CPS120: Introduction to Computer Science Sorting

Abstract Data Types Abstract data type: a data type whose properties (data and operations) are specified independently of any particular implementation The goal in design is to reduce complexity through abstraction

Linked Implementation A linked list

Stacks A stack is an abstract data type in which accesses are made at only one end –LIFO, which stands for Last In First Out –The insert is called Push and the delete is called Pop

Queues Queue is an abstract data type in which items are entered at one end and removed from the other end –FIFO, for First In First Out –Like a waiting line in a bank or supermarket –No standard queue terminology Insert is used for the insertion operation Remove is used for the deletion operation.

Trees ADTs such as lists, stacks, and queues are linear in nature More complex relationships require more complex structures

Binary Search Trees A binary search tree has the shape property of a binary tree

Binary Search Tree The value in any node is greater than the value in any node in its left subtree and less than the value in any node in its right subtree

Basics of Sorting When you rearrange data and put it into a certain kind of order, you are sorting the data. You can sort data alphabetically, numerically, and in other ways. Often you need to sort data before you use searching algorithms to find a particular piece of data.

Key Fields The key field is the field upon which the data is sorted. A key value is a specific value that is stored within the key field. The input size is the number of elements in a list that will eventually be sorted.

Approaches to Sorting There are two basic approaches to sorting data –The incremental approach –The divide and conquer approach. Using the incremental approach, one sorts the whole list at once using loops The divide and conquer approach splits the list up into parts and sorts each part separately. Then this approach manages to join the sorted parts together into a large sorted list

Sorting Algorithms There are a number of different sorting algorithms that are widely used by programmers. Each algorithm has its own advantages and disadvantages.

Selection Sort Sorting a List of names manually –Put them in alphabetical order Find the name that comes first in the alphabet, and write it on a second sheet of paper Cross out the name on the original list Continue this cycle until all the names on the original list have been crossed out and written onto the second list, at which point the second list is sorted

Understanding the Selection Sort The selection sort is an incremental one Every key value is examined starting at the beginning of the list. A temporary variable to "remember" the position of the largest key value By the time you have examined every key value, you swap the key value that was the largest with the last key value in the list Next, you repeat the process again from the beginning of the list, however, you will not need to compare anything to the new last key value in the list since you know it is the largest

Selection Sort Example of a selection sort (sorted elements are shaded)

The Insertion Sort The insertion sort is incremental in nature. This is similar to the way a person usually organizes a hand of playing cards. The insertion sort is relatively quick for small lists that are close to being sorted

Insertion Sorting Mary Gerri TerryGerriKari GerriKariHarry KariHarryBarry HarryBarryMary BarryTerry

Bubble Sort A sort that uses a different scheme for finding the minimum value –Starting with the last list element, we compare successive pairs of elements, swapping whenever the bottom element of the pair is smaller than the one above it

Understanding the Bubble Sort The bubble sort is an incremental sort which is usually faster than the insertion and selection sorts. A bubble sort works similarly to the release of CO 2 in carbonated soda The use of the Boolean variable causes this sort to only sweep the list one extra time after it has been fully sorted. This makes the bubble sort more efficient than a number of other incremental sorts

Bubble Sort Example of a bubble sort

Quicksort Based on the idea that it is faster and easier to sort two small lists than one larger one

Understanding the Quick Sort The quicksort is a divide and conquer algorithm and is more efficient than incremental sorts. It can be difficult to code though since it uses recursion or stacks. The original list is partitioned into two lists. –One of the lists contains elements that are greater than the first original element. –The second list contains elements that are less than or equal to the first original element.

Quicksort Pages 292–293