Create cyclic_sort.py (TheAlgorithms#9256)

* Create cyclic_sort.py

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* Update cyclic_sort.py

* updating DIRECTORY.md

* Update cyclic_sort.py

* Update cyclic_sort.py

* Update cyclic_sort.py

* Update cyclic_sort.py

* Update cyclic_sort.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>
Co-authored-by: MaximSmolskiy <MaximSmolskiy@users.noreply.github.com>

DIRECTORY.md

@@ -1267,6 +1267,7 @@
   * [Comb Sort](sorts/comb_sort.py)
   * [Counting Sort](sorts/counting_sort.py)
   * [Cycle Sort](sorts/cycle_sort.py)
+  * [Cyclic Sort](sorts/cyclic_sort.py)
   * [Double Sort](sorts/double_sort.py)
   * [Dutch National Flag Sort](sorts/dutch_national_flag_sort.py)
   * [Exchange Sort](sorts/exchange_sort.py)

sorts/cyclic_sort.py

@@ -0,0 +1,55 @@
+"""
+This is a pure Python implementation of the Cyclic Sort algorithm.
+
+For doctests run following command:
+python -m doctest -v cyclic_sort.py
+or
+python3 -m doctest -v cyclic_sort.py
+For manual testing run:
+python cyclic_sort.py
+or
+python3 cyclic_sort.py
+"""
+
+
+def cyclic_sort(nums: list[int]) -> list[int]:
+    """
+    Sorts the input list of n integers from 1 to n in-place
+    using the Cyclic Sort algorithm.
+
+    :param nums: List of n integers from 1 to n to be sorted.
+    :return: The same list sorted in ascending order.
+
+    Time complexity: O(n), where n is the number of integers in the list.
+
+    Examples:
+    >>> cyclic_sort([])
+    []
+    >>> cyclic_sort([3, 5, 2, 1, 4])
+    [1, 2, 3, 4, 5]
+    """
+
+    # Perform cyclic sort
+    index = 0
+    while index < len(nums):
+        # Calculate the correct index for the current element
+        correct_index = nums[index] - 1
+        # If the current element is not at its correct position,
+        # swap it with the element at its correct index
+        if index != correct_index:
+            nums[index], nums[correct_index] = nums[correct_index], nums[index]
+        else:
+            # If the current element is already in its correct position,
+            # move to the next element
+            index += 1
+
+    return nums
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    user_input = input("Enter numbers separated by a comma:\n").strip()
+    unsorted = [int(item) for item in user_input.split(",")]
+    print(*cyclic_sort(unsorted), sep=",")