Data Structures (CS212D) Overview & Review

Instructor Information T.Yasmeen Albarrak Room:2.505.21 Email: ysalbarrak@pnu.edu.sa

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.

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

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

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

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%

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 (...)

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

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!

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)

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

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

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!

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

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!!!

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

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?

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

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

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

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

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

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)

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

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

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

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