Summary

Shell Sort is an in-place comparison sort that improves upon Insertion Sort by allowing elements to be moved over larger distances. It works by sorting elements that are far apart first (using a large gap), then progressively reducing the gap. This initial sorting of distant elements, called h-sorting, significantly reduces disorder and the number of shifts required in later stages, making the final passes (with smaller gaps) extremely fast.

How it Works

• 1. Choose a Gap Sequence: Start with a large gap. A common sequence (used in this implementation) is to start with a gap of n/2, then n/4, and so on, until the gap is 1.

• 2. Perform Gapped Insertion Sort: For the current gap, iterate through the array from the gap-th element to the end.

• 3. Compare and Shift: For each element, compare it with the element gap positions behind it (i-gap). If the gapped element is larger, shift it forward to the current position. Continue this process, moving backwards by gap each time, until the correct spot is found.

• 4. Insert: Place the current element into the newly opened position.

• 5. Reduce Gap: After sorting the entire array for the current gap, reduce the gap according to the sequence and repeat the process.

• 6. Final Pass: The final pass is always with a gap of 1. At this point, the array is nearly sorted, so a standard Insertion Sort pass finishes the job very efficiently.