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|9_*1<cb$= ۓ5m.m jb$n|_ǂmV.b$R2pMc³ SCb$;]FR? =L'b$/? kŮ\߽b$z*Tqձn b$>FB=!iP 1b$52o5#7dGuS b$rcTS b$4t=`R) b$8bL-kگ}G b$.U9+*&gHW b$c3|[ρݍy r b$l>P{-=d b$ ;-|Ps;!b$y*:Z*b$KOHT*Cb$s]'-NZR)(mb$o ̀*WsBUE+:b$tӶEy-w(`+b$T$°R+Cb$\͝JQ?֣-4,b$^ʹS1,Cb$dc3ku+ob$a(*_GBsgS-ob$V{X~ εm^{\Ib$$T۱lqc] b$zSrmOuZhb$/ ̯ڏp1]=b$su+H-֌l|P2b$)B_Z {O#߫iTrb$;ȍQԟ"`,Tvb$x$Y[b$* #_t+$b$E|+"*)b$#z[JCQwo6 K$$b$ lB2 Qńfz1b$J:+z'O/Gb$ >MA4to0)=eb$U66lRך_t vc $ 3f3@8d >$ʚ;+4ʚ;g4UdUd@l2J0ppp@ <4!d!d`@)gʚ;<4dddd`@)gʚ;g4\d\d@l2Jp@ pp>___PPT9 h___PPT2001D<4X?-*1.2 2003 W L Truppel \CS 14: Intro. Data Structures & Algs. " Week 1O =Welcome to CS 14Wagner Truppel Lecturer, Dept. of Computer Science & Engineering UC Riverside wagner@cs.ucr.edu http://www.cs.ucr.edu/~wagner http://www.cs.ucr.edu/cs14zO  ՔO`Քa~Քn\Today s TopicsCourse information Structure is much like CS 12 Guest talks Email & Mailing List HWs and Quizzes Lectures don t cover everything Lectures also cover stuff not in the book Regarding my slides A cool algorithm to get you warmed up Quick weekday calculations\ZZ&ZZ&Qo]Weekday calculation&Definition: Special Day (SD): last day of February 2003 s SD is a Friday Even months (other than Feb): Apr: 4/4, Jun: 6/6, Aug: 8/8, Oct: 10/10, Dec: 12/12 are all SDs Odd months (other than Jan): < 7: add 4 Mar: 3/7, May: 5/9 are SDs > 7: subtract 4 Sep: 9/5, Nov: 11/7 are SDs Jul: 7/4 (Independence Day) is a SD Jan 3 is the same as Feb 28 Jan 3 is a SD in non-leap years Jan 4 is a SD in leap years2 Z>ZZAZZ ZZZZ$ZZ<Z  /A    $<>?'|(This Week s Topics IOverview of Data Structures & Algorithms Data Abstraction: Interface Implementation Some notation to describe interfaces Syntax and Semantics, Axioms Abstract Data Types (ADTs) ADT example: Counter Testing ADTst;ZZ]ZZ Z;] $*This Week s Topics IIO Review of Recursion (no slides yet) Review of C++ Templates C++ ExceptionsP$,O>3Overview of DS & AsCS 14 is about how to store, retrieve, and manipulate data efficiently storage/retrieval Data Structures data manipulation Algorithms In CS 10, you learned to crawl& In CS 12, you learned to walk& In CS 14, you ll learn how to run!   _@5Overview of DS & AsRThe  bookstore example How do you find the book you re looking for ? You need to use some kind of algorithm and& & of course, we want the best algorithm possible, but& & what  best means will depend on how the books are organized (stored). Data structures and algorithms are always intertwined.@ZZ7Z7RFMessyBookPile, Inc. TThis bookstore keeps its books all in one big pile, with no organization of any kindUUSGLongBookShelf, Inc.  saLongBookShelf, Inc.  tbLongBookShelf, Inc.  ucLongBookShelf, Inc.  vdLongBookShelf, Inc.  weLongBookShelf, Inc.  xfLongBookShelf, Inc.  ygLongBookShelf, Inc.  zhLongBookShelf, Inc.  {iLongBookShelf, Inc.  |jLongBookShelf, Inc.  ZLLongBookShelf, Inc.  kLongBookShelf, Inc.  lLongBookShelf, Inc.  mLongBookShelf, Inc.  nLongBookShelf, Inc.  l[LongBookShelf, Inc.  VJBinaryBooks, Inc.  oBinaryBooks, Inc.  pBinaryBooks, Inc.  rBinaryBooks, Inc.  sBinaryBooks, Inc.  tBinaryBooks, Inc.  uBinaryBooks, Inc.  MBCategoriesRUs, Inc.  LABottom line& :The choice and efficiency of an algorithm depends on how the data it accesses is organized Likewise, how you re going to store your data depends on what you want to do with it. For example, if you don t care about searching, you might not care if the algorithm is linear search or binary search. That, in turn, helps you decide on which data structure to use to store your data. In addition, a data structure depends on the properties of the data they store Pile of books: requires equality operator Sorted books: requires less than operatornZ  !  NCInterface x Implementation:Consider an int variable int is a data type It could be that the computer you re using stores int s in 1 s complement or 2 s complement format When you use it, you don t care how it s really implemented inside the computer All you care is that the following operations are defined for that particular data type: +, -, *, /, <, >, <=, >=, ==, !=, ++, -- A data type like that is called an Abstract Data Type or ADT8Z)Z=Z  2#> @:ODInterface x ImplementationzSo what you usually care about is the interface of an ADT, not its implementation The interface of an ADT is the set of operations defined for it So, in the bookstore example, you could create a general interface for your bookstore, and then have as many individual implementations as you wanted This sounds like OOP& T>Z  @`MInterface x Implementation)Note that BookSet is an abstract class !J*Z  , aQInterface x Implementation:Consider an int variable int is a data type It could be that the computer you re using stores int s in 1 s complement or 2 s complement format When you use it, you don t care how it s really implemented inside the computer All you care is that the following operations are defined for that particular data type: +, -, *, /, <, >, <=, >=, ==, !=, ++, -- A data type like that is called an Abstract Data Type or ADT 8Z) uZ=Z  2#> @:bRInterface x ImplementationA data type like that is called an Abstract Data Type or ADT Well& not quite: an interface alone does not define an ADT (more on this later) Still& an interface is part of the definition of an ADT How do you describe an interface? We need some notation& XZ#e]cSNotation"Say we want to describe what the operation + does to integers + takes two ints as its operands it s a binary operation + produces an int as a result Same with  But there s another kind of  operation: It takes one int and changes its sign a unary operation In general, then, we need to specify the number of operands and their types (can anyone say signature?), as well as the type of the result >ZYZ5Z:ZZZ+       \ %  >J7NdTNotation+ : int X int int (binary +)  : int X int int (binary  )  : int int (unary  ) Don t panic ! This is just a convenient notation. No deep concepts involved here& Now, is this enough though ? The function int f(int a, int b) { return a; } satisfies the definition for + but it does not correspond to addition !nZ}ZmZ#%}#*ZeUSyntax and SemanticsEThe interface (ie, set of operations) defines the syntax of the ADT We also need to define its semantics Say again ? Take English as an example: The computer went out for lunch. It satisfies the grammatical rules of English (its syntax) It makes no sense, though It violates the semantics of English Semantics defines meaningZZZ2' (T,    5fV Quick SummaryThus, we have: ADT Interface (operations syntax) Axioms (expected semantics) Implementation An ADT is made of an interface and its semantics The semantics is like a contract: It specifies what is expected from the operations defined by the interface;SK;0#KgWBack to + and  Interface (syntax): + : int X int int (binary +)  : int X int int (binary  )  : int int (unary  ) Semantics (contract): + does indeed add its operands Binary  does indeed subtract its operands from one another in a specified order Unary  does indeed change its operand s sign Interface + semantics = ADTFZoZZZZ #%%O'hXAnother example: CounterWe want to define an ADT called Counter What is it good for? Counts up. What should its interface (syntax) be? get: to access the counter s current value inc: to increment the counter s current value Hmm& ok, but just b/c we called them that, it doesn t mean that they do what we expect them to do How do we describe the semantics of the Counter interface? We need more notation: axioms~oZYZZo(+iYCounter adt CounterADT //  filename uses Integer // other adt s used defines Counter // name of type defined operations get: Counter int //  observer inc: Counter Counter //  modifier new: Counter //  constructor preconditions // none for this adt axioms //  contract get( new() ) = 0 // new starts at 0 get( inc(c) ) = get(c) + 1 // inc s by 1 vZ& %N?=)2jZCounterfOk, now what? Now we have an ADT (an interface) for a data type which counts up from zero in steps of 1 Nowhere we said anything about how to implement this ADT Data structures are typically ADTs They define a set of operations and the corresponding semantics But they can be implemented in many different ways, each with its own advantages and disadvantages*p^ Testing ADTsdSuppose I gave you some code and claimed 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-*$ 2q_ 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 "', Or` Testing ADTs`Still 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 casesBP33   P3  3x C++ Templates:Suppose you want to find the maximum of two integer values*;,y C++ TemplatesCSuppose next that you want to find the maximum of two double values*D6z 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.|Another puzzle& How do you swap two integers ? The integers are stored in two variables But you need a third one& @b;}A general swap functionWe d like to be able to say: Give me two values of some type T and I ll swap them with this functionFZHZ '~No problem, right ?fWe could simply write this: void swap(T & var1, T & var2) { T temp = var1; var1 = var2; var2 = temp; }Z Z)ZZ  (No problem, right ?OWe need to tell the compiler that T is a parameter and not an actual type. How?LPZ" Class templateshWe ve       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy{|}~seen function templates (also referred to as template functions) We can also have class templates (never referred to as template classes) Same basic idea, same basic syntax)"($ )($Class templatesWtemplate class Pair { private: T first; T second; public: Pair(const T & frst, const T & sec); T getFirst() const; } template Pair::Pair(const T & frst, const T & sec) { first = frst; second = sec; } Inside the class, just use T as if it was some specific type (class or not) Member functions are then template functionsZ ZZZ9ZcZyZ                 (]PR7Class templates7template class Pair { private: T first; T second; public: Pair(const T & frst, const T & sec); T getFirst() const; } How to use it? Just as before, but now you need to specify what type to use: Pair point(2, 7); // a two dimensional point Pair glasses(Lens(), Lens()); // a pair of lensesNZ ZZZ9ZZZ                U..>R`cCranky Compilers,Many compilers don t like templates very much Make sure to put your template definitions in the same file where they re used, and before they re used$C++ ExceptionsSay 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 because it s locked can t even find the darn file Since you know these problems could happen, you safeguard your program by adding error handlingdZ\Z`ZGQa ZError handling in the past set an error code and check it elsewhere return an error code and check it at the caller level (we did that in CS 12, remember ?) 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 them like the proverbial hot potatoZZZEZ9 6$ hYou 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 There are many kinds of exceptions You can create your own For now, however, use std::domain_errorDZcZ}Qc `try { // & // 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; }Z]ZZZZ] ,/P4psxHH@Rg(HH(dh   ` www3ff` 3fff` ___>?" dF@,?n<d@uA @ " d`  n?" dd@   @@``PR   @ ` `P0p>> z-*1.2 2003 W L Truppel \CS 14: Intro. Data Structures & Algs. " Week 1  h( = 2  N`X?"! :    NXgֳgֳ ?"  T Click to edit Master title style! !<  HXgֳgֳ ?"  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  NPJgֳgֳ ?"`  Z*    NJgֳgֳ ?"`P   l*0    N0Jgֳgֳ ?"`P  \*   N  6n޽h? ? www3ff $Blank PresentationM  -*1.2 2003 W L Truppel \CS 14: Intro. Data Structures & Algs. " Week 1 ;3  ( |  B  N1?"442  NPJ?"! :    NJgֳgֳ ?"`  T Click to edit Master title style! !  HpJgֳgֳ ?"P   W#Click to edit Master subtitle style$ $  NJgֳgֳ ?"`  Z*    NJgֳgֳ ?"`P   l*0    N0Jgֳgֳ ?"`P  \*   N  6n޽h? ?  www3ff `<f(  < < 0 "P    R*   < 0 "    T*  r < c $ ?"  $ < 0 " @  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S < 6@ "`P   R*   < 6 "`   T*  H < 0޽h ? ̙33F D( @ $  D D 0p[S "P    ECS 14 week 1 slides  D 0 "    T*   D 6p0H "`P   ECS 14 week 1 slides  D 6X "`   T*  H D 0޽h ? ̙33  @ L(  P   c $* "P    c $ * "P   B  s *޽h ? 3ff*   pX( 00//   s *R"     s *pR"`  B  s *޽h ? 33̙ff   ( 00// l  C 0R   l  C R  H  0޽h ? www3ff   L(    c $XS"     c $VS"0  B  s *޽h ? 33̙ff*   `X( 00//   s *F"     s * *"0  B  s *޽h ? 33̙ffV   (    s *[S"     s *VS"`<$< p B  s *޽h ? 33̙ffV   ( 00//   s *"     s *0"0<$< p B  s *޽h ? 33̙ff<   :`j( 00// ` ` s * V"!`<$D <  p  ` c $@V"<$< p r ` HVgֳgֳ ?"@,$, VYour algorithm is then: For each book If it is not the book I want, continue searchingFZZ1Z1 ` HVgֳgֳ ?" 0,$, If the bookstore has 1,000,000 books, and if it takes 10 secs for you to check each book, it may take you as long as 4 months to find the book you want Not a very good algorithm, is it ? Note: search time is directly proportional to number of books: O(n)Z8>;8X ` C Afig1.pdf 0015F9D6Earth B9B583FF: 0 ,$D,X '` C A fig1a.pdf 0015F9D6Earth B9B583FF: 0 ,$D,X .` C A fig1a.pdf 0015F9D6Earth B9B583FF: 0 ,$D,X /` C A fig1b.pdf 0015F9D6Earth B9B583FF: 0 ,$D,X 0` C A fig1c.pdf 0015F9D6Earth B9B583FF: 0 ,$D,X 1` C A fig1d.pdf 0015F9D6Earth B9B583FF: 0 ,$D ,X 2` C A  fig1e.pdf 0015F9D6Earth B9B583FF: 0 ,$D ,X 3` C A  fig1f.pdf 0015F9D6Earth B9B583FF: 0 ,$D ,X 4` C A  fig1g.pdf 0015F9D6Earth B9B583FF: 0 ,$D ,X 5` C A  fig1h.pdf 0015F9D6Earth B9B583FF: 0 ,$D ,X 6` C A  fig1i.pdf 0015F9D6Earth B9B583FF: 0 ,$D,X 7` C A fig1j.pdf 0015F9D6Earth B9B583FF: 0 ,$D,X 8` C A fig1k.pdf 0015F9D6Earth B9B583FF: 0 ,$D,X 9` C A fig1l.pdf 0015F9D6Earth B9B583FF: 0 ,$D,X :` C A fig1a.pdf 0015F9D6Earth B9B583FF: 0 ,$D,B ` s *޽h ? 33̙ff   "&d(  d d s * NT"!`<$D <  p ` d HQTgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?X d C Afig2.pdf 002E4D4AEarth B9B583FF:P0,$D,B d s *޽h ? 33̙ff+   Y( 00//   s *@OT"!`<$<  p `  HNTgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?  HOTgֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1X  C A fig2a.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff+    Y( 00//   s *PT"!`<$<  p `  H QTgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?  HRTgֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1X  C A fig2b.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff+   0Y( 00//   s * 'T"!`<$<  p `  H"Tgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?  H&Tgֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1X  C A fig2c.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff+   @Y( 00//   s *'T"!`<$<  p `  H)Tgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?  H@+Tgֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1X  C A fig2d.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff+   PY(    s *,T"!`<$<  p `  H`,Tgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?  H&Tgֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1X  C A fig2e.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff+   `Y( 00//   s *PTS"!`<$<  p `  H\Sgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?  HXSgֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1X  C A fig2f.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff+   pY( 0ApiA   s *US"!`<$<  p `  H0\Sgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?  HLRgֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1X  C A fig2g.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff+   Y(    s *0"!`<$<  p `  H.Hgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?  HJgֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1X  C A fig2h.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff+   Y( 00//   s *X"!`<$<  p `  HYgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?  HSgֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1X  C A$ fig2i.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff#     Q(      s *`S"!`<$<  p `   HTgֳgֳ ?",$, TThis competitor bookstore keeps its books all in one very long array, sorted by ISBN6U?   H@Ugֳgֳ ?"0 ,$, mOne possible algorithm is again linear search: For each book If it is not the book I want, continue searchingV/1  1   HVgֳgֳ ?" ,$, 6This is the same algorithm used by MessyBookPile,Inc. Again& search time is directly proportional to number of books: O(n) Note that the algorithm did not make use of the fact that the books are sorteddw0"X   C A& fig2j.pdf 002E4D4AEarth B9B583FF:P0,$,B   s *޽h ? 33̙ff    9(    s *W"!`<$<  p   HWgֳgֳ ?" ,$, '?Another possible algorithm is binary search: Look at the middle book If it is the book I want, stop If the book I want comes before the middle book, search the first half of the array using this same algorithm If the book I want comes after the middle book, search the second half of the array using this same algorithm- 8 A 'X  C A( fig3a.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff     H9( 00// H H s *X"!`<$<  p  H HYgֳgֳ ?" ,$, '?Another possible algorithm is binary search: Look at the middle book If it is the book I want, stop If the book I want comes before the middle book, search the first half of the array using this same algorithm If the book I want comes after the middle book, search the second half of the array using this same algorithm- 8 A 'X  H C A, fig3b.pdf 002E4D4AEarth B9B583FF:P0,$,B H s *޽h ? 33̙ff     L9( 00// L L s *Y"!`<$<  p  L H Zgֳgֳ ?" ,$, '?Another possible algorithm is binary search: Look at the middle book If it is the book I want, stop If the book I want comes before the middle book, search the first half of the array using this same algorithm If the book I want comes after the middle book, search the second half of the array using this same algorithm- 8 A 'X  L C A- fig3c.pdf 002E4D4AEarth B9B583FF:P0,$,B L s *޽h ? 33̙ff     P9( 00// P P s *Z"!`<$<  p  P H@[gֳgֳ ?" ,$, '?Another possible algorithm is binary search: Look at the middle book If it is the book I want, stop If the book I want comes before the middle book, search the first half of the array using this same algorithm If the book I want comes after the middle book, search the second half of the array using this same algorithm- 8 A 'X  P C A. fig3d.pdf 002E4D4AEarth B9B583FF:P0,$,B P s *޽h ? 33̙ffK     Ty( 00// T T s *\"!`<$<  p  T H`\gֳgֳ ?" ,$, '?Another possible algorithm is binary search: Look at the middle book If it is the book I want, stop If the book I want comes before the middle book, search the first half of the array using this same algorithm If the book I want comes after the middle book, search the second half of the array using this same algorithm- 8 A '8 T H ]gֳgֳ ?"` 0,$, ~This does make use of the fact that the books are sorted Note: recursive algorithm ! Now& search time is proportional to the logarithm of the number of books: O(log2 n) 1,000,000 books, 10 secs/book = ? 0@  " X  T C A/ fig3e.pdf 002E4D4AEarth B9B583FF:P0,$,B T s *޽h ? 33̙ff       ) ( `\`   s *^"!`<$<  p   H_gֳgֳ ?" ,$, '?Another possible algorithm is binary search: Look at the middle book If it is the book I want, stop If the book I want comes before the middle book, search the first half of the array using this same algorithm If the book I want comes after the middle book, search the second half of the array using this same algorithm- 8 A '  Hdgֳgֳ ?"` 0,$, .This does make use of the fact that the books are sorted Note: recursive algorithm ! Now& search time is proportional to the logarithm of the number of books: O(log2 n) 1,000,000 books, 10 secs/book = 200 s < 4 min !!! [ 220 = 1,048,576 so log2(1,000,000) H" 20 ]-0@  "  GX   C A/ fig3e.pdf 002E4D4AEarth B9B583FF:P0,$,B  s *޽h ? 33̙ff`    t(  t t s * d"!`<$D <  p 6 t Hdgֳgֳ ?",$, |@This bookstore keeps its books organized in a binary search tree A.X t C Afig4.pdf 002E4D4AEarth B9B583FF: ,$D,B t s *޽h ? 33̙ff>     `l( $H ` ` s *@d"!`<$<  p 6 ` Hdgֳgֳ ?",$, |@This bookstore keeps its books organized in a binary search tree A.  ` H`dgֳgֳ ?"p ,$, P~The algorithm is binary search: Look at a node of the tree If it contains the book I want, stop If the book I want comes before the book in this node, search this node s left child, using this same algorithm If the book I want comes after the book in this node, search this node s right child, using this same algorithm  >+;+"$  ` C A fig4a.pdf 002E4D4AEarth B9B583FF: B ` s *޽h ? 33̙ff>   0 dl(  d d s * d"!`<$<  p 6 d Hdgֳgֳ ?",$, |@This bookstore keeps its books organized in a binary search tree A.  d H@dgֳgֳ ?"p ,$, P~The algorithm is binary search: Look at a node of the tree If it contains the book I want, stop If the book I want comes before the book in this node, search this node s left child, using this same algorithm If the book I want comes after the book in this node, search this node s right child, using this same algorithm  >+;+"$  d C A fig4b.pdf 002E4D4AEarth B9B583FF: B d s *޽h ? 33̙ff>   @ ll( O` l l s *d"!`<$<  p 6 l H`dgֳgֳ ?",$, |@This bookstore keeps its books organized in a binary search tree A.  l H dgֳgֳ ?"p ,$, P~The algorithm is binary search: Look at a node of the tree If it contains the book I want, stop If the book I want comes before the book in this node, search this node s left child, using this same algorithm If the book I want comes after the book in this node, search this node s right child, using this same algorithm  >+;+"$  l C A fig4c.pdf 002E4D4AEarth B9B583FF: B l s *޽h ? 33̙ff>   P pl(  p p s *d"!`<$<  p 6 p H@dgֳgֳ ?",$, |@This bookstore keeps its books organized in a binary search tree A.  p Hdgֳgֳ ?"p ,$, P~The algorithm is binary search: Look at a node of the tree If it contains the book I want, stop If the book I want comes before the book in this node, search this node s left child, using this same algorithm If the book I want comes after the book in this node, search this node s right child, using this same algorithm  >+;+"$  p C A  fig4d.pdf 002E4D4AEarth B9B583FF: B p s *޽h ? 33̙ff>   ` tl( ~ t t s *d"!`<$<  p 6 t H dgֳgֳ ?",$, |@This bookstore keeps its books organized in a binary search tree A.  t Hdgֳgֳ ?"p ,$, P~The algorithm is binary search: Look at a node of the tree If it contains the book I want, stop If the book I want comes before the book in this node, search this node s left child, using this same algorithm If the book I want comes after the book in this node, search this node s right child, using this same algorithm  >+;+"$  t C A! fig4e.pdf 002E4D4AEarth B9B583FF: B t s *޽h ? 33̙ff>   p xl(  x x s *X"!`<$<  p 6 x HSgֳgֳ ?",$, |@This bookstore keeps its books organized in a binary search tree A.  x HSgֳgֳ ?"p ,$, P~The algorithm is binary search: Look at a node of the tree If it contains the book I want, stop If the book I want comes before the book in this node, search this node s left child, using this same algorithm If the book I want comes after the book in this node, search this node s right child, using this same algorithm  >+;+"$  x C A fig4f.pdf 002E4D4AEarth B9B583FF: B x s *޽h ? 33̙ff     L( 00// L L s *S"!`<$D <  p ? L HSgֳgֳ ?",$, IThis other competitor bookstore keeps its books all organized by sections JA  L HSgֳgֳ ?"p ,$, The search algorithm is now: For each section If it is the section of the book I want Search each book in that section using one of the previous algorithmsXZZ(ZFZ(F F L H`Sgֳgֳ ?" ,$, ZThis is typically much faster than the corresponding algorithm used in the previous slides[Z[X  L C A)fig5.pdf 0015F9D6Earth B9B583FF:@ ,$D,B L s *޽h ? 33̙ffP   H~( 00// H H s * S"!`    H c $S"0<$< p B H s *޽h ? 33̙ff   PL(  P P c $`S"`    P c $S"  B P s *޽h ? 33̙ffJ   Tx( 0 T T c $f"`    T c $f"<$< p B T s *޽h ? 33̙ff   >6( X:   c $Pf"`   $  C Afig1.pdf 000E8A38Earth B9B583FF:`0S  Tfgֳgֳ ?"` P <$< p B  s *޽h ? 33̙ff   L( L   c $f"`     c $f"  B  s *޽h ? 33̙ff   :2(    c $f"`      c $pf"$ pPH___PPT2001$ B  s *޽h ? 33̙ff   :2( $¿   c $0f"`      c $0f"$ pPH___PPT2001$ B  s *޽h ? 33̙ff   :2(    c $f"`      c $f"$ pPH___PPT2001$ B  s *޽h ? 33̙ff   :2(    c $0"`      c $0"$ pPH___PPT2001$ B  s *޽h ? 33̙ff   :2 (    c $0"`      c $@0"0$ pPH___PPT2001$ B  s *޽h ? 33̙ff   :20(    c $`0"`      c $0"0$ pPH___PPT2001$ B  s *޽h ? 33̙ff   :2@(    c $0"`      c $@0"0$ pPH___PPT2001$ B  s *޽h ? 33̙ff   :2P(    c $`0"`      c $@0"00$ pPH___PPT2001$ B  s *޽h ? 33̙ff   :2`(    c $l"`      c $l"$ pPH___PPT2001$ B  s *޽h ? 33̙ff   p( 00//   c $l"<$< p    `lgֳgֳ ?"   B  s *޽h ? 33̙ffP   ~(    s *@l"     c $l"`<$< p B  s *޽h ? 33̙ffP   0~(    s **"     c $`*"<$< p B  s *޽h ? 33̙ff   (  x  c $0i,     S i,<$< p   Hj,gֳgֳ ?,$D, -cYou could write a function for that: int max(int a, int b) { if (a > b) return a; else return b; }h%?%->%,3  HPg,gֳgֳ ? ,$D, ASuppose now that you want to find the maximum of two float values*B5  H0,gֳgֳ ? ,$D, oYou could write another function for that: float max(float a, float b) { if (a > b) return a; else return b; }h+E+-H  0޽h ? www3ff   ;(  x  c $,     S p,<$< p   H0,gֳgֳ ?,$D, pYou could write a function for that too: double max(double a, double b) { if (a > b) return a; else return b; }h)H)-+  H,gֳgֳ ? ,$D, 9What if you want to find the maximum of two Speed values?*:,   H,gֳgֳ ? ,$D, rYou could also write a function for that: Speed max(Speed & a, Speed & b) { if (a > b) return a; else return b; }h*I*/X  C A couch.gif 00173889Earth B9B583FF:  ,$D,H  0޽h ? www3ff   C( ? x  c $Л,p     S ,p<$< p X  C Afig1.pdf 00132CB4Earth B9B583FF:`,$D,%  HP,gֳgֳ ?@p ,$, yeNow suppose that for some reason, you want to swap the contents of the two glasses. How do you do it?X  C A" drinking.gif 00173889Earth B9B583FF:P Pp ,$D,H  0޽h ? www3ffB   j( DR x  c $p,p     S 0,p<$< p   H,gֳgֳ ?@p ,$, :Now suppose that for some reason, you want to swap the contents of the two glasses. How do you do it? 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Bottom lineInterface x ImplementationInterface x ImplementationInterface x ImplementationInterface x ImplementationInterface x Implementation Notation NotationSyntax and SemanticsQuick SummaryBack to + and Another example: CounterCounterCounter Testing ADTs Testing ADTs Testing ADTsC++ TemplatesC++ TemplatesA simple puzzleA simple puzzleAnother puzzleA general swap functionNo problem, right ?No problem, right ?Class templatesClass templatesClass templatesCranky CompilersC++ ExceptionsPowerPoint PresentationPowerPoint PresentationPowerPoint Presentation  Fonts UsedDesign Template Slide TitlesB 8@ _PID_HLINKS'AHmailto:Wagner@cs.ucr.eduhttp://www.cs.ucr.edu/~wagnerhttp://www.cs.ucr.edu/cs12&_Wagner Truppel