Insertion and Shell Sorts 2-19-2019

Learning Objective Review the Bubble, and Selection sorts Be able to describe the speed, stability and how a Insertion sort works Be able to describe the speed, stability and how a Shell sort works Write a program that uses the Shell or Insertion Sort.

Review Show after the third pass of the Bubble Sort Low High 10 6 20 15 90 12 14 Show after the third pass of the Selection Sort

Insertion Sort Can you describe how it works? Animation https://www.cs.usfca.edu/~galles/visualization/ComparisonSort.html

Insertion Sort Details Speed Stability How it works Your turn Low High 20 10 8 12 31 9 15

Procedure insertion(var theArray:theArrayType; size:integer); dummy:integer; pass, check:integer; Begin for pass:= 2 to size do begin dummy:= theArray[pass]; check := pass-1; while (theArray[check]>dummy) and (check>=1) do theArray[check+1] := theArray[check]; check:=check-1; end; theArray[check+1] := dummy; End;

Shellsort Founded by Donald Shell and named the sorting algorithm after himself in 1959. 1st algorithm to break the quadratic time barrier O(n^2) but few years later, a sub quadratic time bound was proven Shellsort works by comparing elements that are distant rather than adjacent elements in an array or list where adjacent elements are compared.

Shellsort How it works Uniquely grouped insertion sort.

Shellsort Shellsort is also known as diminishing increment sort. The distance between comparisons decreases as the sorting algorithm runs until the last phase in which adjacent elements are compared

Empirical Analysis of Shellsort (Advantage) Advantage of Shellsort is that its only efficient for medium size lists. For bigger lists, the algorithm is not the best choice. Speed: Different sources with different speeds. O(N1.25) 5 times faster than the bubble sort and a little over twice as fast as the insertion sort, its closest competitor. Not Stable

Empirical Analysis of Shellsort (Disadvantage) Disadvantage of Shellsort is that it is a complex algorithm and its not nearly as efficient as the merge, heap, and quick sorts. The shell sort is still significantly slower than the merge, heap, and quick sorts, but its relatively simple algorithm makes it a good choice for sorting lists of less than 5000 items unless speed important. It's also an excellent choice for repetitive sorting of smaller lists.

Shellsort Best Case Best Case: The best case in the shell sort is when the array is already sorted in the right order. The number of comparisons is less.

Shellsort Example Sort: 18 32 12 5 38 33 16 2

Shell Sort Summary Speed: O(n^1.25) Stability: Not Stable How it works: A uniquely grouped insertion sort.

procedure shellSort(var numbers:ArrayType; size:integer); pass, check, increment, dummy : integer; begin increment := size DIV 2; while (increment > 0) do for pass:= 2 to size do //Insertion Sort check := pass; dummy := numbers[pass]; //Dummy while ((check >= increment) AND (numbers[check-increment] > dummy))do numbers[check] := numbers[check - increment]; //Slide check := check - increment; end; numbers[check] := dummy; // Back if (increment div 2 <> 0) then increment := increment div 2 else if (increment = 1) then increment := 0 else increment := 1; end; //Shell sort procedure Shell Sort Code

Shell Sort Program Options Complete one of the program options. Either Shell or Insertion. Sorting Names Input: 10 names Show the names after they are sorted using the Shell Sort. Push: Handle names entered with DiFfErEnT CaSeS. Sorting Numbers Input: 8 Numbers Show the numbers after each pass of the Shell sort. Push: Color coordinate the numbers to show which are being compared. Extension: Create your own sorting algorithm. Possibly combine the best of the algorithms discussed in class.

Insertion Sort Program Options Complete one of the program options. Either Shell or Insertion. Sort Race Randomly generate 50000 integers (from 1-100) Time how long it takes the insertion sort to put the values in order. Push: Time sorting the same values with all of the sorts and rate their speed. Name, height (in inches) Sort Input: 10 names and heights Output: The names and corresponding heights in a chart sorted by age using an Insertion sort. Push: Let the user decide if they want to sort by height or name, then sort and show the chart. Push: Input an unknown number of names and heights to sort.