >>> msd_radix_sort([])
+    []
+    >>> msd_radix_sort([123, 345, 123, 80])
+    [80, 123, 123, 345]
+    >>> msd_radix_sort([1209, 834598, 1, 540402, 45])
+    [1, 45, 1209, 540402, 834598]
+    >>> msd_radix_sort([-1, 34, 45])
+    Traceback (most recent call last):
+    ...
+    ValueError: All numbers must be positive
+    """
+    if not list_of_ints:
+        return []
+
+    if min(list_of_ints) < 0:
+        raise ValueError("All numbers must be positive")
+
+    most_bits = max(len(bin(x)[2:]) for x in list_of_ints)
+    return _msd_radix_sort(list_of_ints, most_bits)
+
+
+def _msd_radix_sort(list_of_ints: List[int], bit_position: int) -> List[int]:
+    """
+    Sort the given list based on the bit at bit_position. Numbers with a
+    0 at that position will be at the start of the list, numbers with a
+    1 at the end.
+    :param list_of_ints: A list of integers
+    :param bit_position: the position of the bit that gets compared
+    :return: Returns a partially sorted list
+    >>> _msd_radix_sort([45, 2, 32], 1)
+    [2, 32, 45]
+    >>> _msd_radix_sort([10, 4, 12], 2)
+    [4, 12, 10]
+    """
+    if bit_position == 0 or len(list_of_ints) in [0, 1]:
+        return list_of_ints
+
+    zeros = list()
+    ones = list()
+    # Split numbers based on bit at bit_position from the right
+    for number in list_of_ints:
+        if (number >> (bit_position - 1)) & 1:
+            # number has a one at bit bit_position
+            ones.append(number)
+        else:
+            # number has a zero at bit bit_position
+            zeros.append(number)
+
+    # recursively split both lists further
+    zeros = _msd_radix_sort(zeros, bit_position - 1)
+    ones = _msd_radix_sort(ones, bit_position - 1)
+
+    # recombine lists
+    res = zeros
+    res.extend(ones)
+
+    return res
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()