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Shellsort

Read this in other languages: Português.

Shellsort, also known as Shell sort or Shell's method, is an in-place comparison sort. It can be seen as either a generalization of sorting by exchange (bubble sort) or sorting by insertion (insertion sort). The method starts by sorting pairs of elements far apart from each other, then progressively reducing the gap between elements to be compared. Starting with far apart elements, it can move some out-of-place elements into position faster than a simple nearest neighbor exchange

Shellsort

How Shell Sort Works

For our example and ease of understanding, we take the interval of 4. Make a virtual sub-list of all values located at the interval of 4 positions. Here these values are {35, 14}, {33, 19}, {42, 27} and {10, 44}

Shellsort

We compare values in each sub-list and swap them (if necessary) in the original array. After this step, the new array should look like this

Shellsort

Then, we take interval of 2 and this gap generates two sub-lists

  • {14, 27, 35, 42}, {19, 10, 33, 44}

Shellsort

We compare and swap the values, if required, in the original array. After this step, the array should look like this

Shellsort

UPD: On the picture below there is a typo and result array is supposed to be [14, 10, 27, 19, 35, 33, 42, 44].

Finally, we sort the rest of the array using interval of value 1. Shell sort uses insertion sort to sort the array.

Shellsort

Complexity

Name Best Average Worst Memory Stable Comments
Shell sort n log(n) depends on gap sequence n (log(n))2 1 No

References