Algorithms & Data Structures - David Vernon

617 Pages·2007·0.75 MB·English

by  David Vernon

Algorithms & Data Structures
David Vernon
Copyright ©2007 David Vernon (www.vernon.eu)
Course Content
Introduction to Complexity of Algorithms
•
– Performance of algorithms
– Time and space tradeoff
– Worst case and average case performance
– The big O notation
– Example calculations of complexity
Complexity and Intractability
•
– NP Completeness and Approximation
Algorithms
Copyright ©2007 David Vernon (www.vernon.eu)
Course Content
Simple Searching Algorithms
•
– Linear Search
– Binary Search
Simple Sorting Algorithms
•
– Bubblesort
– Quicksort
Copyright ©2007 David Vernon (www.vernon.eu)
Course Content
Abstract Data Types (ADTs)
•
Lists, Stacks, and Queues
•
– ADT specification
– Array implementation
– Linked-list implementation
Copyright ©2007 David Vernon (www.vernon.eu)
Course Content
Trees
•
– Binary Trees
– Binary Search Trees
– Traversals
– Applications of Trees
» Huffman Coding
– Height-balanced Trees
» AVL Trees
» Red-Black Trees
Copyright ©2007 David Vernon (www.vernon.eu)
Introduction to
Analysis of Algorithms
&
Complexity Theory
Copyright ©2007 David Vernon (www.vernon.eu)
Complexity
Analysis of complexity of programs
•
– Time complexity
– Space complexity
– Big-Oh Notation
Introduction to complexity theory
•
– P, NP, and NP-Complete classes of
algorithm
Copyright ©2007 David Vernon (www.vernon.eu)
Complexity
Suppose there is an assignment
•
statement
x := x +1
in your program.
We’d like to determine:
•
– The time a single execution would take
– The number of times it is executed
FFrreeqquueennccyy CCoouunntt
Copyright ©2007 David Vernon (www.vernon.eu)
Complexity
Product of time and frequency is the
•
total time taken
Frequency count will vary from data set
•
to data set
Copyright ©2007 David Vernon (www.vernon.eu)
Complexity
Since the execution time will be very
•
machine dependent (and compiler
dependent), we neglect it and
concentrate on the frequency count
Consider the following three examples:
•
Copyright ©2007 David Vernon (www.vernon.eu)