Kirkpatrcik Reisch Sort

sorts/kirkpatrick_reisch_sort.py

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+import heapq
+import random
+from typing import List
+
+"""
+Kirkpatrick-Reisch sorting algorithm.
+Divides input into sqrt(n) blocks, sorts each, then merges using a min-heap.
+
+Time Complexity:
+- Average case: O(n * sqrt(n))
+- Worst case: O(n * sqrt(n))
+- Best case: O(n * sqrt(n))
+
+Space Complexity: O(n)
+
+Explanation Links:
+https://en.wikipedia.org/wiki/Kirkpatrick%E2%80%93Reisch_sort
+https://sortingsearching.com/2020/06/06/kirkpatrick-reisch.html
+"""
+
+
+def kirkpatrick_reisch_sort(arr) -> List[int]:
+    """
+    Implements the Kirkpatrick-Reisch sorting algorithm.
+
+    Args:
+    arr (list): The input list to be sorted.
+
+    Returns:
+    list: A new list containing the sorted elements.
+
+    Examples:
+    >>> kirkpatrick_reisch_sort([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5])
+    [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9]
+
+    >>> kirkpatrick_reisch_sort([])
+    []
+
+    >>> kirkpatrick_reisch_sort([1])
+    [1]
+
+    >>> kirkpatrick_reisch_sort([5, 4, 3, 2, 1])
+    [1, 2, 3, 4, 5]
+
+    >>> kirkpatrick_reisch_sort([-1, -3, 5, 0, 2])
+    [-3, -1, 0, 2, 5]
+    """
+    n = len(arr)
+    if n <= 1:
+        return arr
+
+    # Step 1: Divide the input into sqrt(n) blocks
+    block_size = int(n**0.5)
+    blocks = [arr[i : i + block_size] for i in range(0, n, block_size)]
+
+    # Step 2: Sort each block
+    for block in blocks:
+        block.sort()
+
+    # Step 3: Create a min-heap of the first elements of each block
+    heap = [(block[0], i, 0) for i, block in enumerate(blocks) if block]
+    heapq.heapify(heap)
+
+    # Step 4: Extract elements from the heap and refill from blocks
+    sorted_arr = []
+    while heap:
+        val, block_index, element_index = heapq.heappop(heap)
+        sorted_arr.append(val)
+
+        if element_index + 1 < len(blocks[block_index]):
+            next_element = blocks[block_index][element_index + 1]
+            heapq.heappush(heap, (next_element, block_index, element_index + 1))
+
+    return sorted_arr
+
+
+if __name__ == "__main__":
+    # Generate a random list of integers
+    arr = [random.randint(1, 1000) for _ in range(100)]
+
+    print("Original Array:", arr)
+    sorted_arr = kirkpatrick_reisch_sort(arr)
+    print("Sorted Array:", sorted_arr)
+
+    # Verify the result
+    assert sorted_arr == sorted(arr)