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What is an Algorithm, Data Structures - Lecture Slides | CS 361L, Study notes of Computer Science

University of New Mexico (UNM) - GallupComputer Science

Material Type: Notes; Class: Data Structures and Algorithms; Subject: Computer Science; University: University of New Mexico; Term: Unknown 2003;

Typology: Study notes

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CS 361, Lecture 1
Jared Saia
University of New Mexico
Todayā€™s Outline
ā€¢Administrative Info
ā€¢Course Overview
ā€¢What is an Algorithm? Data Structure?
ā€¢Why study algorithms?
ā€¢Todo list for next class
1
CS361: Algorithms and Data
Structures
ā€¢Instructor: Jared Saia, FEC 301H (Third floor of FEC, on
the side facing Central Avenue)
ā€¢Phone: 277-5446
ā€¢Office Hours: Tuesdays 10:45-11:45, Fridays 2-3pm, or by
appointment. Note that Tuedays and Fridays are the best
time to schedule an appointment, other days Iā€™m less likely
to be in my office.
ā€¢TA: Kanglin Xu, Office Hours: TBA
2
Who am I?
ā€¢1st year as a Professor at UNM, PhD last year from University
of Washington. Masterā€™s degree from UNM.
ā€¢My research area is algorithms, My recent focus is on algo-
rithms for creating p2p networks which are provably censor-
ship resistant (check out my web page for papers)
ā€¢Call me Jared, Professor Saia, or, if you must, Herr Doktor
Saia
3
What you should know
ā€¢concept of abstract data type (ADT)
ā€¢good programming skills in C, C++, or Java
ā€¢2 semesters of calculus (infinite sums and limits, derivatives,
etc)
4
What you will learn
ā€¢Learn to analyze and improve algorithms (both to improve
time complexity and to prove correctness)
ā€¢Learn to see and solve problems abstractly
ā€¢Learn many data structures, some of which you will almost
certainly use again in your career
ā€¢Learn many algorithms, some of which you will almost cer-
tainly use again in your career
5
pf3
pf4
pf5

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Download What is an Algorithm, Data Structures - Lecture Slides | CS 361L and more Study notes Computer Science in PDF only on Docsity!

CS 361, Lecture 1

Jared Saia University of New Mexico

Todayā€™s Outline

  • Administrative Info
  • Course Overview
  • What is an Algorithm? Data Structure?
  • Why study algorithms?
  • Todo list for next class

CS361: Algorithms and Data

Structures

  • Instructor: Jared Saia, FEC 301H (Third floor of FEC, on the side facing Central Avenue)
  • Phone: 277-
  • Office Hours: Tuesdays 10:45-11:45, Fridays 2-3pm, or by appointment. Note that Tuedays and Fridays are the best time to schedule an appointment, other days Iā€™m less likely to be in my office.
  • TA: Kanglin Xu, Office Hours: TBA

Who am I?

  • 1st year as a Professor at UNM, PhD last year from University of Washington. Masterā€™s degree from UNM.
  • My research area is algorithms, My recent focus is on algo- rithms for creating p2p networks which are provably censor- ship resistant (check out my web page for papers)
  • Call me Jared, Professor Saia, or, if you must, Herr Doktor Saia

What you should know

  • concept of abstract data type (ADT)
  • good programming skills in C, C++, or Java
  • 2 semesters of calculus (infinite sums and limits, derivatives, etc)

What you will learn

  • Learn to analyze and improve algorithms (both to improve time complexity and to prove correctness)
  • Learn to see and solve problems abstractly
  • Learn many data structures, some of which you will almost certainly use again in your career
  • Learn many algorithms, some of which you will almost cer- tainly use again in your career

What you will learn (details)

  • Asymptotic analysis and recurrence relations (mathematical tools for finding the run time of an algorithm)
  • Intermediate level data structures (heaps, balanced trees, hash tables)
  • Intermediate level algorithms (sorting, introduction to graphs)
  • Basic knowledge of how to construct formal proofs regarding algorithm efficiency and correctness
  • How to code up intermediate algorithms and data structures, how to design experiments to compare efficiencies of imple- mentations

Course Assessment

Grading:

  • Class Project, 30%
  • Homeworks, 30%
  • Midterm and Final, 30% (20% final and 10% midterm)
  • Class Participation, 10%

Note on Homeworks

  • Homeworks and the project are due at the beginning of class, and should be turned in on the table in front of me.
  • Late hws will not be accepted without prior approval from Prof. Saia (easy to do for one, harder for two, very difficult for three)
  • Put pages of hw in order. We donā€™t care what order you solve the hw in, but before you turn it in, you must put the problems in order (this makes grading easier)
  • Staple hws, do not use paper clips, folding, tape, putty, gum, etc. Prof Saia and Kanglin do not bring staplers to class, so make sure you staple the hw before class (stapling helps us keep together all pages of your hw)

Working in groups

  • The class project, homeworks, and in-class exercises will be done in groups
  • Iā€™ll divide class up into groups based on pretest (and your preferences)
  • If necessary, you can switch groups or work on your own.
  • For group assignments, Iā€™ll ask you to grade the performance of your fellow group members on that assignment.

Why work in groups?

  • Many studies show that students at all levels learn signifi- cantly better by working in groups (well-prepared students learn by teaching, less-prepared students learn by peer in- struction)
  • When you get a job, you will almost certainly work in a group, so working with a group is a good skill to have
  • Will be more fun

Class Participation

  • I expect you to show up for 90% of the classes
  • There will be frequent in-class exercises
  • You can work on these with your group
  • At the end of these, I will call on a random member of a random group
  • What I expect is either a correct answer, a partial answer, an idea on how to approach the problem, or a reasonably intelligent question about the problem.

A Real Job Interview Question

The following is a question commonly asked in job interviews in 2002 (thanks to Maksim Noy, see my web page for the full compilation of questions):

  • You are given an array with integers between 1 and 1, 000 , 000.
  • All integers between 1 and 1, 000 , 000 are in the array at least once, and one of those integers is in the array twice
  • Q: Can you determine which integer is in the array twice? Can you do it while iterating through the array only once?

Solution

  • Ideas on how to solve this problem?? What if we allowed multiple iterations?

Naive Algorithm

  • Create a new array of ints between 1 and 1, 000 , 000, which weā€™ll use to count the occurences of each number. Initialize all entries to 0
  • Go through the input array and each time a number is seen, update its count in the new array
  • Go through the count array and see which number occurs twice.
  • Return this number

Naive Algorithm Analysis

  • Q: How long will this algorithm take?
  • A: We iterate through the numbers 1 to 1, 000 , 000 three times!
  • Note that we also use up a lot of space with the extra array
  • This is wasteful of time and space, particularly as the input array gets very large (e.g. it might be a huge data stream)
  • Q: Can we do better?

Ideas for a better Algorithm

  • Note that

āˆ‘n i=1 i^ = (n^ + 1)n/^2

  • Let S be the sum of the input array
  • Let x be the value of the repeated number
  • Then S = (1, 000 , 000 + 1)1, 000 , 000 /2 + x
  • Thus x = S āˆ’ (1, 000 , 000 + 1)1, 000 , 000 / 2

A better Algorithm

  • Iterate through the input array, summing up all the numbers, let S be this sum
  • Let x = S āˆ’ (1, 000 , 000 + 1)1, 000 , 000 / 2
  • Return x

Analysis

  • This algorithm takes iterates through the input array just once
  • It uses up essentially no extra space
  • It is at least three times faster than the naive algorithm
  • Further, if the input array is so large that it wonā€™t fit in memory, this is the only algorithm which will work!
  • These time and space bounds are the best possible

Take Away

  • Designing good algorithms matters!
  • Not always this easy to improve an algorithm
  • However, with some thought and work, you can almost al- ways get a better algorithm than the naive approach

Todo

  • Work on pretest, due next Tuesday!
  • Visit the class web page: www.cs.unm.edu/~saia/361/
  • Sign up for the class mailing list (cs361)
  • Start reading Chapter 1 in textbook