Add Dutch National Flag sorting algorithm

DIRECTORY.md

@@ -235,6 +235,7 @@
 
 ## [Data Structures](data_structures)
   * Arrays
+    * [Dutch National Flag Sort](data_structures/arrays/dutch_national_flag_sort.py)
     * [Equilibrium Index In Array](data_structures/arrays/equilibrium_index_in_array.py)
     * [Find Triplets With 0 Sum](data_structures/arrays/find_triplets_with_0_sum.py)
     * [Index 2D Array In 1D](data_structures/arrays/index_2d_array_in_1d.py)
@@ -533,7 +534,9 @@
   * [Geometry](geometry/geometry.py)
   * [Graham Scan](geometry/graham_scan.py)
   * [Jarvis March](geometry/jarvis_march.py)
+  * [Monotone Chain](geometry/monotone_chain.py)
   * [Ramer Douglas Peucker](geometry/ramer_douglas_peucker.py)
+  * [Rotating Calipers](geometry/rotating_calipers.py)
   * [Segment Intersection](geometry/segment_intersection.py)
   * Tests
     * [Test Graham Scan](geometry/tests/test_graham_scan.py)

data_structures/arrays/dutch_national_flag_sort.py

@@ -0,0 +1,108 @@
+"""
+Implements the Dutch National Flag algorithm to sort an array of 0s, 1s, and 2s
+in-place. Includes error handling for invalid values and examples in the docstring.
+
+This algorithm runs in O(n) time and O(1) space using three pointers.
+See: https://en.wikipedia.org/wiki/Dutch_national_flag_problem
+"""
+
+from __future__ import annotations
+
+
+def dutch_flag_sort(arr: list[int]) -> None:
+    """
+    Sorts an array of 0s, 1s, and 2s in-place.
+
+    Args:
+        arr: List containing only 0, 1, or 2.
+
+    Returns:
+        None
+
+    Raises:
+        ValueError: If array contains values other than 0, 1, or 2.
+
+    Examples:
+        >>> arr = [2, 0, 2, 1, 1, 0]
+        >>> dutch_flag_sort(arr)
+        >>> arr
+        [0, 0, 1, 1, 2, 2]
+
+        >>> arr = [2, 0, 1]
+        >>> dutch_flag_sort(arr)
+        >>> arr
+        [0, 1, 2]
+
+        >>> arr = []
+        >>> dutch_flag_sort(arr)
+        >>> arr
+        []
+
+        >>> arr = [1]
+        >>> dutch_flag_sort(arr)
+        >>> arr
+        [1]
+
+        >>> arr = [0, 0, 0]
+        >>> dutch_flag_sort(arr)
+        >>> arr
+        [0, 0, 0]
+
+        >>> arr = [3]
+        >>> dutch_flag_sort(arr)
+        Traceback (most recent call last):
+        ...
+        ValueError: Array contains invalid value: 3
+
+        >>> arr = [-1, 0, 1]
+        >>> dutch_flag_sort(arr)
+        Traceback (most recent call last):
+        ...
+        ValueError: Array contains invalid value: -1
+
+        >>> arr = [2, 0, '1']
+        >>> dutch_flag_sort(arr)
+        Traceback (most recent call last):
+        ...
+        ValueError: Array contains invalid value: 1
+    """
+    if not arr:
+        return
+
+    low = mid = 0
+    high = len(arr) - 1
+
+    while mid <= high:
+        value = arr[mid]
+        if value == 0:
+            arr[low], arr[mid] = arr[mid], arr[low]
+            low += 1
+            mid += 1
+        elif value == 1:
+            mid += 1
+        elif value == 2:
+            arr[mid], arr[high] = arr[high], arr[mid]
+            high -= 1
+        else:
+            msg = f"Array contains invalid value: {value}"
+            raise ValueError(msg)
+
+
+if __name__ == "__main__":
+    examples = [
+        [2, 0, 2, 1, 1, 0],
+        [2, 0, 1],
+        [],
+        [1],
+        [0, 0, 0],
+        [2, 2, 2],
+        [1, 1, 1],
+        [0, 1, 2, 0, 1, 2],
+        [2, 1, 0, 2, 1, 0],
+    ]
+
+    for test_arr in examples:
+        arr = test_arr.copy()
+        print(f"Before: {arr}")
+        dutch_flag_sort(arr)
+        print(f"After : {arr}\n")