The Shell sort is a variation of the bubble sort. Instead of comparing adjacent values, the Shell sort adapts a concept from the binary search to determine a gap across which values are compared before any swap takes place. In the first pass, the gap is half the size of the array. For each subsequent pass, the gap size is cut in half. For the final pass(es), the gap size is 1, so it would be the same as a bubble sort. The passes continue until no swaps occur.

Below is the same set of values as per the bubble sort example in Chapter 18 (p. 681), showing the first pass of the Shell sort:

The pseudo-code for the Shell sort is as follows:

Create a class called ShellArray. It should create and populate an array of random integers based on a size supplied to the constructor. Implement the Shell sort as a method of this class. Create a driver class to instantiate and sort several different arrays of different sizes.

Hint: Implement a toString method for the ShellArray class, so it is easy to output the results of each swap to demonstrate that your algorithm is working correctly.

9 6 8 12 3 1 7 -- size of array is 7, so gap would be 3 9 6 8 12 3 1 7 -- 9 and 12 are already in order, so no swap A----- ---- 9 6 8 12 3 1 7 -- 6 and 3 are not in order, so swap A-- -- 9 3 8 12 6 1 7 -- 8 and 1 are not in order, so swap A ------- -- 9 3 1 12 6 8 7 -- 12 and 7 are not in order, so swap A -------- - 9 3 8 7 6 1 12 -- end of pass 1 The pseudo-code for the Shell sort is as follows: gap = size / 2 do until gap nums + gap] swap num [s] with num( 3 + gap] swapflag = true end-if end-for end-do gap = gap / 2 end-do 9 6 8 12 3 1 7 -- size of array is 7, so gap would be 3 9 6 8 12 3 1 7 -- 9 and 12 are already in order, so no swap A----- ---- 9 6 8 12 3 1 7 -- 6 and 3 are not in order, so swap A-- -- 9 3 8 12 6 1 7 -- 8 and 1 are not in order, so swap A ------- -- 9 3 1 12 6 8 7 -- 12 and 7 are not in order, so swap A -------- - 9 3 8 7 6 1 12 -- end of pass 1 The pseudo-code for the Shell sort is as follows: gap = size / 2 do until gap nums + gap] swap num [s] with num( 3 + gap] swapflag = true end-if end-for end-do gap = gap / 2 end-do