Shell Sort

Author: hashfx

DSA-Python/Algorithms/ShellSort.py

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+"""
+Shell Sort
+    Shell sort is an optimization over Insertion sort
+    Aim is to reduce swaps and comparisons by swapping greater elements at right side of array and light element at left
+Algorithm
+    Start with gap = n/2 and sort sub arrays
+    Keep reducing gap by n/2 and keep on sorting sub arrays
+    Last iteration should have gap = 1. At this point it is same as insertion sort
+        Actually, we are doing insertion sort but with some optimization
+        so that number of swaps and comparisons can be reduced
+Disadvantage of Insertion sort over Shell Sort
+    When small elements are towards the end of array it takes many:
+        Comparisons
+        Swaps
+Worst-case Performance
+    O(n^2) (worst known worst-case gap sequence)
+    O(n log^2(n)) (best known worst-case gap sequence)
+Best-case Performance
+    O(n log n) (most gap sequences)
+    O(n log^2(n)) (best known worst-case gap sequence)
+
+"""
+
+def ShellSort(arr):
+    # gap = 3  # initialised gap to 3
+    size = len(arr)
+    gap = size // 2  # initialised gap to half of size of array
+    while gap > 0:
+        for i in range(gap, size):
+            pointer = arr[i]  # pointer initialised to array such that gap is maintained
+            j = i
+            # get element which is at gap 3 and compare with current pointer element AND j>=gap else (j-gap) would be negative
+            while j >= gap and arr[j - gap] > pointer:
+                arr[j] = arr[j-gap]  # swapped elements
+                j -= gap  # In each while loop iteration, reduce by gap for comparison with previous elements
+            arr[j] = pointer  # after while loop ends, all elements have been swapped
+            # after function end, all heavy values are at right side and light values at left of partially-sorted array
+        gap = gap // 2  # gap reduced by half
+
+
+if __name__ == '__main__':
+    elements = [21, 38, 29, 17, 4, 25, 11, 32, 9]
+    # Partially sorted array after Shell Sort[11, 4, 9, 17, 32, 25, 21, 38, 29]
+    ShellSort(elements)
+    print(elements)
+
+    # Test Cases
+    tests = [
+        [89, 78, 61, 53, 23, 21, 17, 12, 9, 7, 6, 2, 1],  # DESC sorted array
+        [],  # empty array
+        [1, 5, 8, 9],  # sorted array
+        [234, 3, 1, 56, 34, 12, 9, 12, 1300],  # array with uneven elements
+        [5]  # array with single element
+    ]
+
+    for elements in tests:
+        ShellSort(elements)
+        print(elements)