CPS120: Introduction to Computer Science

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CPS120 Introduction to Computer Science

• Sorting

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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

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Linked Implementation
A linked list
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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

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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.

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Trees

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

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Binary Search Trees

• A binary search tree has the shape property of a
  binary tree

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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
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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.

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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.

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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

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Sorting Algorithms

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

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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

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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

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

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Insertion Sorting
Mary Mary Gerri
Terry Gerri Kari
Gerri Kari Harry
Kari Harry Barry
Harry Barry Mary
Barry Terry Terry
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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

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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
  CO2 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

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Bubble Sort
Example of a bubble sort
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Quicksort
Based on the idea that it is faster and easier to
sort two small lists than one larger one
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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.

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Quicksort
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