UMass Lowell Computer Science Analysis of Algorithms Prof. Karen Daniels Fall, 2001 Lecture 1 Introduction/Overview Wed. 9/5/01

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Nature of the Course ä Core course: required for all CS majors ä Advanced undergraduate level ä Graduate students take separate course (91.503) ä No programming required ä “Pencil-and-paper” exercises ä Lectures supplemented by: ä Programs ä Real-world examples

What’s It All About? ä Algorithm: ä steps for the computer to follow to solve a problem ä Some of our goals: ä recognize structure of some common problems ä understand important characteristics of algorithms to solve common problems ä select appropriate algorithm to solve a problem ä tailor existing algorithms ä create new algorithms

Some Algorithm Application Areas Computer Graphics Geographic Information Systems Robotics Bioinformatics Astrophysics Medical Imaging Telecommunications Design Apply Analyze

Some Typical Problems Sorting Input: Set of items Problem: Arrange items “in order” Median finding Input: Set of numbers or keys Problem: Find item smaller than half of items and bigger than half of items SOURCE: Steve Skiena’s Algorithm Design Manual (for problem descriptions, see graphics gallery at ) (for problem descriptions, see graphics gallery at Minimum Spanning Tree Input: Graph G = (V,E) with weighted edges Problem: Find subset of E of G of minimum weight which forms a tree on V Shortest Path Input: Edge-weighted graph G, with start vertex and end vertex t Problem: Find the shortest path from to t in G

Tools of the Trade ä Algorithm Design Patterns such as: ä binary search ä divide-and-conquer ä Data Structures such as: ä trees, linked lists, hash tables, graphs ä Theoretical Computer Science principles such as: ä NP-completeness, hardness Growth of Functions Summations Recurrences Sets Probability MATH Proofs Logarithms Permutations Combinations

Tools of the Trade: (continued) Algorithm Animation

Prerequisites ä Computing I (91.101) ä Computing II (91.102) ä Discrete Math I & II (92.321, ) ä Statistics for Scientists and Engineers (92.386) ä Calculus I-III ( ) Growth of Functions Summations Recurrences Sets Probability MATH Proofs Logarithms Permutations Combinations

Course Structure: 5 Parts ä Discrete Math Review ä Growth of Functions, Summations, Recurrences, Sets, Counting and Probability ä Sorting ä Heapsort, Priority Queues, Quicksort, Sorting in Linear Time, Medians and Order Statistics ä Data Structures ä Stacks and Queues, Linked Lists, Introduction to Trees, Hash Tables, Binary Search Trees, Balancing Trees: Red- Black Trees ä Advanced Techniques ä Dynamic Programming, Greedy Algorithms ä Graph Algorithms ä DFS, BFS, Topological Sort, MST, Shortest paths

Textbook - - Required: ä Introduction to Algorithms ä by T.H. Corman, C.E. Leiserson, R.L. Rivest ä McGraw-Hill + MIT Press ä 1993 ä ISBN ä see course web site (MiscDocuments) for errata Available in UML bookstore

Syllabus (current plan)

Syllabus (continued)

Important Dates ä Exam :Friday, 9/28 ä Exam (Chapters 1-6) :Friday, 9/28 ä Midterm Exam :Friday, 10/19 ä Midterm Exam (Chapters 1-10) :Friday, 10/19 ä Final Exam:TBA

Grading ä ä Homework40% ä ä Exam (Chapters 1-6) 15% (closed book) ä ä Midterm (Chapters 1-10) 20% (open book, notes ) ä ä Final Exam25% (open book, notes )

Homework 1 Wed, 9/5 Wed, 9/12 Chapters 1, 2 HW# Assigned Due Content