COMP3001/3901 Algorithms
Lecture 1
Introduction
COMP3001/3901 Algorithms
• Two lectures
– Tuesday (10 -11 am in Carslaw Theatre 157)
– Wednesday (10 -11 am in Chemistry Theatre 1)
• One tutorial
• http://www.it.usyd.edu.au/~shhong/comp3001.html
• Dr. Seokhee Hong
([email protected], Madsen G86, 9351-6092)
• Consultation time: Wednesday 3-4pm.
Textbook & References
Introduction to Algorithms, second edition
by Cormen, Leiserson, Rivest & Stein,
MIT Press, 2001
Solving a Computational Problem
Step 1. Problem definition & specification
– specify input, output and constraints
Step 2. Algorithm design & analysis
• The Design and Analysis of Computer
Algorithms, by Aho, Hopcroft and Ullman
• Algorithmics: Theory & Practice, by Brassard
& Bratley
• Fundamentals of data structures in C(C++), by
Horowitz, Sahni and Anderson-Freed
– devise a correct & efficient algorithm
This
course
Step 3. Implementation (coding)
Step 4. Testing
Step 5. Verification
• Algorithms, by Sedgewick
Aim
• Primary aim: Develop thinking ability
– problem solving skills
(algorithm design and application)
– formal thinking
(proof techniques & analysis)
• Secondary aim: have fun with algorithms
To achieve the aim, we will…
• Examine interesting problems
• Devise algorithms for solving them
• Prove their correctness
• Analyze their runtime performance
• Study advanced data structures & core
algorithms
• Learn problem-solving techniques
• Applications in real-world problems
1
Specific Goals
• Be familiar with a collection of core algorithms
• Be fluent in algorithm design paradigms: divide &
conquer, greedy algorithms, dynamic programming.
• Be able to analyze the correctness and runtime
performance of a given algorithm
• Be familiar with the inherent complexity (lower
bounds & intractability) of some problems
• Be familiar with advanced data structures
• Be able to apply techniques in practical problems
Assessment
• Assignments (20%): 2 assignments (10% each)
• Tutorial (10%)
• Written exam (70%): closed book
• Assignments
– Week 6: September 4
– Week 12: October 23
– Submit to your tutor.
– Exact deadline: tutorial? Or same deadline?
Assignments
• Late policy: within one week (-50%)
– No submission allowed after one week.
• Plagiarism is not allowed.
– For details, see USyd code of practice on plagiarism.
– http://www.usyd.edu.au/su/planning/policy/exams/14_0pla.html
• Be neat, clear, precise and formal
– you will be graded on correctness, time complexity, simplicity,
elegance & clarity.
Assumed Knowledge
• We assume that you know the basic material in the following
chapters: chapter 2, 3, 4, 6, 7, 10, 11, 12 (from DDS, 2001)
–
–
–
–
–
–
–
–
–
Basic notation: asymptotic notation
Recursion and recurrence: analyze time complexity
Sorting: heap sort, quick sort
Elementary data structures: stack, queue, linked list
Hash tables
Priority queues: heaps
Search trees: BST
Trees & tree traversal
Graphs & graph traversal
Planned Course Outline
Algorithm Analysis
• Introduction (week1)
• Divide and Conquer (week 1,2)
• Dynamic Programming (week 3,4)
• Greedy Method (week 5,6)
• Graph Algorithm (week 7,8)
• Asymptotic Notation
• Recurrence Relations
• Proof Techniques
• Inherent Complexity
• GOAL:
• Advanced Data Structure (week 9,10)
– Know how to write a problem specification.
• Advanced Topics (week 11,12)
– Know how to measure the efficiency of an algorithm.
• Review (week 13)
– Know the difference between upper and lower bounds
for an algorithm.
– Be able to prove the correctness of an algorithm.
• Note: topics are subject to change.
2
Algorithm Design Paradigms
• Divide and Conquer
Divide and Conquer
• Merge sort
• Closest pair
• Selection
• Dynamic Programming
• Greedy Methods
Greedy Algorithms
• GOAL:
– Know when the divide-and-conquer paradigm is an appropriate
one, and the general structure of such algorithms.
– Be able to characterize their complexity using techniques for
solving recurrences.
– Memorize the common case solutions for recurrence relations.
Dynamic Programming
• Huffman Codes
• Minimum Spanning Trees
• Shortest Paths
• Longest common subsequences
• Matrix chain multiplication
• Optimal binary search tree
• GOAL:
– Know when to use greedy algorithms and their essential
characteristics.
– Be able to prove the correctness of a greedy algorithm in
solving an optimization problem.
– Understand where minimum spanning trees and shortest path
computations arise in practice.
• GOAL
– Know what problem characteristics make it appropriate to
use dynamic programming and how it differs from divideand-conquer.
– Be able to move systematically from one to the other.
Graph Algorithms
• Basic Graph Algorithms: biconnected components
• Minimum Spanning Trees
• Shortest Paths
• GOAL
– Know how graphs arise, their definition and implications.
– Be able to use the adjacency matrix representation of a graph
and the edge list representation appropriately.
– Understand and be able to use the techniques as seen in the
basic graph algorithms.
Advanced Data Structures
• Heap structures: Binomial heaps, Fibonacci heaps
• Search trees: 2-3 trees, Red-Black trees
• Quad tree
• GOAL
– Know the fundamental ideas behind maintaining balance in
insertions/deletion.
– Be able to use these ideas in other balanced tree data
structures.
– Understand what they can represent and why they are
useful.
– Know the special features of the data structure listed above.
3
Advanced Topics
How to Succeed in this Course
• Case Studies of Real-World Problems: Geometric Algorithms
– Computational geometry
– Graph drawing
• Do suggested pre-reading before class.
• NP-completeness
• Approximation algorithm if time permits.
• Review after each class.
• Attend each class.
• Think in class.
• Do pre-work before tutorial.
• Attend each tutorial.
• GOAL: See how core algorithms can be put to use in real-world
applications and geometric problems.
Tutorial
• Each student must attend one tutorial per week, as allocated by
the University timetable system.
• Tutorials commence in week 2 (no tutorial in week 1).
• Attendance at your assigned tutorials is very important.
• You should have read and answered the "pre-work" before you
come to the tutorial.
• All tutorial activity is done in groups of up to 3 people.
• It is important to be able to explain your ideas to others and to
contribute effectively to a collaborative solution.
• The tutor will discuss the solution and comment on issues raised
by the exercise.
• Start early on assignments.
• Be formal and precise.
Basic Courtesy
• Write your assignments neatly & formally.
• Please do not read newspapers and other materials in class.
• When coming to the class late or leaving early, please take an
aisle seat quietly.
• Remain quiet, except asking questions or answering questions
posed by instructors.
– no whispers or private conversation.
THANK YOU!!!
• You must submit 1 page result to your tutor (10%).
COMP3901 Advanced Course
• This Advanced unit covers all the material of
COMP3001, plus extra topics.
• The two units share the same lectures, but have
different tutorials and assessment.
• There will be some lectures on advanced topics in
the tutorials.
Communications
• Pls check the course website regularly, at least once per week.
• Lecture notes will be available either on the website or at the
University Copy Centre (this will be posted on the web).
– Note that the lecture notes will not contain everything.
– You need to attend class to add your own notes.
– Some topics are subject to change.
• Tutorials will be available on the web.
– pls download & print it and Think!
• To contact me, send an email or pls use consultation hour.
• Suggested Reading for Week 1: chapter 2, 3, 4.
4