Shell Sort

Stats

Worst Case Performance: O(n²)

Best Case Performance: O(n log n)

Created in 1959 by Donald Shell

Psuedocode

// This is the array to be sorted
gaps = [701, 301, 132, 57, 23, 10, 4, 1]
// Start with the largest gap and work down to a gap of 1
foreach(gap in gaps) {
  // Do a gapped insertion sort for this gap size.
  // The first gap elements a[0..gap-1] are already in gapped order
  // keep adding one more element until the entire array is gap sorted
  for(i = gap; i < n; i += 1) {
    // Add gaps[i] to the elements that have been gap sorted
    // save gaps[i] in temp and make a hole at position i
    temp = gaps[i]
    // Shift earlier gap-sorted elements up until the correct location for gaps[i] is found
    for(j = i; j >= gap and gaps[j - gap] > temp; j -= gap) {
      gaps[j] = gaps[j - gap]
    }
    // Put temp (the original gaps[i]) in its correct location
    gaps[j] = temp
  }
}

Additional Info

Wikipedia Article: [http://en.wikipedia.org/wiki/Shell_sort]