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 T%  $          !" #% b$R2pMc³ SC۰b$xӆyDF 3O73۰B$:~g`(G5۰b$Vï^>{O#߫i@<۰b$)B_Z $ʚ;+4ʚ;g4UdUd@t@ppp@ <4!d!d,gX<4dddd,gXg4\d\d4@@8p@ pp>___PPT9 h___PPT2001D<4X?-"2003 W L Truppel bCS 14: Intro. Data Structures & Algs. " Lecture 2O =ZU%Intro to Data Structures & AlgorithmsWagner Truppel Lecturer, Dept. of Computer Science & Engineering UC Riverside wagner@cs.ucr.edu http://www.cs.ucr.edu/~wagner http://www.cs.ucr.edu/cs14zO  O`a~AAnnouncements IVEmail us using only your UCR address If you re not a CS or ENG major, use the account created for you in the lab Example: cs14ab@cs.ucr.edu TAs and I will not reply to messages with non-UCR addresses Email with missing information Please make your messages easy for us to deal with so that you can get a prompt reply Include your complete name, student ID, the course you re taking, your lecture section, and your lab section %ZZZZZv+c    > BAnnouncements IINWe re not using ilearn/Blackboard Class mailing list See the course web page for directions You must add yourself to the list Read it frequently! You can only sign in with a UCR address Use the list to ask questions and interact with us and with other CS 14 students No postings containing codep6-+Today s TopicskTesting ADTs C++ Exceptions Algorithm Quality Introduction to Complexity Theory Review of C++ TemplateslZl^m `Suppose I give you some code and claim that it performs some function. How can you verify my claim ? Example: I give you a Counter class and I claim it does indeed implement the ADT Counter interface. How can you prove that it does ? You could look at the source code& What if the source code isn t available ? You can verify adherence to the ADT interface but that isn t enough Verifying adherence to the full ADT is more difficultZ#Z*ZzZ{0-*$ 2t  Testing ADTsTo verify full compliance to an ADT you need to test the axioms defined by the ADT Example: ADT Counter axioms get(new()) = 0 get(inc(c)) = get(c) + 1 How do you test the axioms ? Counter c = Counter(); if (c.get() == 0) print  Fine. ; else print  Test failed. ; int old = c.get(); c.inc(); int new = c.get(); if (old + 1 == new) print  Fine. ; else print  Test failed. ;oZ(ZZZ "', Ou  Testing ADTsStill not enough, however& Testing can only show the presence of errors, not their absence ! The more you test, the more confident you become Two kinds of test environments Black-box test Use only the ADT axioms to come up with test cases White-box test Look at the source code to come up with test cases In this week s lab you ll have a chance to implement and test the ADT Counter DZBZPZZ3ZZ3ZNZZ   P3  2MEC++ ExceptionszSay that you re writing a program that reads and writes files When the program is running, it could encounter the following problems can t read a file can t write to a file b/c it s locked can t even find the darn file Since you know these problems could happen, you safeguard your program by adding error handlingdZXZ`ZCQaF Error handling in the past set an error code and check it elsewhere return an error code and check it at the caller level just ignore the error and pray that things will work Is there a better way? If you get a problem (expected or not) and you know how to fix it, then fix it right there and then ! If you get a problem (expected or not) and you don t know how to fix it, pass it to the caller Ok& but how do you pass an error ? Easy& if errors are represented as data types, you throw themZZZ&Z9 6G You should always throw exceptions when you expect potential problems whose fault isn t your own You should throw exceptions only for exceptional cases Exceptions in C++ and in Java belong to a class hierarchy For now, use std::domain_error*}pH Xtry { & // code that might raise an exception // such as opening a file that doesn t exist, etc } catch (std::exception &e) { // here you can fix the problem if you know how // and have enough information to do so // you can also get information on the exception std::cout << e.what() << std::endl; }ZZZZZZZ , @Algorithm Quality@Effectiveness we can actually use them ! Correctness hey, if it s broken, why use it ? Finiteness it d better terminate ! Efficiency memory and time are precious Understandability if no one can understand your algorithm, what s the point in writing it ? Maintenance someone s gotta do it& ZZ Z"Z ZZ ZZZJZ ZZ "     J sComplexity TheoryDeals with efficiency only Runtime efficiency: simple instructions are assumed to take constant time Additions & subtractions Assignments Simple comparisons We re not saying that they all take the exact same amount of time  they surely don t !fe8X 58X|Complexity Theory4We re not even saying that they each take the same amount of time in different computers  they don t ! All we re saying is that the time each of those operations takes does not grow with the size of the input for (int i = 0; i < n; i++) { a[i] = 0;  !" } We say that the above loop has a runtime complexity of O(n) [ Order n ]  Order means we don t care about specific numbers but only about general behavior\Z.ZZ ~Complexity Theoryint i = 0; O(1) steps constant time binary search O(log2n) steps logarithmic growth array init O(n) steps linear growth O(1) is faster than O(log2n) which is faster than O(n) Always faster? No& for small values of n, it may be the case that the order is violated. But we never really care about small n values. Three complexity cases: worst case, best case, average case Runtime complexity depends on the input to the algorithm and not just on the algorithm itselfyZ^nZ8 Z )K  L  Complexity TheoryExample: linear search Best case: you get lucky and find it the very first time you try& O(1) ! Worst case: you get unlucky and have to check every case& O(n) Average case: you only have to check about half the number of elements& O(n/2) = O(n) (b/c constants don t matter& ) Runtime complexity depends on the input to the algorithm and not just on the algorithm itself ^E O"              Complexity Theory.Best case: the algorithm executes only the minimum number of steps needed to complete its task Worst case: the algorithm executes the maximum number of steps needed to complete its task Average case: the complexity obtained by averaging over the complexities achieved for random inputs to the algorithmd/'-"-nComplexity TheoryWhat we d always like to have: O(1) Yeah, well, dream on& what we often get are (these are fine) O(n), O(n log2n) Sometimes, we also get (great !) O(log2n) But other times, we have to bite the bullet and use algorithms that are O(n2), O(n3), or even worse There are problems for which the only exact algorithms known have an exponential runtime complexity They re the worst of the lot NaZZ!Z ZHZZdZZ Q  ! H  &    9  \ C++ Templates:Suppose you want to find the maximum of two integer values*;,] C++ TemplatesCSuppose next that you want to find the maximum of two double values*D6N A simple puzzle& <Say you have a glass of beer and another glass, of red wine.[ A simple puzzle& <Say you have a glass of beer and another glass, of red wine.PAnother puzzle& How do you swap two integers ? The integers are stored in two variables But you need a third one& @b;QA general swap functionWe d l