New Mexico Computer Science For All Sorting Algorithms Maureen Psaila-Dombrowski

Sorting Sorting is something we do without even thinking about it.  Some one deals us a hand of cards - we put them in order  Empty the dishwasher – silverware goes one place, plates and glasses go to another…. Sorting is arranging a group of things (set) according to some criteria:  Increasing/decreasing order  Size  Kind  Class  Brightness  Nearly anything that can describe the items

So What? No big deal – just sort it! But what about …

So What? OR the phone numbers of everyone in US

Sorting in Computer Science Sorting is extremely and increasingly important.  Data sets can be HUGE  Bring order to the mess  Need order to better access and use the data Goal of Sorting in Computer Science  Given a set (container) of n elements  Figure out how to sort them (the criteria to use).  Create an Algorithm to sort them  Have the computer sort them!

Sorting Algorithms Many types of sorting algorithms, a few are:  Insertion Sort  Bubble Sort  Merge Sort  Selection Sort  Quick Sort  Heap Sort  Shell Sort Each has its place Look at two of them (sort numbers in ascending order)

Insertion Sort Commonly done by everyone  don’t think about it Looks like:  Start with an Unsorted List (think of a hand of cards)  Take the first number  new Sorted List  Then ▫Take next number from Unsorted List ▫Put in its correct sorted place in the Sorted List  Keep doing that until entire Unsorted List is Sorted!

Insertion Sort - Example

Insertion Sort - Example

Insertion Sort - Example

Insertion Sort - Example

Insertion Sort - Example

Insertion Sort - Example

Insertion Sort - Example

Insertion Sort Pros ▫Very simple to understand ▫Very simple to implement ▫Little memory needed ▫Efficient for small data sets Cons ▫Takes a long time ▫Inefficient for large data sets ▫Requires a large number of operations (shifts) ▫O(n 2 )

Merge Sort Commonly used by programmers A Recursive, Divide and Conquer technique Looks like: ▫Keep Dividing the unsorted list (recursive)  smaller and smaller lists  until you get n sublists, each containing 1 element  a list of 1 element is considered sorted ▫Keep Merge and Sort pairs of lists  compare the first element in each unsorted list and put the smallest into a new sorted list  each iteration creates larger lists  repeat until all lists are sorted.

Merge Sort - Example

Merge Sort - Example

Merge Sort - Example

Merge Sort - Example

Merge Sort - Example

Merge Sort - Example

Merge Sort Pros ▫Takes less memory than other sorting methods ▫Takes less time than other sorting methods ▫O(n(logn)) Cons ▫More difficult to understand ▫More difficult to implement

Summary Sorting: arranging a group of things (set) according to some criteria (Increasing/decreasing order, Size, Kind…)  Sorting is extremely and increasingly important.  Many types of sorting algorithms Insertion Sort: Commonly done by everyone  Very simple to understand and implement, Little memory needed, Efficient for small data sets  Takes a long time, Inefficient for large data sets, Requires a large number of operations (shifts), and is O(n 2 ) Merge Sort: Commonly used by Programmers  A Recursive, Divide and Conquer technique  Takes less time and memory than other sorting methods (O(n(logn))  Somewhat more difficult to understand and implement