In this chapter, we examine algorithms for sorting data that are more complex than the algorithms examined in Chapter 4. These algorithms are also more efficient, and one of them, the QuickSort algorithm, is generally considered to be the most efficient sort to use in most situations. The other sorting algorithms we'll examine are the ShellSort, the MergeSort, and the HeapSort.

To compare these advanced sorting algorithms, we'll first discuss how each of them is implemented, and in the exercises you will use the Timing class to determine the efficiency of these algorithms.

THE SHELLSORT ALGORITHM

The ShellSort algorithm is named after its inventor Donald Shell. This algorithm is fundamentally an improvement of the insertion sort. The key concept in this algorithm is that it compares items that are distant rather than adjacent items, as is done in the insertion sort. As the algorithm loops through the data set, the distance between each item decreases until at the end the algorithm is comparing items that are adjacent.

ShellSort sorts distant elements by using an increment sequence. The sequence must start with 1, but can then be incremented by any amount.