ITEC 2620M Introduction to Data Structures

1. ITEC 2620MIntroduction to Data Structures Instructor: Prof. Z. Yang Course Website: http://people.math.yorku.ca/~zyang/itec2620m.htm Office: DB 3049

2. Course Objective • Course is about concepts • what you can program, not how • Traditionally, second course in computer science • still separates top third of programmers • not taught in any known college diploma program • Learn and use efficient programming patterns • “an efficient programmer can often produce programs that run five times faster than an inefficient programmer”

3. Textbooks • “Data Structures and Algorithm Analysis in Java” third edition by Clifford A. Shaffer. • Lecture notes and announcements will be made available at: http://people.math.yorku.ca/~zyang/itec2620m.htm

4. Marking Scheme • Assignment 1: 10% • Midterm:30% • about 1/3 code, 2/3 concepts • Final:60% • about 1/3 code, 2/3 concepts • Late Policy • Late assignments will NOT be accepted. If you miss it for an approved excuse, the weight will be added to the midterm. NO makeup assignment will be provided. • If you miss the midterm for an approved excuse, the weight will be added to the weight of the final exam. A medical note is required. NO makeup midterm will be provided.

5. Course Organization • Key concepts first • searching, sorting, complexity analysis, linked structures • Concrete to concept • searching  sorting  complexity analysis • binary tree  recursion

6. Introduction

7. Need for Data Structure • Computer • Store and retrieve information • Perform calculation • Costs and benefits • A data structure requires a certain amount of space for each data item it stores, a certain amount of time to perform a single basic operation, and a certain amount of programming effort.

8. Problem, Algorithms and Programs • Problem: a task to be performed • Algorithm: a method or a process followed to solve a problem • Program: an instance, or concrete representation, of an algorithm in some programming language.

9. Algorithm Efficiency • Design goals: • Design an algorithm that is easy to understand, code, and debug. • Design an algorithm that makes efficient use of the computer’s resources. • Algorithm analysis

10. Three keys to programming • Algorithm Design • Sequence, branching, looping – flowcharts and pseudocode • Efficiency and time-space tradeoffs (linkages between algorithms and data structures) • Data Organization • objects and classes • data structures • Modularization • methods (modularization of algorithms) • classes and inheritance (modularization of data/objects)

11. Searching

12. Key Points • Searching arrays • Linear search • Binary search • Best, average, and worst cases

13. Searching in General • “A query for the existence and location of an element in a set of distinct elements” • Elements have searchable keys associated with a stored record. • search on keys – e.g. name • to find an element – e.g. phone number • Two goals of searching • existence  does the person exist? • location  where are they in the phone book? • Isolate searching for “keys” – all keys have the same data type

14. Definition • Suppose k1, k2, …, kn are distinct keys, and that we have a collection T of n records of the form (k1, I1), (k2, I2), …, (kn, In), where Ij is information associated with key kj. Given a particular key value K, the search problem is to locate the record (kj, Ij) in T such that kj = K. • Exact-match query • Range query

15. Review of Array Algorithms • Write a static method that determines the range (the difference between the largest and smallest element) for a fully populated array of ints. • How is the above example similar to searching? • find the largest/smallest value in a set of elements • Searching  find a given value in a set of elements

16. Searching Arrays • Write a static method that determines the location (the array index) for a given value in a fully populated array of ints, return “–1” if the value is not in the array. • Example

17. Binary Search • Make your first guess in the middle of the range. • If not the target element, determine which sub-range you have to search. • Make your next guess in the middle of this sub-range. • Repeat • Example

18. Best, Worst and Average • What’s the best case for search? • Linear  first element  1 compare • Binary  middle element  1 compare • What’s the worst case for search? • Linear  not there  n compares • Binary  not there  logn compares • What’s the average case for search? • Linear  middle element  n/2 compares • Binary  50/50…  logn - 1 compares

19. What’s the difference? • Toronto phone book  2 million names • Avg. Linear  1 million compares • Avg. Binary  20 compares • For 2 million records, binary search is 50,000 times faster on average. • What’s the cost • To do binary search, we need a sorted array • Sorting…next lecture!