Added Dutch National Flag algorithm TheAlgorithms#4636 (TheAlgorithms#4639)

* Added Dutch national flag sort Algorithm

* Changed file name to dnf_sort.py

* Added descriptive name and type hint 

Added descriptive name and type hint  for parameter with doctest for the function dnf_sort.

* Added test cases

* Added doctest cases

* Update sorts/dnf_sort.py

* Added doctest for dutch_national_flag_sort sorts/dnf_sort.py

* Update sorts/dnf_sort.py

* Added doctest for the function
dutch_national_flag_sort

* update file as per black code formatter

* Update dnf_sort.py

* Update and rename dnf_sort.py to dutch_national_flag_sort.py

Co-authored-by: Christian Clauss <[email protected]>

Author: KiranHipparagi

sorts/dutch_national_flag_sort.py

@@ -0,0 +1,100 @@
+"""
+A pure implementation of Dutch national flag (DNF) sort algorithm in Python.
+Dutch National Flag algorithm is an algorithm originally designed by Edsger Dijkstra.
+It is the most optimal sort for 3 unique values (eg. 0, 1, 2) in a sequence.  DNF can
+sort a sequence of n size with [0 <= a[i] <= 2] at guaranteed O(n) complexity in a
+single pass.
+
+The flag of the Netherlands consists of three colors: white, red, and blue.
+The task is to randomly arrange balls of white, red, and blue in such a way that balls
+of the same color are placed together.  DNF sorts a sequence of 0, 1, and 2's in linear
+time that does not consume any extra space.  This algorithm can be implemented only on
+a sequence that contains three unique elements.
+
+1) Time complexity is O(n).
+2) Space complexity is O(1).
+
+More info on: https://en.wikipedia.org/wiki/Dutch_national_flag_problem
+
+For doctests run following command:
+python3 -m doctest -v dutch_national_flag_sort.py
+
+For manual testing run:
+python dnf_sort.py
+"""
+
+
+# Python program to sort a sequence containing only 0, 1 and 2 in a single pass.
+red = 0  # The first color of the flag.
+white = 1  # The second color of the flag.
+blue = 2  # The third color of the flag.
+colors = (red, white, blue)
+
+
+def dutch_national_flag_sort(sequence: list) -> list:
+    """
+    A pure Python implementation of Dutch National Flag sort algorithm.
+    :param data: 3 unique integer values (e.g., 0, 1, 2) in an sequence
+    :return: The same collection in ascending order
+
+    >>> dutch_national_flag_sort([])
+    []
+    >>> dutch_national_flag_sort([0])
+    [0]
+    >>> dutch_national_flag_sort([2, 1, 0, 0, 1, 2])
+    [0, 0, 1, 1, 2, 2]
+    >>> dutch_national_flag_sort([0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1])
+    [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2]
+    >>> dutch_national_flag_sort("abacab")
+    Traceback (most recent call last):
+      ...
+    ValueError: The elements inside the sequence must contains only (0, 1, 2) values
+    >>> dutch_national_flag_sort("Abacab")
+    Traceback (most recent call last):
+      ...
+    ValueError: The elements inside the sequence must contains only (0, 1, 2) values
+    >>> dutch_national_flag_sort([3, 2, 3, 1, 3, 0, 3])
+    Traceback (most recent call last):
+      ...
+    ValueError: The elements inside the sequence must contains only (0, 1, 2) values
+    >>> dutch_national_flag_sort([-1, 2, -1, 1, -1, 0, -1])
+    Traceback (most recent call last):
+      ...
+    ValueError: The elements inside the sequence must contains only (0, 1, 2) values
+    >>> dutch_national_flag_sort([1.1, 2, 1.1, 1, 1.1, 0, 1.1])
+    Traceback (most recent call last):
+      ...
+    ValueError: The elements inside the sequence must contains only (0, 1, 2) values
+    """
+    if not sequence:
+        return []
+    if len(sequence) == 1:
+        return list(sequence)
+    low = 0
+    high = len(sequence) - 1
+    mid = 0
+    while mid <= high:
+        if sequence[mid] == colors[0]:
+            sequence[low], sequence[mid] = sequence[mid], sequence[low]
+            low += 1
+            mid += 1
+        elif sequence[mid] == colors[1]:
+            mid += 1
+        elif sequence[mid] == colors[2]:
+            sequence[mid], sequence[high] = sequence[high], sequence[mid]
+            high -= 1
+        else:
+            raise ValueError(
+                f"The elements inside the sequence must contains only {colors} values"
+            )
+    return sequence
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    user_input = input("Enter numbers separated by commas:\n").strip()
+    unsorted = [int(item.strip()) for item in user_input.split(",")]
+    print(f"{dutch_national_flag_sort(unsorted)}")