Addition of Library_sort

Author: Aayaan Singh

sorts/library_sort.py

@@ -0,0 +1,105 @@
+from typing import List
+
+
+def library_sort(collection: List[int], reverse: bool = False) -> List[int]:
+    """
+    A pure Python implementation of library sort (also called gapped insertion sort).
+
+    It w orks like insertion sort, but leaves empty gaps in the array so a new item can
+    be placed without shifting everything after it. When the gaps fill up, the array is
+    rebalanced. Expected time is O(n log n).
+
+    Reference: https://en.wikipedia.org/wiki/Library_sort
+
+    For doctests run the following command:
+    python3 -m doctest -v library_sort.py
+
+    For manual testing run:
+    python3 library_sort.py
+    Time Complexity: O(N log N) average, O(N^2) worst-case
+    Space Complexity: O(N)
+
+    Examples:
+    >>> library_sort([5, 2, 9, 1, 5, 6])
+    [1, 2, 5, 5, 6, 9]
+    >>> library_sort([3, 1, 4, 1, 5, 9, 2])
+    [1, 1, 2, 3, 4, 5, 9]
+    >>> library_sort([])
+    []
+    >>> library_sort([1])
+    [1]
+    >>> library_sort([5, 2, 9, 1], reverse=True)
+    [9, 5, 2, 1]
+    """
+    if not collection:
+        return []
+
+    n = len(collection)
+    gapped = [None] * (2 * n)
+    gapped[0] = collection[0]
+
+    for i in range(1, n):
+        val = collection[i]
+        valid_indices = [idx for idx, x in enumerate(gapped) if x is not None]
+        valid_vals = [gapped[idx] for idx in valid_indices]
+
+        low, high = 0, len(valid_vals) - 1
+        pos = len(valid_vals)
+        while low <= high:
+            mid = (low + high) // 2
+            if valid_vals[mid] >= val:
+                pos = mid
+                high = mid - 1
+            else:
+                low = mid + 1
+
+        if pos == len(valid_vals):
+            target_idx = valid_indices[-1] + 1 if valid_indices else 0
+        else:
+            target_idx = valid_indices[pos]
+
+        if target_idx < len(gapped) and gapped[target_idx] is None:
+            gapped[target_idx] = val
+        else:
+            current_elements = [x for x in gapped if x is not None]
+            current_elements.append(val)
+            current_elements.sort()
+
+            gapped = [None] * (2 * len(current_elements))
+            step = len(gapped) // len(current_elements)
+            for idx, elem in enumerate(current_elements):
+                gapped[idx * step] = elem
+
+    sorted_arr = [x for x in gapped if x is not None]
+    if reverse:
+        sorted_arr.reverse()
+    return sorted_arr
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    print("\nLibrarySort Interactive Testing")
+    print("=" * 40)
+
+    try:
+        user_input = input("Enter numbers separated by a comma:\n").strip()
+        if user_input == "":
+            unsorted = []
+        else:
+            unsorted = [int(item.strip()) for item in user_input.split(",")]
+
+        print(f"\nOriginal: {unsorted}")
+        sorted_list = library_sort(unsorted)
+        print(f"Sorted:   {sorted_list}")
+
+        # Test reverse
+        sorted_reverse = library_sort(unsorted, reverse=True)
+        print(f"Reverse:  {sorted_reverse}")
+
+    except ValueError:
+        print("Invalid input. Please enter valid integers separated by commas.")
+    except KeyboardInterrupt:
+        print("\n\nGoodbye!")