Data Structures and Algorithm Analysis Introduction

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Data Structures and Algorithm AnalysisIntroductio
n

• Lecturer Ligang Dong, egan 
• Email donglg_at_zjgsu.edu.cn
• Tel [phone]
• Office SIEE Building 305

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Textbook

• Mark Allen Weiss, Data Structures and Algorithm
  Analysis in C, China Machine Press.
• E-book is available. http//netcom.zjsu.edu.cn/per
  son/dlg/data_structure.htm

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Scheduling

• Instruction Lectures Tuesday 805am
• Programming Practices Friday 950am

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Grading

• Final exam 55
• Weekly Homeworks45(153)
• Posted every Tuesday
• Due Next Tuesday before class (solution posted
  after class)
• If you have difficulties in solving the homework,
  please ask for help during Programming Practices
  in Friday.
• No late submission accepted

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Why Learn Data Structures and Algorithms?

• One of the basic rules concerning programming is
  to break the program down into modules.
• Each module is a logical unit and does a specific
  job. Its size is kept small by calling other
  modules.
• Two types of modules
• data module ------ data structure
• procedure module ------ algorithm

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Why Learn Data Structures and Algorithms?

• Modularity has several advantages.
• It is much easier to debug small routines than
  large routines
• It is easier for several people to work on a
  modular program simultaneously
• A well-written modular program places certain
  dependencies in only one routing, making changes
  easier.

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What are Data Structures and Algorithms?

• Data Structures are methods of organizing large
  amounts of data.
• An algorithm is a procedure that consists of
  finite set of instructions which, given an input
  from some set of possible inputs, enables us to
  obtain an output through a systematic execution
  of the instructions.

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Data Structure
ADT(Abstract Data Types)
Algorithms
Programming Languages
Programs
Software
Software Engineering
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Abstract Data Types (ADTs)

• An abstract data type (ADT) is a set of objects
  such as lists, sets, and graphs, along with their
  operations (e.g., insert, delete)
• Integers, reals, and booleans are data types.
  Integers, reals, and booleans have operations
  associated with them, and so do ADTs.
• Nowhere in an ADTs definition is there any
  mention of how the set of operations is
  implemented.

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Example

• Problem Given 10 test results (80, 85, 77, 56, 68
  , 83, 90, 92, 80, 98) of C language programming
  of Tom, what is the average score?

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Example

• Solution
• main()
• int sum,average
• int t1,t2,t3,t4,t5,t6,t7,t8,t9,t10
• t180t285t377t456t568
• t683t790t892t980t1098
• sum t1t2t3t4t5t6t7t8t9t10
• averagesum/10
• printf(Sumd\n,sum)
• printf(Averaged\n, average)

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Example
By using an array instead of n variables, with a
loop instead of n assignments, the program is
simpler.

• Better Solution
• main()
• int sum,averageint i
• int t10 80,85,77,56,68,83,90,92,80,98
• sum0
• for(i0 ilt10 i)
• sumsumti
• averagesum/10
• printf(Sumd\n,sum)
• printf(Averaged\n, average)

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Contents

• Chapter 1 Introduction(0.5 Week)
• C Review(1.5 Week)
• Chapter 2 Algorithm Analysis(1 Week)
• Chapter 3 Lists, Stacks, and Queues(1 Week)
• Chapter 4 Trees (2 Weeks)
• Chapter 5 Hashing(1 Week)
• Chapter 6 Priority Queues (Heaps) (1 Week)
• Chapter 7 Sorting (2 Weeks)
• Chapter 8 Disjoint Set ADT(1 Week)
• Chapter 9 Graph Algorithms(2 Weeks)
• Chapter 10 Algorithm Design Techniques (2 Weeks)

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Mathematical Foundation
Series and summation 1 2 3 . N
N(N1)/2 (arithmetic series)
1 r2 r3 rN-1 (1- rN)/(1-r),
(geometric series)
? 1/(1-r) , r lt 1, large N
Sum of squares 1 22 32 N2 N(N
1)(2N 1)/6
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Mathematical Foundation
logxa b if xb a
we will use base 2 mostly, but may use other
bases occasionally
Will encounter log functions again and again!
log (ab ) log a log b log (a/b ) log a -
log b log ab b log a
logba logca/ logcb
alog n nlog a
amn (am )n (an)m
amn am an
(2?n)0.5 (n/e)n ? n? ? (2?n)0.5 (n/e)n
(1/12n)
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Mathematical Foundation

• Proof Method1 Proof By Induction
• Prove that a property holds for input size 1
• Assume that the property holds for input size n.
  Show that the property holds for input size n1.
• Then, the property holds for all input sizes, n.

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Mathematical Foundation

• Example of Proof By Induction Prove that the sum
  of 12..n n(n1)/2
• Holds for n 1
• Let it hold for n
• 12.n n(n1)/2
• When n1
• 12.n(n1) n(n1)/2 (n1)
  (n1)(n2)/2.

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Mathematical Foundation

• Proof Method2 Proof By Counter Example
• Want to prove something is not true!
• Give an example to show that it does not hold!

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Mathematical Foundation

• Proof Method3 Proof By Contradiction
• Suppose, you want to prove something.
• Assume that what you want to prove does not hold.
• Then show that you arrive at an impossiblity.

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Mathematical Foundation

• Example of Proof By ContradictionThe number of
  prime numbers is not finite!
• Suppose there are finite number of primes, k
  primes. (we do not include 1 in primes here)
• We know k?2.
• Let the primes be P1, P2 , Pk
• Z P1 P2 Pk 1
• Z is not divisible by P1, P2 , Pk
• Z is greater than P1, P2 , Pk Thus Z
  is not a prime.
• We know that a number is either prime or
  divisible by primes. Hence contradiction.
• So our assumption that there are finite number of
  primes is not true.

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Homework 1

• At least complete two of the following
• 1.1 Prove the following formulas
• 1.2 Write a program to solve the selection
  problem. (Suppose you have a group of n numbers
  and would like to determine the kth largest.)
• 1.3 Based on 1.2, let k n/2, show the original
  location of kth largest. And draw a table showing
  the running time of your program for various
  values of n (4ltnlt20).

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Hint

• You should submit the homework using the WS Word
  file through email.
• Your program must be submitted with output.
• DO NOT write any code until you understand what
  the program does, the design of the program, and
  the output that it produces.  Writing code before
  understanding the program will simply be a waste
  of your time, and will result in a program that
  does not work!!
• As with any large program, it is probably a good
  idea to finish the easy parts first and then
  slowly complete the harder parts.
• Develop your code in small pieces, and test each
  part of your code as you write it. 
• Your program is graded according to
  correctness, readability, robustness, efficiency.