CS223 Algorithms D-Term 2013 Instructor: Mohamed Eltabakh WPI, CS Introduction Slide 1

Lecture Outline Introduction and Definitions Example Problems Course Logistics Slide 2

Definition An algorithm is a finite sequence of step by step, discrete, unambiguous instructions for solving a particular problem –Receives input data –Produces output data –Each instruction can be carried out in a finite amount of time in a deterministic way Slide 3

Definition In simple terms, an algorithm is a series of instructions to solve a problem (complete a task) We focus on Deterministic Algorithms –Under the same input it must produce the same output Algorithm inputoutput Well defined sequence of computer instructions Slide 4

Two Key Properties Correctness –An algorithm is correct if under all valid inputs, it produces the correct output Efficiency –Same problem can have many ways (algorithms) to solve it –Which one is more efficient? –Efficiency means: How long will it take? How much storage will it need? TimeCPU# of instructionsStorageSpaceMemory Slide 5

CS223 Algorithms D-Term 2013 Representative Problems Slide 6

Problem Family I: Sorting –Input A list of unsorted values –Output The corresponding sorted list The algorithm must know how to compare values ( ) Slide 7

Problem Family II: Searching –Input A list of values L, and a key (single value) K –Output The position in L that contain K (if exists) Search for 33? Search for C? Will it make a difference if the list is sorted ??? Slide 8

Problem Family III: Trees –Input A tree of values –Different problems Traverse the tree and list the values Search for a value in the tree Deletion from or insertion into the tree Can you notice a certain order in this tree? Binary Tree Binary Search Tree Left  smaller than Right  greater than Slide 9

Problem Family IV: Graphs –Input A graph of values G –Different problems Traverse the graph Searching for a value in the graph Shortest path from one node to another What is the shortest path from F to B? What is the shortest path from F to all other nodes? Find a minimum spanning tree? Slide 10

Problem Family V: String Processing –Input One or multiple strings –Different problems Search for one string in another Edit distance between strings String alignment Search for sentence “algorithms are fun” Find the smallest difference between this document and another document Slide 11

Too Many Others Protein networks DNA sequence alignment Matrix multiplication Scheduling problem Greatest Common Divisor (GCD) Nearest neighbor (closest gas station to me) Slide 12

Algorithm Design Phases -- What are the inputs? -- What are the outputs? -- What is the functionality? -- Correctness? -- Efficiency? Must give the correct answer under all valid inputs Analyze your algorithm * How fast is it? * Does it consume much resources (CPU, memory, disk, etc…) -- Choose a language to implement your algorithm (E.g., C, Java, Perl, etc…) -- Correct implementation !!! -- Test you algorithm -- Try different inputs -- Check special and corner cases Slide 13

Course Outline (What You Will Learn) Algorithmic Strategies and Methodologies –Tree and graph traversal, Greedy Algorithms, Dynamic Programming, Divide and Conquer Problem Types/Families –Sorting, Searching, Graph and Tree Algorithms, Scheduling and Optimization, String Processing Algorithms on Different Data Structures –Arrays, Trees, Queues, Graphs, Strings, Hash Tables, Linked Lists Analysis and Evaluation –Coding and running algorithms, –Analytical analysis using big-O notation Slide 14

CS223 Algorithms D-Term 2013 Course Logistics Slide 15

Textbook Required Introduction to Algorithms T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein. Third Edition, MIT Press, ISBN URL: Book Website Slide 16 Available in bookstore Several copies on reserve in library

Course Logistics Website: Electronic WPI system: blackboard.wpi.edu Lectures –MTRF (2:00pm - 2:50pm) Grading –All assignments are done individually Slide 17

Tentative Scheduling Tentative scheduling for assignments, exams, and quizzes –Visit the website: Late Submission Policy –One-day late  10% off the max grade –Two-day late  20% off the max grade –Three-day late  30% off the max grade –Beyond that  no late submission is accepted Slide 18

Course Management Two systems will be maintained –Web Page: –Electronic WPI system: blackboard.wpi.edu Homework/Project submissions –Either at the beginning of class on the due date –Or electronically on blackboard.wpi.edu (Recommended) Viewing Grades –On blackboard.wpi.edu Slide 19

Office Hours Posted on the course web page Covers most days of the week Make use of them– they are there for YOU ! Feel free to send me or stop by my office Slide 20

Programming Language In assignments, use a language of your choice –Most students use either Java, C, or Python In lectures, I will use pseudocode closer to Java or C Slide 21

Slide 22