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79 changes: 40 additions & 39 deletions sorts/dutch_national_flag_sort.py
Original file line number Diff line number Diff line change
@@ -1,40 +1,36 @@
"""
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.
Originally designed by Edsger Dijkstra, it optimally sorts a sequence of three unique values

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(e.g., 0, 1, 2) with [0 <= a[i] <= 2] in 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.
The task is to randomly arrange balls of white, red, and blue so that balls of the same color

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are grouped together. DNF sorts a sequence of 0, 1, and 2's in linear time without consuming

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extra space. The algorithm works only on sequences with 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 more info: https://en.wikipedia.org/wiki/Dutch_national_flag_problem

For doctests run following command:
For doctests run:
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)
# Python program to sort a sequence containing only 0, 1, and 2 in a single pass.
RED = 0 # The first color (red).
WHITE = 1 # The second color (white).
BLUE = 2 # The third color (blue).
ALLOWED_VALUES = (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
A Python implementation of the Dutch National Flag sorting algorithm.
:param sequence: A list of integers containing only 0, 1, and 2
:return: Sorted sequence with the values 0, 1, 2 in ascending order

>>> dutch_national_flag_sort([])
[]
Expand All @@ -47,44 +43,42 @@
>>> 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
ValueError: The elements inside the sequence must contain 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
ValueError: The elements inside the sequence must contain 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
ValueError: The elements inside the sequence must contain 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
ValueError: The elements inside the sequence must contain only (0, 1, 2) values
"""
if not sequence:
return []
if len(sequence) == 1:
return list(sequence)
low = 0
high = len(sequence) - 1
mid = 0
return sequence

low, mid, high = 0, 0, len(sequence) - 1

while mid <= high:
if sequence[mid] == colors[0]:
if sequence[mid] == RED:
sequence[low], sequence[mid] = sequence[mid], sequence[low]
low += 1
mid += 1
elif sequence[mid] == colors[1]:
elif sequence[mid] == WHITE:
mid += 1
elif sequence[mid] == colors[2]:
elif sequence[mid] == BLUE:
sequence[mid], sequence[high] = sequence[high], sequence[mid]
high -= 1
else:
msg = f"The elements inside the sequence must contains only {colors} values"
raise ValueError(msg)
raise ValueError(
f"The elements inside the sequence must contain only {ALLOWED_VALUES} values"

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)

return sequence


Expand All @@ -93,6 +87,13 @@

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)}")
# User input for manual testing
user_input = input("Enter numbers separated by commas (0, 1, 2 only):\n").strip()
try:
unsorted = [int(item.strip()) for item in user_input.split(",")]
if all(x in ALLOWED_VALUES for x in unsorted):
print(f"Sorted sequence: {dutch_national_flag_sort(unsorted)}")
else:
print("Error: Input must only contain the values 0, 1, and 2.")
except ValueError:
print("Error: Invalid input. Please enter integers only.")
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