1. Data Structures (CS212D)
Overview & Review

2. Instructor Information
T.Yasmeen Albarrak
Room:

3. Course objectives Be familiar with problem solving.
Be familiar with basic techniques of algorithm analysis.
Be familiar with the concept of recursion.
Master the implementation of linked data structures such as linked lists, stacks, and queues.

4. Course objectives Cont.
Be familiar with advanced data structures such as balanced search trees, graphs and hash tables.
Master analyzing problems and writing program solutions to problems using the above techniques
Be able to select appropriate data structures and algorithms for given problems

5. Course Outline Introduction to data structures Arrays Recursion
Linked Lists
Stacks and queues
Trees
Graphs
Hash tables

6. Course Material
Textbook: Data Structures & Algorithms in JAVA (6th Edition), by M. Goodrich, R. Tamassia and M. Goldwasser , John Wiley & Sons, inc., 2014.
Lecture hand-outs
Lab notes and exercises

7. Grading/Evaluation Course Assessment Tools Percent Week Mid term 1 15%
7(29/10)
Mid term 2
11(26/11)
Lab assignments, quizzes and participation
10%
Final lab
20%
Final
40%

8. What is data? Data Types of data
A collection of facts from which conclusion may be drawn
e.g. Data: Temperature 35°C; Conclusion: It is hot.
Types of data
Textual: For example, your name (Nourah)
Numeric: For example, your ID (090254)
Audio: For example, your voice
Video: For example, your voice and picture
(...)

9. What is data structure?
A particular way of storing and organizing data in a computer so that it can be used efficiently and effectively.
Data structure is the logical or mathematical model of a particular organization of data.
A group of data elements grouped together under one name.
For example, an array of integers

10. Types of data structures
Array
Linked List
Queue
Tree
Stack
There are many, but we named a few. We’ll learn these data structures in details through this term!

11. The Need for Data Structures
Goal: to organize data
Criteria: to facilitate efficient
storage of data
retrieval of data
manipulation of data
Design Issue:
select and design appropriate data types (This is the main motivation to learn and understand data structures)

12. Data Structure Operations
Traversing
Accessing each data element exactly once so that certain items in the data may be processed
Searching
Finding the location of the data element (key) in the structure
Insertion
Adding a new data element to the structure

13. Data Structure Operations (cont.)
Deletion
Removing a data element from the structure
Sorting
Arrange the data elements in a logical order (ascending/descending)
Merging
Combining data elements from two or more data structures into one

14. Algorithm = Input + Process + Output
What is algorithm?
A finite set of instructions which accomplish a particular task
A method or process to solve a problem
Transforms input of a problem to output
Algorithm = Input + Process + Output
Algorithm development is an art – it needs practice, practice and only practice!

15. What is a good algorithm?
It must be correct
It must be finite (in terms of time and size)
It must terminate
It must be unambiguous
Which step is next?
It must be space and time efficient
A program is an instance of an algorithm, written in some specific programming language

16. Order is very important!!!
A simple algorithm
Problem: Find maximum of a, b, c
Algorithm
Input = a, b, c
Output = max
Process
Let max = a
If b > max then
max = b
If c > max then
max = c
Display max
Order is very important!!!

17. Algorithm Design: Practice
Example 1: Determining even/odd number
A number divisible by 2 is considered an even number, while a number which is not divisible by 2 is considered an odd number. Write pseudo-code to display first N odd/even numbers.
Example 2: Computing Weekly Wages
Gross pay depends on the pay rate and the number of hours worked per week. However, if you work more than 40 hours, you get paid time-and-a-half for all hours worked over 40. Write the pseudo-code to compute gross pay given pay rate and hours worked

18. Algorithm development: Basics
Clearly identify:
what output is required?
what is the input?
What steps are required to transform input into output
The most crucial bit
Needs problem solving skills
A problem can be solved in many different ways
Which solution, amongst the different possible solutions is optimal?

19. Even/ Odd Numbers Input range for num←0; num<=range; num←num+1 do
if num % 2 = 0 then
print num is even
else
print num is odd
endif
endfor

20. Computing weekly wages
Input hours_worked, pay_rate
if hours_worked <= 40 then
gross_pay ← pay_rate x hours_worked
else
basic_pay ← pay_rate x 40
over_time ← hours_worked – 40
over_time_pay ← 1.5 x pay_rate x over_time
gross_pay ← basic_pay + over_time_pay
endfor
print gross_pay

21. What is algorithm analysis?
A methodology to predict the resources that the algorithm requires
Computer memory
Computational time
We’ll focus on computational time
It does not mean memory is not important
Generally, there is a trade-off between the two factors
Space-time trade-off is a common term

22. How to analyse algorithms?
Experimental Approach
Implement algorithms as programs and run them on computers
Not a good approach, though!
Results only for a limited set of test inputs
Difficult comparisons due to the experiment environments (need the same computers, same operating systems, etc.)
Full implementation and execution of an algorithm
We need an approach which allows us to avoid experimental study

23. How to analyse algorithms?
Theoretical Approach
General methodology for analysing the running time
Considers all possible inputs
Evaluates algorithms in a way that is independent from the hardware and software environments
Analyses an algorithm without implementing it
Count only primitive operations used in an algorithm
Associate each algorithm with a function f(n) that characterises the running time of the algorithm as a function of the input size n
A good approximation of the total number of primitive operations

24. Primitive Operations Basic computations performed by an algorithm
Each operation corresponding to a low-level instruction with a constant execution time
Largely independent from the programming language
Examples
Evaluating an expression (x + y)
Assigning a value to a variable (x ←5)
Comparing two numbers (x < y)
Indexing into an array (A[i])
Calling a method (mycalculator.sum())
Returning from a method (return result)

25. Counting Primitive Operations
Total number of primitive operations executed
is the running time of an algorithms
is a function of the input size
Example
Algorithm ArrayMax(A, n) # operations
currentMax ←A[0] 2: (1 +1)
for i←1;i<n; i←i+1 do 3n-1: (1 + n+2(n- 1))
if A[i]>currentMax then 2(n − 1)
currentMax ←A[i] 2(n − 1)
endif
endfor
return currentMax 1
Total: 7n − 2

26. Algorithm efficiency: growth rate
An algorithm’s time requirements can be expressed as a function of (problem) input size
Problem size depends on the particular problem:
For a search problem, the problem size is the number of elements in the search space
For a sorting problem, the problem size is the number of elements in the given list
How quickly the time of an algorithm grows as a function of problem size -- this is often called an algorithm’s growth rate

27. Algorithm growth rate
Which algorithm is the most efficient? [The one with the growth rate Log N.]

28. Homework
Write an algorithm to find the largest of a set of numbers. You do not know the number of numbers.
Write an algorithm that finds the average of (n) numbers.
For example numbers are [4,5,14,20,3,6]s