adding shell sort

Author: mcleber

README.md

@@ -16,6 +16,7 @@ This is my study repository.
 * bubble sort.
 * selection sort.
 * insertion sort.
+* shell sort.
 
 ## Link
 

src/shell_sort.py

@@ -0,0 +1,52 @@
+#!/usr/bin/env python3
+
+##
+# Shell Sort
+##
+
+import numpy as np
+
+def shell_sort(array):
+    """
+    Sorts an array using the Shell Sort algorithm.
+
+    Shell Sort is an in-place comparison-based sorting algorithm
+    that generalizes insertion sort to allow the exchange of items 
+    that are far apart. The idea is to arrange the list of elements 
+    so that, starting anywhere, taking every `gap`-th element produces 
+    a sorted list. The algorithm gradually reduces the gap between 
+    elements to be compared.
+
+    Parameters:
+    array (numpy.ndarray): The array to be sorted.
+
+    Returns:
+    numpy.ndarray: The sorted array.
+    """
+    
+    # Start with a gap size of half the length of the array
+    gap = len(array) // 2
+
+    # Continue reducing the gap until it becomes zero
+    while gap > 0:
+        # Perform a modified insertion sort for each gap
+        for i in range(gap, len(array)):
+            temp = array[i]  # Store the current element
+            j = i  # Initialize index j to the current index i
+
+            # Shift elements that are greater than temp to the right
+            while j >= gap and array[j - gap] > temp:
+                array[j] = array[j - gap]
+                j -= gap
+
+            # Place the temp element in the correct position
+            array[j] = temp
+        
+        # Reduce the gap for the next iteration
+        gap //= 2
+
+    return array
+
+# Example usage
+sorted_array = shell_sort(np.array([8, 5, 1, 4, 2, 3]))
+print(sorted_array)