1. Advanced Data Structures
Cpt S 223
Advanced Data Structures
Washington State University

2. Topics Data structures Algorithm design & analysis Queue Tree Graph
Cpt S 223
Topics
Data structures
Algorithm design & analysis
Queue
Tree
Graph
Washington State University

3. What is a “data structure”?

4. Why study data structures?
Cpt S 223
Why study data structures?
Example problem
Given: a set of N numbers
Goal: search for number k
Solution
Store numbers in an array of size N
Linearly scan array until k is found or array is exhausted
Number of checks
Best case: 1
Worst case: N
Average case: N/2 3 7 6 1 10 8 43
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5. Why study data structures?
Cpt S 223
Why study data structures?
Solution #2
Store numbers in a binary search tree
Search tree until find k
Number of checks
Best case: 1
Worst case: log2N
Average case: (log2N)/2 7 3 10 1 6 8 43
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6. Analysis Does it matter? N vs. log2N Cpt S 223
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7. Analysis Does it matter? Assume 1 cycle per transaction O(N) algorithm
Cpt S 223
Analysis
Does it matter?
Assume
N = 1,000,000,000
1 billion (Walmart transactions in 100 days)
1 GHz processor = 109 cycles per second
1 cycle per transaction
O(N) algorithm
1 billion transactions = > 1 billion clock cycles
O(lg N) algorithm
1 billion transactions => 30 clock cycles
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8. Example 2 Scheduling job in a printer
Cpt S 223
Example 2
Scheduling job in a printer
Write a code to manage the printer queue
Functions to support
Insert, delete
Special accommodations needed for:
Priority
Dynamic update
Scheduling challenges
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9. Example 3 Exploring the Facebook connection network
Cpt S 223
Example 3
Exploring the Facebook connection network
Write a code to tell who is connected to who (directly or indirectly) through your Facebook profile
6-degrees of separation
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10. Example 4 Pattern matching
Cpt S 223
Example 4
Pattern matching
Write a code to do Google search on your web database
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11. Summary Keep the data organized Choice of data structures matters
Cpt S 223
Summary
Keep the data organized
Choice of data structures matters
Appropriate data structures ease design & improve performance
Challenge
Design appropriate data structure & associated algorithms for a problem
Analyze to show improved performance
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12. Queue ADT
Like a stack, a queue is also a list. However, with a queue, insertion is done at one end, while deletion is performed at the other end.
Accessing the elements of queues follows a First In, First Out (FIFO) order.
Like customers standing in a check-out line in a store, the first customer in is the first customer served.

13. : Basic operations enqueue: insert an element at the rear of the list
dequeue: delete the element at the front of the list

14. Implementation of Queue
Just as stacks can be implemented as arrays or linked lists, so with queues.
Dynamic queues have the same advantages over static queues as dynamic stacks have over static stacks

15. Trees Linear access time of linked lists is prohibitive
Does there exist any simple data structure for which the running time of most operations (search, insert, delete) is O(log N)?
Trees
Basic concepts
Tree traversal
Binary tree
Binary search tree and its operations

16. Trees A tree T is a collection of nodes T can be empty
(recursive definition) If not empty, a tree T consists of
a (distinguished) node r (the root),
and zero or more nonempty subtrees T1, T2, ...., Tk

17. Continue..

18. Tree Traversal Used to print out the data in a tree in a certain order
Pre-order traversal (Root, left, right)
Print the data at the root
Recursively print out all data in the leftmost sub tree
Recursively print out all data in the rightmost sub tree

19. Continue…

20. Continue…. Inorder traversal (left, root, right)
Recursively print out all data in the leftmost sub tree
Print the data at the root
Recursively print out all data in the rightmost sub tree

21. Continue…

22. Continue.. Post-order traversal (left, right, root)
Recursively print out all data in the leftmost sub tree
Recursively print out all data in the rightmost sub tree
Print the data at the root

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24. Binary Trees
A tree in which no node can have more than two children

25. Continue..
The depth of an “average” binary tree is considerably smaller than N, even though in the worst case, the depth can be as large as N – 1.

26. Binary Search Trees (BST)
A data structure for efficient searching, inser-tion and deletion
Binary search tree property
For every node X
All the keys in its left subtree are smaller than the key value in X
All the keys in its right subtree are larger than the key value in X

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28. Graph
A Simple graph G = (V, E) consists of a nonempty set V of vertices and a possibly empty set E of edges, each edge being a set of two vertices from V.
The number of vertices and edges are denoted by |V| and |E|, respectively.

29. Graph Representation There are variety of ways to represent a graph.
Adjacency lists.
An adjacency matrix of graph G = (V, E) is a binary |V| x |V| matrix such that each entry of this matrix
An incident matrix of graph G = (V, E) is a binary |V| x |E| matrix such that each entry of this matrix

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31. Continue..
Adjacency matrix
Incident matrix

32. Graph Traversal
As in trees, traversing a graph consists of visiting each vertex only one time. The simple traversal algorithm used for trees can not be applied here because graph may include cycles (result in to infinite loop) or, isolated vertices (left some nodes).
The most popular algorithms for traversing in graphs are:
Depth First Search
Breadth First search

33. Thank you