n Maurice Wilkes, 1949 n Organize software to minimize errors. n Eliminate most of the errors we made anyway.

Size: px
Start display at page:

Download "n Maurice Wilkes, 1949 n Organize software to minimize errors. n Eliminate most of the errors we made anyway."

Transcription

1 Bjare Stroustrup Chapter 5 Errors Abstract Whe we program, we have to deal with errors. Our most basic aim is correctess, but we must deal with icomplete problem specificatios, icomplete programs, ad our ow errors. Here, we ll cocetrate o a key area: how to deal with uexpected fuctio argumets. We ll also discuss techiques for fidig errors i programs: debuggig ad testig. 2 Kids of errors Argumet checkig Error reportig Error detectio Exceptios Debuggig Testig Overview Errors I realized that from ow o a large part of my life would be spet fidig ad correctig my ow mistakes. Maurice Wilkes, 1949 Whe we write programs, errors are atural ad uavoidable; the questio is, how do we deal with them? Orgaize software to miimize errors. Elimiate most of the errors we made ayway. Debuggig Testig Make sure the remaiig errors are ot serious. My guess is that avoidig, fidig, ad correctig errors is 95% or more of the effort for serious software developmet. You ca do much better for small programs. or worse, if you re sloppy 3 4 1

2 Your Program 1. Should produce the desired results for all legal iputs 2. Should give reasoable error messages for illegal iputs 3. Need ot worry about misbehavig hardware 4. Need ot worry about misbehavig system software 5. Is allowed to termiate after fidig a error 3, 4, ad 5 are true for begier s code; ofte, we have to worry about those i real software. Sources of errors Poor specificatio What s this supposed to do? Icomplete programs but I ll ot get aroud to doig that util tomorrow Uexpected argumets but sqrt() is t supposed to be called with -1 as its argumet Uexpected iput but the user was supposed to iput a iteger Code that simply does t do what it was supposed to do so fix it! 5 6 Kids of Errors Check your iputs Compile-time errors Sytax errors Type errors Warigs Lik-time errors Ru-time errors Detected by computer (crash) Detected by library (exceptios) Detected by user code Logic errors Detected by programmer (code rus, but produces icorrect output) Before tryig to use a iput value, check that it meets your expectatios/requiremets Fuctio argumets Data from iput (istream) 7 8 2

3 Bad fuctio argumets The compiler helps: Number ad types of argumets must match it area(it legth, it width) retur legth*width; it x1 = area(7); // error: wrog umber of argumets it x2 = area("seve", 2); // error: 1 st argumet has a wrog type it x3 = area(7, 10); // ok it x5 = area(7.5, 10); // ok, but dagerous: 7.5 trucated to 7; // most compilers will war you it x = area(10, -7); // this is a difficult case: // the types are correct, // but the values make o sese Bad Fuctio Argumets So, how about it x = area(10, -7);? Alteratives Just do t do that Rarely a satisfactory aswer The caller should check Hard to do systematically The fuctio should check Retur a error value (ot geeral, problematic) Set a error status idicator (ot geeral, problematic do t do this) Throw a exceptio Note: sometimes we ca t chage a fuctio that hadles errors i a way we do ot like Someoe else wrote it ad we ca t or do t wat to chage their code 9 10 Why worry? Bad fuctio argumets You wat your programs to be correct Typically the writer of a fuctio has o cotrol over how it is called Writig do it this way i the maual (or i commets) is o solutio may people do t read mauals The begiig of a fuctio is ofte a good place to check Before the computatio gets complicated Whe to worry? If it does t make sese to test every fuctio, test some How to report a error Retur a error value (ot geeral, problematic) it area(it legth, it width) // retur a egative value for bad iput if(legth <=0 width <= 0) retur -1; retur legth*width; So, let the caller beware it z = area(x,y); if (z<0) error("bad area computatio"); // 11 Problems What if I forget to check that retur value? For some fuctios there is t a bad value to retur (e.g., max()) 12 3

4 How to report a error Set a error status idicator (ot geeral, problematic, do t!) it erro = 0; // used to idicate errors it area(it legth, it width) if (legth<=0 width<=0) erro = 7; // meas or retur legth*width; So, let the caller check it z = area(x,y); if (erro==7) error("bad area computatio"); // Problems What if I forget to check erro? How do I pick a value for erro that s differet from all others? How do I deal with that error? 13 How to report a error Report a error by throwig a exceptio class Bad_area ; // a class is a user defied type // Bad_area is a type to be used as a exceptio it area(it legth, it width) if (legth<=0 width<=0) throw Bad_area; retur legth*width; // ote the a value Catch ad deal with the error (e.g., i mai()) try it z = area(x,y); // if area() does t throw a exceptio // make the assigmet ad proceed catch(bad_area) // if area() throws Bad_area, respod cerr << "oops! Bad area calculatio fix program\"; 14 Exceptios Out of rage Exceptio hadlig is geeral You ca t forget about a exceptio: the program will termiate if someoe does t hadle it (usig a try catch) Just about every kid of error ca be reported usig exceptios You still have to figure out what to do about a exceptio (every exceptio throw i your program) Error hadlig is ever really simple Try this vector<it> v(10); // a vector of 10 its, // each iitialized to the default value, 0, // referred to as v[0].. v[9] // set values for (it i = 0; i<v.size(); ++i) v[i] = i; for (it i = 0; i<=10; ++i) // prit 10 values (???) cout << "v[" << i << "] == " << v[i] << edl; vector s operator[ ] (subscript operator) reports a bad idex (its argumet) by throwig a Rage_error if you use #iclude "std_lib_facilities.h" The default behavior ca differ You ca t make this mistake with a rage-for

5 Exceptios for ow For ow, just use exceptios to termiate programs gracefully, like this it mai() try // catch (out_of_rage&) // out_of_rage exceptios cerr << "oops some vector idex out of rage\"; catch ( ) // all other exceptios cerr << "oops some exceptio\"; A fuctio error() Here is a simple error() fuctio as provided i std_lib_facilities.h This allows you to prit a error message by callig error() It works by disguisig throws, like this: void error(strig s) // oe error strig throw rutime_error(s); void error(strig s1, strig s2) // two error strigs error(s1 + s2); // cocateates Usig error( ) How to look for errors Example cout << "please eter iteger i rage [1..10]\"; it x = -1; // iitialize with uacceptable value (if possible) ci >> x; if (!ci) // check that ci read a iteger error("did t get a value"); if (x < 1 10 < x) // check if value is out of rage error("x is out of rage"); // if we get this far, we ca use x with cofidece Whe you have writte (drafted?) a program, it ll have errors (commoly called bugs ) It ll do somethig, but ot what you expected How do you fid out what it actually does? How do you correct it? This process is usually called debuggig

6 Debuggig How ot to do it while (program does t appear to work) // pseudo code Radomly look at the program for somethig that looks odd Chage it to look better Key questio How would I kow if the program actually worked correctly? Program structure Make the program easy to read so that you have a chace of spottig the bugs Commet Explai desig ideas Use meaigful ames Idet Use a cosistet layout Your IDE tries to help (but it ca t do everythig) You are the oe resposible Break code ito small fuctios Try to avoid fuctios loger tha a page Avoid complicated code sequeces Try to avoid ested loops, ested if-statemets, etc. (But, obviously, you sometimes eed those) Use library facilities First get the program to compile Is every strig literal termiated? cout << "Hello, << ame << '\'; // oops! Is every character literal termiated? cout << "Hello, " << ame << '\; // oops! Is every block termiated? if (a>0) /* do somethig */ else /* do somethig else */ // oops! Is every set of paretheses matched? if (a // oops! x = f(y); The compiler geerally reports this kid of error late It does t kow you did t mea to close it later 23 First get the program to compile Is every ame declared? Did you iclude eeded headers? (e.g., std_lib_facilities.h) Is every ame declared before it s used? Did you spell all ames correctly? it cout; /* */ ++Cout; // oops! char ch; /* */ Ci>>c; // double oops! Did you termiate each expressio statemet with a semicolo? x = sqrt(y)+2 z = x+3; // oops! 24 6

7 Debuggig Carefully follow the program through the specified sequece of steps Preted you re the computer executig the program Does the output match your expectatios? If there is t eough output to help, add a few debug output statemets cerr << "x == " << x << ", y == " << y << '\'; Be very careful See what the program specifies, ot what you thik it should say That s much harder to do tha it souds for (it i=0; 0<moth.size(); ++i) for( it i = 0; i<=max; ++j) // oops! // oops! (twice) 25 Debuggig Whe you write the program, isert some checks ( saity checks ) that variables have reasoable values Fuctio argumet checks are promiet examples of this if (umber_of_elemets<0) error("impossible: egative umber of elemets"); if (largest_reasoable<umber_of_elemets) error("uexpectedly large umber of elemets"); if (x<y) error("impossible: x<y"); Desig these checks so that some ca be left i the program eve after you believe it to be correct It s almost always better for a program to stop tha to give wrog results 26 Debuggig Pay special attetio to ed cases (begiigs ad eds) Did you iitialize every variable? To a reasoable value Did the fuctio get the right argumets? Did the fuctio retur the right value? Did you hadle the first elemet correctly? The last elemet? Did you hadle the empty case correctly? No elemets No iput Did you ope your files correctly? more o this i chapter 11 Did you actually read that iput? Write that output? Debuggig If you ca t see the bug, you re lookig i the wrog place It s easy to be coviced that you kow what the problem is ad stubborly keep lookig i the wrog place Do t just guess, be guided by output Work forward through the code from a place you kow is right so what happes ext? Why? Work backwards from some bad output how could that possibly happe? Oce you have foud the bug carefully cosider if fixig it solves the whole problem It s commo to itroduce ew bugs with a quick fix I foud the last bug is a programmer s joke

8 Note Error hadlig is fudametally more difficult ad messy tha ordiary code There is basically just oe way thigs ca work right There are may ways that thigs ca go wrog The more people use a program, the better the error hadlig must be If you break your ow code, that s your ow problem Ad you ll lear the hard way If your code is used by your frieds, ucaught errors ca cause you to lose frieds If your code is used by stragers, ucaught errors ca cause serious grief Ad they may ot have a way of recoverig Pre-coditios What does a fuctio require of its argumets? Such a requiremet is called a pre-coditio Sometimes, it s a good idea to check it it area(it legth, it width) // calculate area of a rectagle // legth ad width must be positive if (legth<=0 width <=0) throw Bad_area; retur legth*width; Post-coditios Pre- ad post-coditios What must be true whe a fuctio returs? Such a requiremet is called a post-coditio it area(it legth, it width) // calculate area of a rectagle // legth ad width must be positive if (legth<=0 width <=0) throw Bad_area; // the result must be a positive it that is the area // o variables had their values chaged retur legth*width; Always thik about them If othig else write them as commets Check them where reasoable Check a lot whe you are lookig for a bug This ca be tricky How could the post-coditio for area() fail after the precoditio succeeded (held)?

9 Testig How do we test a program? Be systematic peckig at the keyboard is okay for very small programs ad for very iitial tests, but is isufficiet for real systems Thik of testig ad correctess from the very start Whe possible, test parts of a program i isolatio E.g., whe you write a complicated fuctio write a little program that simply calls it with a lot of argumets to see how it behaves i isolatio before puttig it ito the real program (this is typically called uit testig ) We ll retur to this questio i Chapter 26 The ext lecture I the ext two lectures, we ll discuss the desig ad implemetatio of a complete small program a simple desk calculator

Chapter 5 Errors. Hyunyoung Lee. Based on slides by Bjarne Stroustrup.

Chapter 5 Errors. Hyunyoung Lee. Based on slides by Bjarne Stroustrup. Chapter 5 Errors Hyunyoung Lee Based on slides by Bjarne Stroustrup www.stroustrup.com/programming 1 Abstract When we program, we have to deal with errors. Our most basic aim is correctness, but we must

More information

Chapter 5 Errors. Bjarne Stroustrup

Chapter 5 Errors. Bjarne Stroustrup Chapter 5 Errors Bjarne Stroustrup www.stroustrup.com/programming Abstract When we program, we have to deal with errors. Our most basic aim is correctness, but we must deal with incomplete problem specifications,

More information

Errors. Lecture 6. Hartmut Kaiser hkaiser/fall_2011/csc1254.html

Errors. Lecture 6. Hartmut Kaiser  hkaiser/fall_2011/csc1254.html Hartmut Kaiser hkaiser@cct.lsu.edu http://www.cct.lsu.edu/ hkaiser/fall_2011/csc1254.html 2 Abstract When we program, we have to deal with errors. Our most basic aim is correctness, but we must deal with

More information

n Some thoughts on software development n The idea of a calculator n Using a grammar n Expression evaluation n Program organization n Analysis

n Some thoughts on software development n The idea of a calculator n Using a grammar n Expression evaluation n Program organization n Analysis Overview Chapter 6 Writig a Program Bjare Stroustrup Some thoughts o software developmet The idea of a calculator Usig a grammar Expressio evaluatio Program orgaizatio www.stroustrup.com/programmig 3 Buildig

More information

CS 11 C track: lecture 1

CS 11 C track: lecture 1 CS 11 C track: lecture 1 Prelimiaries Need a CMS cluster accout http://acctreq.cms.caltech.edu/cgi-bi/request.cgi Need to kow UNIX IMSS tutorial liked from track home page Track home page: http://courses.cms.caltech.edu/courses/cs11/material

More information

Abstract. Chapter 4 Computation. Overview 8/13/18. Bjarne Stroustrup Note:

Abstract. Chapter 4 Computation. Overview 8/13/18. Bjarne Stroustrup   Note: Chapter 4 Computatio Bjare Stroustrup www.stroustrup.com/programmig Abstract Today, I ll preset the basics of computatio. I particular, we ll discuss expressios, how to iterate over a series of values

More information

CMPT 125 Assignment 2 Solutions

CMPT 125 Assignment 2 Solutions CMPT 25 Assigmet 2 Solutios Questio (20 marks total) a) Let s cosider a iteger array of size 0. (0 marks, each part is 2 marks) it a[0]; I. How would you assig a poiter, called pa, to store the address

More information

Chapter 5. Functions for All Subtasks. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 5. Functions for All Subtasks. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 5 Fuctios for All Subtasks Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 5.1 void Fuctios 5.2 Call-By-Referece Parameters 5.3 Usig Procedural Abstractio 5.4 Testig ad Debuggig

More information

Overview. Chapter 18 Vectors and Arrays. Reminder. vector. Bjarne Stroustrup

Overview. Chapter 18 Vectors and Arrays. Reminder. vector. Bjarne Stroustrup Chapter 18 Vectors ad Arrays Bjare Stroustrup Vector revisited How are they implemeted? Poiters ad free store Destructors Iitializatio Copy ad move Arrays Array ad poiter problems Chagig size Templates

More information

10/23/18. File class in Java. Scanner reminder. Files. Opening a file for reading. Scanner reminder. File Input and Output

10/23/18. File class in Java. Scanner reminder. Files. Opening a file for reading. Scanner reminder. File Input and Output File class i Java File Iput ad Output TOPICS File Iput Exceptio Hadlig File Output Programmers refer to iput/output as "I/O". The File class represets files as objects. The class is defied i the java.io

More information

Exceptions. Your computer takes exception. The Exception Class. Causes of Exceptions

Exceptions. Your computer takes exception. The Exception Class. Causes of Exceptions Your computer takes exceptio s s are errors i the logic of a program (ru-time errors). Examples: i thread mai java.io.filenotfoud: studet.txt (The system caot fid the file specified.) i thread mai java.lag.nullpoiter:

More information

Python Programming: An Introduction to Computer Science

Python Programming: An Introduction to Computer Science Pytho Programmig: A Itroductio to Computer Sciece Chapter 1 Computers ad Programs 1 Objectives To uderstad the respective roles of hardware ad software i a computig system. To lear what computer scietists

More information

. Written in factored form it is easy to see that the roots are 2, 2, i,

. Written in factored form it is easy to see that the roots are 2, 2, i, CMPS A Itroductio to Programmig Programmig Assigmet 4 I this assigmet you will write a java program that determies the real roots of a polyomial that lie withi a specified rage. Recall that the roots (or

More information

Chapter 1. Introduction to Computers and C++ Programming. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 1. Introduction to Computers and C++ Programming. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 1 Itroductio to Computers ad C++ Programmig Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 1.1 Computer Systems 1.2 Programmig ad Problem Solvig 1.3 Itroductio to C++ 1.4 Testig

More information

Chapter 8. Strings and Vectors. Copyright 2014 Pearson Addison-Wesley. All rights reserved.

Chapter 8. Strings and Vectors. Copyright 2014 Pearson Addison-Wesley. All rights reserved. Chapter 8 Strigs ad Vectors Overview 8.1 A Array Type for Strigs 8.2 The Stadard strig Class 8.3 Vectors Slide 8-3 8.1 A Array Type for Strigs A Array Type for Strigs C-strigs ca be used to represet strigs

More information

CS 111: Program Design I Lecture # 7: First Loop, Web Crawler, Functions

CS 111: Program Design I Lecture # 7: First Loop, Web Crawler, Functions CS 111: Program Desig I Lecture # 7: First Loop, Web Crawler, Fuctios Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago September 18, 2018 What will this prit? x = 5 if x == 3: prit("hi!")

More information

Chapter 8. Strings and Vectors. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 8. Strings and Vectors. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 8 Strigs ad Vectors Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 8.1 A Array Type for Strigs 8.2 The Stadard strig Class 8.3 Vectors Copyright 2015 Pearso Educatio, Ltd..

More information

CS 111: Program Design I Lecture 16: Module Review, Encodings, Lists

CS 111: Program Design I Lecture 16: Module Review, Encodings, Lists CS 111: Program Desig I Lecture 16: Module Review, Ecodigs, Lists Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago October 18, 2016 Last time Dot otatio ad methods Padas: user maual poit

More information

Chapter 9. Pointers and Dynamic Arrays. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 9. Pointers and Dynamic Arrays. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 9 Poiters ad Dyamic Arrays Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 9.1 Poiters 9.2 Dyamic Arrays Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Slide 9-3

More information

Chapter 11. Friends, Overloaded Operators, and Arrays in Classes. Copyright 2014 Pearson Addison-Wesley. All rights reserved.

Chapter 11. Friends, Overloaded Operators, and Arrays in Classes. Copyright 2014 Pearson Addison-Wesley. All rights reserved. Chapter 11 Frieds, Overloaded Operators, ad Arrays i Classes Copyright 2014 Pearso Addiso-Wesley. All rights reserved. Overview 11.1 Fried Fuctios 11.2 Overloadig Operators 11.3 Arrays ad Classes 11.4

More information

Overview. Common tasks. Observation. Chapter 20 The STL (containers, iterators, and algorithms) 8/13/18. Bjarne Stroustrup

Overview. Common tasks. Observation. Chapter 20 The STL (containers, iterators, and algorithms) 8/13/18. Bjarne Stroustrup Overview Chapter 20 The STL (cotaiers, iterators, ad algorithms) Bjare Stroustrup www.stroustrup.com/programmig Commo tasks ad ideals Geeric programmig Cotaiers, algorithms, ad iterators The simplest algorithm:

More information

Chapter 3. More Flow of Control. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 3. More Flow of Control. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 3 More Flow of Cotrol Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 3.1 Usig Boolea Expressios 3.2 Multiway Braches 3.3 More about C++ Loop Statemets 3.4 Desigig Loops Copyright

More information

Python Programming: An Introduction to Computer Science

Python Programming: An Introduction to Computer Science Pytho Programmig: A Itroductio to Computer Sciece Chapter 6 Defiig Fuctios Pytho Programmig, 2/e 1 Objectives To uderstad why programmers divide programs up ito sets of cooperatig fuctios. To be able to

More information

Recursion. Computer Science S-111 Harvard University David G. Sullivan, Ph.D. Review: Method Frames

Recursion. Computer Science S-111 Harvard University David G. Sullivan, Ph.D. Review: Method Frames Uit 4, Part 3 Recursio Computer Sciece S-111 Harvard Uiversity David G. Sulliva, Ph.D. Review: Method Frames Whe you make a method call, the Java rutime sets aside a block of memory kow as the frame of

More information

How do we evaluate algorithms?

How do we evaluate algorithms? F2 Readig referece: chapter 2 + slides Algorithm complexity Big O ad big Ω To calculate ruig time Aalysis of recursive Algorithms Next time: Litterature: slides mostly The first Algorithm desig methods:

More information

CS211 Fall 2003 Prelim 2 Solutions and Grading Guide

CS211 Fall 2003 Prelim 2 Solutions and Grading Guide CS11 Fall 003 Prelim Solutios ad Gradig Guide Problem 1: (a) obj = obj1; ILLEGAL because type of referece must always be a supertype of type of object (b) obj3 = obj1; ILLEGAL because type of referece

More information

Chapter 10. Defining Classes. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 10. Defining Classes. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 10 Defiig Classes Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 10.1 Structures 10.2 Classes 10.3 Abstract Data Types 10.4 Itroductio to Iheritace Copyright 2015 Pearso Educatio,

More information

Structuring Redundancy for Fault Tolerance. CSE 598D: Fault Tolerant Software

Structuring Redundancy for Fault Tolerance. CSE 598D: Fault Tolerant Software Structurig Redudacy for Fault Tolerace CSE 598D: Fault Tolerat Software What do we wat to achieve? Versios Damage Assessmet Versio 1 Error Detectio Iputs Versio 2 Voter Outputs State Restoratio Cotiued

More information

Module 8-7: Pascal s Triangle and the Binomial Theorem

Module 8-7: Pascal s Triangle and the Binomial Theorem Module 8-7: Pascal s Triagle ad the Biomial Theorem Gregory V. Bard April 5, 017 A Note about Notatio Just to recall, all of the followig mea the same thig: ( 7 7C 4 C4 7 7C4 5 4 ad they are (all proouced

More information

Lecture 9: Exam I Review

Lecture 9: Exam I Review CS 111 (Law): Program Desig I Lecture 9: Exam I Review Robert H. Sloa & Richard Warer Uiversity of Illiois, Chicago September 22, 2016 This Class Discuss midterm topics Go over practice examples Aswer

More information

Examples and Applications of Binary Search

Examples and Applications of Binary Search Toy Gog ITEE Uiersity of Queeslad I the secod lecture last week we studied the biary search algorithm that soles the problem of determiig if a particular alue appears i a sorted list of iteger or ot. We

More information

Threads and Concurrency in Java: Part 2

Threads and Concurrency in Java: Part 2 Threads ad Cocurrecy i Java: Part 2 1 Waitig Sychroized methods itroduce oe kid of coordiatio betwee threads. Sometimes we eed a thread to wait util a specific coditio has arise. 2003--09 T. S. Norvell

More information

The number n of subintervals times the length h of subintervals gives length of interval (b-a).

The number n of subintervals times the length h of subintervals gives length of interval (b-a). Simulator with MadMath Kit: Riema Sums (Teacher s pages) I your kit: 1. GeoGebra file: Ready-to-use projector sized simulator: RiemaSumMM.ggb 2. RiemaSumMM.pdf (this file) ad RiemaSumMMEd.pdf (educator's

More information

prerequisites: 6.046, 6.041/2, ability to do proofs Randomized algorithms: make random choices during run. Main benefits:

prerequisites: 6.046, 6.041/2, ability to do proofs Randomized algorithms: make random choices during run. Main benefits: Itro Admiistrivia. Sigup sheet. prerequisites: 6.046, 6.041/2, ability to do proofs homework weekly (first ext week) collaboratio idepedet homeworks gradig requiremet term project books. questio: scribig?

More information

The isoperimetric problem on the hypercube

The isoperimetric problem on the hypercube The isoperimetric problem o the hypercube Prepared by: Steve Butler November 2, 2005 1 The isoperimetric problem We will cosider the -dimesioal hypercube Q Recall that the hypercube Q is a graph whose

More information

Chapter 4. Procedural Abstraction and Functions That Return a Value. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 4. Procedural Abstraction and Functions That Return a Value. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 4 Procedural Abstractio ad Fuctios That Retur a Value Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 4.1 Top-Dow Desig 4.2 Predefied Fuctios 4.3 Programmer-Defied Fuctios 4.4

More information

Hash Tables. Presentation for use with the textbook Algorithm Design and Applications, by M. T. Goodrich and R. Tamassia, Wiley, 2015.

Hash Tables. Presentation for use with the textbook Algorithm Design and Applications, by M. T. Goodrich and R. Tamassia, Wiley, 2015. Presetatio for use with the textbook Algorithm Desig ad Applicatios, by M. T. Goodrich ad R. Tamassia, Wiley, 2015 Hash Tables xkcd. http://xkcd.com/221/. Radom Number. Used with permissio uder Creative

More information

CSE 111 Bio: Program Design I Class 11: loops

CSE 111 Bio: Program Design I Class 11: loops SE 111 Bio: Program Desig I lass 11: loops Radall Muroe, xkcd.com/1411/ Robert H. Sloa (S) & Rachel Poretsky (Bio) Uiversity of Illiois, hicago October 2, 2016 Pytho ets Loopy! he Pytho, Busch ardes Florida

More information

Chapter 6. I/O Streams as an Introduction to Objects and Classes. Copyright 2014 Pearson Addison-Wesley. All rights reserved.

Chapter 6. I/O Streams as an Introduction to Objects and Classes. Copyright 2014 Pearson Addison-Wesley. All rights reserved. Chapter 6 I/O Streams as a Itroductio to Objects ad Classes Overview 6.1 Streams ad Basic File I/O 6.2 Tools for Stream I/O 6.3 Character I/O Slide 6-3 6.1 Streams ad Basic File I/O I/O Streams I/O refers

More information

Our Learning Problem, Again

Our Learning Problem, Again Noparametric Desity Estimatio Matthew Stoe CS 520, Sprig 2000 Lecture 6 Our Learig Problem, Agai Use traiig data to estimate ukow probabilities ad probability desity fuctios So far, we have depeded o describig

More information

Exercise 6 (Week 42) For the foreign students only.

Exercise 6 (Week 42) For the foreign students only. These are the last exercises of the course. Please, remember that to pass exercises, the sum of the poits gathered by solvig the questios ad attedig the exercise groups must be at least 4% ( poits) of

More information

Copyright 2016 Ramez Elmasri and Shamkant B. Navathe

Copyright 2016 Ramez Elmasri and Shamkant B. Navathe Copyright 2016 Ramez Elmasri ad Shamkat B. Navathe CHAPTER 20 Itroductio to Trasactio Processig Cocepts ad Theory Copyright 2016 Ramez Elmasri ad Shamkat B. Navathe Itroductio Trasactio Describes local

More information

University of Waterloo Department of Electrical and Computer Engineering ECE 250 Algorithms and Data Structures

University of Waterloo Department of Electrical and Computer Engineering ECE 250 Algorithms and Data Structures Uiversity of Waterloo Departmet of Electrical ad Computer Egieerig ECE 250 Algorithms ad Data Structures Midterm Examiatio ( pages) Istructor: Douglas Harder February 7, 2004 7:30-9:00 Name (last, first)

More information

CS 111 Green: Program Design I Lecture 27: Speed (cont.); parting thoughts

CS 111 Green: Program Design I Lecture 27: Speed (cont.); parting thoughts CS 111 Gree: Program Desig I Lecture 27: Speed (cot.); partig thoughts By Nascarkig - Ow work, CC BY-SA 4.0, https://commos.wikimedia.org/w/idex.php?curid=38671041 Robert H. Sloa (CS) & Rachel Poretsky

More information

CSE 111 Bio: Program Design I Lecture 17: software development, list methods

CSE 111 Bio: Program Design I Lecture 17: software development, list methods CSE 111 Bio: Program Desig I Lecture 17: software developmet, list methods Robert H. Sloa(CS) & Rachel Poretsky(Bio) Uiversity of Illiois, Chicago October 19, 2017 NESTED LOOPS: REVIEW Geerate times table

More information

Chapter 2. C++ Basics. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 2. C++ Basics. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 2 C++ Basics Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 2.1 Variables ad Assigmets 2.2 Iput ad Output 2.3 Data Types ad Expressios 2.4 Simple Flow of Cotrol 2.5 Program

More information

Abstract Data Types (ADTs) Stacks. The Stack ADT ( 4.2) Stack Interface in Java

Abstract Data Types (ADTs) Stacks. The Stack ADT ( 4.2) Stack Interface in Java Abstract Data Types (ADTs) tacks A abstract data type (ADT) is a abstractio of a data structure A ADT specifies: Data stored Operatios o the data Error coditios associated with operatios Example: ADT modelig

More information

One advantage that SONAR has over any other music-sequencing product I ve worked

One advantage that SONAR has over any other music-sequencing product I ve worked *gajedra* D:/Thomso_Learig_Projects/Garrigus_163132/z_productio/z_3B2_3D_files/Garrigus_163132_ch17.3d, 14/11/08/16:26:39, 16:26, page: 647 17 CAL 101 Oe advatage that SONAR has over ay other music-sequecig

More information

Lecture 5. Counting Sort / Radix Sort

Lecture 5. Counting Sort / Radix Sort Lecture 5. Coutig Sort / Radix Sort T. H. Corme, C. E. Leiserso ad R. L. Rivest Itroductio to Algorithms, 3rd Editio, MIT Press, 2009 Sugkyukwa Uiversity Hyuseug Choo choo@skku.edu Copyright 2000-2018

More information

CIS 121 Data Structures and Algorithms with Java Spring Stacks, Queues, and Heaps Monday, February 18 / Tuesday, February 19

CIS 121 Data Structures and Algorithms with Java Spring Stacks, Queues, and Heaps Monday, February 18 / Tuesday, February 19 CIS Data Structures ad Algorithms with Java Sprig 09 Stacks, Queues, ad Heaps Moday, February 8 / Tuesday, February 9 Stacks ad Queues Recall the stack ad queue ADTs (abstract data types from lecture.

More information

Lecture Notes 6 Introduction to algorithm analysis CSS 501 Data Structures and Object-Oriented Programming

Lecture Notes 6 Introduction to algorithm analysis CSS 501 Data Structures and Object-Oriented Programming Lecture Notes 6 Itroductio to algorithm aalysis CSS 501 Data Structures ad Object-Orieted Programmig Readig for this lecture: Carrao, Chapter 10 To be covered i this lecture: Itroductio to algorithm aalysis

More information

COSC 1P03. Ch 7 Recursion. Introduction to Data Structures 8.1

COSC 1P03. Ch 7 Recursion. Introduction to Data Structures 8.1 COSC 1P03 Ch 7 Recursio Itroductio to Data Structures 8.1 COSC 1P03 Recursio Recursio I Mathematics factorial Fiboacci umbers defie ifiite set with fiite defiitio I Computer Sciece sytax rules fiite defiitio,

More information

What are we going to learn? CSC Data Structures Analysis of Algorithms. Overview. Algorithm, and Inputs

What are we going to learn? CSC Data Structures Analysis of Algorithms. Overview. Algorithm, and Inputs What are we goig to lear? CSC316-003 Data Structures Aalysis of Algorithms Computer Sciece North Carolia State Uiversity Need to say that some algorithms are better tha others Criteria for evaluatio Structure

More information

Major CSL Write your name and entry no on every sheet of the answer script. Time 2 Hrs Max Marks 70

Major CSL Write your name and entry no on every sheet of the answer script. Time 2 Hrs Max Marks 70 NOTE:. Attempt all seve questios. Major CSL 02 2. Write your ame ad etry o o every sheet of the aswer script. Time 2 Hrs Max Marks 70 Q No Q Q 2 Q 3 Q 4 Q 5 Q 6 Q 7 Total MM 6 2 4 0 8 4 6 70 Q. Write a

More information

Reliable Transmission. Spring 2018 CS 438 Staff - University of Illinois 1

Reliable Transmission. Spring 2018 CS 438 Staff - University of Illinois 1 Reliable Trasmissio Sprig 2018 CS 438 Staff - Uiversity of Illiois 1 Reliable Trasmissio Hello! My computer s ame is Alice. Alice Bob Hello! Alice. Sprig 2018 CS 438 Staff - Uiversity of Illiois 2 Reliable

More information

COP4020 Programming Languages. Functional Programming Prof. Robert van Engelen

COP4020 Programming Languages. Functional Programming Prof. Robert van Engelen COP4020 Programmig Laguages Fuctioal Programmig Prof. Robert va Egele Overview What is fuctioal programmig? Historical origis of fuctioal programmig Fuctioal programmig today Cocepts of fuctioal programmig

More information

CS : Programming for Non-Majors, Summer 2007 Programming Project #3: Two Little Calculations Due by 12:00pm (noon) Wednesday June

CS : Programming for Non-Majors, Summer 2007 Programming Project #3: Two Little Calculations Due by 12:00pm (noon) Wednesday June CS 1313 010: Programmig for No-Majors, Summer 2007 Programmig Project #3: Two Little Calculatios Due by 12:00pm (oo) Wedesday Jue 27 2007 This third assigmet will give you experiece writig programs that

More information

Pseudocode ( 1.1) Analysis of Algorithms. Primitive Operations. Pseudocode Details. Running Time ( 1.1) Estimating performance

Pseudocode ( 1.1) Analysis of Algorithms. Primitive Operations. Pseudocode Details. Running Time ( 1.1) Estimating performance Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Pseudocode ( 1.1) High-level descriptio of a algorithm More structured

More information

CIS 121 Data Structures and Algorithms with Java Spring Stacks and Queues Monday, February 12 / Tuesday, February 13

CIS 121 Data Structures and Algorithms with Java Spring Stacks and Queues Monday, February 12 / Tuesday, February 13 CIS Data Structures ad Algorithms with Java Sprig 08 Stacks ad Queues Moday, February / Tuesday, February Learig Goals Durig this lab, you will: Review stacks ad queues. Lear amortized ruig time aalysis

More information

CS 111: Program Design I Lecture 5: US Law when others have encryption keys; if, for

CS 111: Program Design I Lecture 5: US Law when others have encryption keys; if, for CS 111: Program Desig I Lecture 5: US Law whe others have ecryptio keys; if, for Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago September 8, 2016 Lavabit ad Sowde Lavabit was a ecrypted

More information

CS200: Hash Tables. Prichard Ch CS200 - Hash Tables 1

CS200: Hash Tables. Prichard Ch CS200 - Hash Tables 1 CS200: Hash Tables Prichard Ch. 13.2 CS200 - Hash Tables 1 Table Implemetatios: average cases Search Add Remove Sorted array-based Usorted array-based Balaced Search Trees O(log ) O() O() O() O(1) O()

More information

Computers and Scientific Thinking

Computers and Scientific Thinking Computers ad Scietific Thikig David Reed, Creighto Uiversity Chapter 15 JavaScript Strigs 1 Strigs as Objects so far, your iteractive Web pages have maipulated strigs i simple ways use text box to iput

More information

9.1. Sequences and Series. Sequences. What you should learn. Why you should learn it. Definition of Sequence

9.1. Sequences and Series. Sequences. What you should learn. Why you should learn it. Definition of Sequence _9.qxd // : AM Page Chapter 9 Sequeces, Series, ad Probability 9. Sequeces ad Series What you should lear Use sequece otatio to write the terms of sequeces. Use factorial otatio. Use summatio otatio to

More information

Parabolic Path to a Best Best-Fit Line:

Parabolic Path to a Best Best-Fit Line: Studet Activity : Fidig the Least Squares Regressio Lie By Explorig the Relatioship betwee Slope ad Residuals Objective: How does oe determie a best best-fit lie for a set of data? Eyeballig it may be

More information

Numerical Methods Lecture 6 - Curve Fitting Techniques

Numerical Methods Lecture 6 - Curve Fitting Techniques Numerical Methods Lecture 6 - Curve Fittig Techiques Topics motivatio iterpolatio liear regressio higher order polyomial form expoetial form Curve fittig - motivatio For root fidig, we used a give fuctio

More information

COP4020 Programming Languages. Subroutines and Parameter Passing Prof. Robert van Engelen

COP4020 Programming Languages. Subroutines and Parameter Passing Prof. Robert van Engelen COP4020 Programmig Laguages Subrouties ad Parameter Passig Prof. Robert va Egele Overview Parameter passig modes Subroutie closures as parameters Special-purpose parameters Fuctio returs COP4020 Fall 2016

More information

MR-2010I %MktBSize Macro 989. %MktBSize Macro

MR-2010I %MktBSize Macro 989. %MktBSize Macro MR-2010I %MktBSize Macro 989 %MktBSize Macro The %MktBSize autocall macro suggests sizes for balaced icomplete block desigs (BIBDs). The sizes that it reports are sizes that meet ecessary but ot sufficiet

More information

Overview Chapter 12 A display model

Overview Chapter 12 A display model Overview Chapter 12 A display model Why graphics? A graphics model Examples Bjare Stroustrup www.stroustrup.com/programmig 3 Why bother with graphics ad GUI? Why bother with graphics ad GUI? It s very

More information

Linked Lists 11/16/18. Preliminaries. Java References. Objects and references. Self references. Linking self-referential nodes

Linked Lists 11/16/18. Preliminaries. Java References. Objects and references. Self references. Linking self-referential nodes Prelimiaries Liked Lists public class StrageObject { Strig ame; StrageObject other; Arrays are ot always the optimal data structure: A array has fixed size eeds to be copied to expad its capacity Addig

More information

Investigation Monitoring Inventory

Investigation Monitoring Inventory Ivestigatio Moitorig Ivetory Name Period Date Art Smith has bee providig the prits of a egravig to FieArt Gallery. He plas to make just 2000 more prits. FieArt has already received 70 of Art s prits. The

More information

n The C++ template facility provides the ability to define n A generic facility allows code to be written once then

n The C++ template facility provides the ability to define n A generic facility allows code to be written once then UCLA PIC 10 B Problem Solvig usig C++ Programmig Ivo Diov, Asst. Prof. i Mathematics, Neurology, Statistics Istructor: Teachig Assistat: Suzae Nezzar, Mathematics Chapter 13 Templates for More Abstractio

More information

The Open University, Walton Hall, Milton Keynes, MK7 6AA First published 2004

The Open University, Walton Hall, Milton Keynes, MK7 6AA First published 2004 8 Programs ad data This publicatio forms part of a Ope Uiversity course M150 Data, Computig ad Iformatio. Details of this ad other Ope Uiversity courses ca be obtaied from the Course Iformatio ad Advice

More information

CS 111: Program Design I Lecture # 7: Web Crawler, Functions; Open Access

CS 111: Program Design I Lecture # 7: Web Crawler, Functions; Open Access CS 111: Program Desig I Lecture # 7: Web Crawler, Fuctios; Ope Access Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago September 13, 2016 Lab Hit/Remider word = "hi" word.upper() à "HI" Questio

More information

Solution printed. Do not start the test until instructed to do so! CS 2604 Data Structures Midterm Spring, Instructions:

Solution printed. Do not start the test until instructed to do so! CS 2604 Data Structures Midterm Spring, Instructions: CS 604 Data Structures Midterm Sprig, 00 VIRG INIA POLYTECHNIC INSTITUTE AND STATE U T PROSI M UNI VERSI TY Istructios: Prit your ame i the space provided below. This examiatio is closed book ad closed

More information

Mathematical Stat I: solutions of homework 1

Mathematical Stat I: solutions of homework 1 Mathematical Stat I: solutios of homework Name: Studet Id N:. Suppose we tur over cards simultaeously from two well shuffled decks of ordiary playig cards. We say we obtai a exact match o a particular

More information

WORKED EXAMPLE 7.1. Producing a Mass Mailing. We want to automate the process of producing mass mailings. A typical letter might look as follows:

WORKED EXAMPLE 7.1. Producing a Mass Mailing. We want to automate the process of producing mass mailings. A typical letter might look as follows: Worked Example 7.1 Producig a Mass Mailig 1 WORKED EXAMPLE 7.1 Producig a Mass Mailig We wat to automate the process of producig mass mailigs. A typical letter might look as follows: To: Ms. Sally Smith

More information

Definitions. Error. A wrong decision made during software development

Definitions. Error. A wrong decision made during software development Debuggig Defiitios Error A wrog decisio made durig software developmet Defiitios 2 Error A wrog decisio made durig software developmet Defect bug sometimes meas this The term Fault is also used Property

More information

Lecture 28: Data Link Layer

Lecture 28: Data Link Layer Automatic Repeat Request (ARQ) 2. Go ack N ARQ Although the Stop ad Wait ARQ is very simple, you ca easily show that it has very the low efficiecy. The low efficiecy comes from the fact that the trasmittig

More information

From last week. Lecture 5. Outline. Principles of programming languages

From last week. Lecture 5. Outline. Principles of programming languages Priciples of programmig laguages From last week Lecture 5 http://few.vu.l/~silvis/ppl/2007 Natalia Silvis-Cividjia e-mail: silvis@few.vu.l ML has o assigmet. Explai how to access a old bidig? Is & for

More information

CSC 220: Computer Organization Unit 11 Basic Computer Organization and Design

CSC 220: Computer Organization Unit 11 Basic Computer Organization and Design College of Computer ad Iformatio Scieces Departmet of Computer Sciece CSC 220: Computer Orgaizatio Uit 11 Basic Computer Orgaizatio ad Desig 1 For the rest of the semester, we ll focus o computer architecture:

More information

Behavioral Modeling in Verilog

Behavioral Modeling in Verilog Behavioral Modelig i Verilog COE 202 Digital Logic Desig Dr. Muhamed Mudawar Kig Fahd Uiversity of Petroleum ad Mierals Presetatio Outlie Itroductio to Dataflow ad Behavioral Modelig Verilog Operators

More information

Homework 1 Solutions MA 522 Fall 2017

Homework 1 Solutions MA 522 Fall 2017 Homework 1 Solutios MA 5 Fall 017 1. Cosider the searchig problem: Iput A sequece of umbers A = [a 1,..., a ] ad a value v. Output A idex i such that v = A[i] or the special value NIL if v does ot appear

More information

CHAPTER IV: GRAPH THEORY. Section 1: Introduction to Graphs

CHAPTER IV: GRAPH THEORY. Section 1: Introduction to Graphs CHAPTER IV: GRAPH THEORY Sectio : Itroductio to Graphs Sice this class is called Number-Theoretic ad Discrete Structures, it would be a crime to oly focus o umber theory regardless how woderful those topics

More information

Computational Geometry

Computational Geometry Computatioal Geometry Chapter 4 Liear programmig Duality Smallest eclosig disk O the Ageda Liear Programmig Slides courtesy of Craig Gotsma 4. 4. Liear Programmig - Example Defie: (amout amout cosumed

More information

A graphical view of big-o notation. c*g(n) f(n) f(n) = O(g(n))

A graphical view of big-o notation. c*g(n) f(n) f(n) = O(g(n)) ca see that time required to search/sort grows with size of We How do space/time eeds of program grow with iput size? iput. time: cout umber of operatios as fuctio of iput Executio size operatio Assigmet:

More information

Workflow model GM AR. Gumpy. Dynagump. At a very high level, this is what gump does. We ll be looking at each of the items described here seperately.

Workflow model GM AR. Gumpy. Dynagump. At a very high level, this is what gump does. We ll be looking at each of the items described here seperately. Workflow model GM AR Gumpy RM Dyagump At a very high level, this is what gump does. We ll be lookig at each of the items described here seperately. User edits project descriptor ad commits s maitai their

More information

Computer Science Foundation Exam. August 12, Computer Science. Section 1A. No Calculators! KEY. Solutions and Grading Criteria.

Computer Science Foundation Exam. August 12, Computer Science. Section 1A. No Calculators! KEY. Solutions and Grading Criteria. Computer Sciece Foudatio Exam August, 005 Computer Sciece Sectio A No Calculators! Name: SSN: KEY Solutios ad Gradig Criteria Score: 50 I this sectio of the exam, there are four (4) problems. You must

More information

CS 111: Program Design I Lecture 21: Network Analysis. Robert H. Sloan & Richard Warner University of Illinois at Chicago April 10, 2018

CS 111: Program Design I Lecture 21: Network Analysis. Robert H. Sloan & Richard Warner University of Illinois at Chicago April 10, 2018 CS 111: Program Desig I Lecture 21: Network Aalysis Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago April 10, 2018 NETWORK ANALYSIS Which displays a graph i the sese of graph/etwork aalysis?

More information

top() Applications of Stacks

top() Applications of Stacks CS22 Algorithms ad Data Structures MW :00 am - 2: pm, MSEC 0 Istructor: Xiao Qi Lecture 6: Stacks ad Queues Aoucemets Quiz results Homework 2 is available Due o September 29 th, 2004 www.cs.mt.edu~xqicoursescs22

More information

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor. Part A Datapath Design

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor. Part A Datapath Design COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Chapter The Processor Part A path Desig Itroductio CPU performace factors Istructio cout Determied by ISA ad compiler. CPI ad

More information

Learning to Shoot a Goal Lecture 8: Learning Models and Skills

Learning to Shoot a Goal Lecture 8: Learning Models and Skills Learig to Shoot a Goal Lecture 8: Learig Models ad Skills How do we acquire skill at shootig goals? CS 344R/393R: Robotics Bejami Kuipers Learig to Shoot a Goal The robot eeds to shoot the ball i the goal.

More information

Data diverse software fault tolerance techniques

Data diverse software fault tolerance techniques Data diverse software fault tolerace techiques Complemets desig diversity by compesatig for desig diversity s s limitatios Ivolves obtaiig a related set of poits i the program data space, executig the

More information

CS 111: Program Design I Lecture 15: Objects, Pandas, Modules. Robert H. Sloan & Richard Warner University of Illinois at Chicago October 13, 2016

CS 111: Program Design I Lecture 15: Objects, Pandas, Modules. Robert H. Sloan & Richard Warner University of Illinois at Chicago October 13, 2016 CS 111: Program Desig I Lecture 15: Objects, Padas, Modules Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago October 13, 2016 OBJECTS AND DOT NOTATION Objects (Implicit i Chapter 2, Variables,

More information

Analysis Metrics. Intro to Algorithm Analysis. Slides. 12. Alg Analysis. 12. Alg Analysis

Analysis Metrics. Intro to Algorithm Analysis. Slides. 12. Alg Analysis. 12. Alg Analysis Itro to Algorithm Aalysis Aalysis Metrics Slides. Table of Cotets. Aalysis Metrics 3. Exact Aalysis Rules 4. Simple Summatio 5. Summatio Formulas 6. Order of Magitude 7. Big-O otatio 8. Big-O Theorems

More information

Administrative UNSUPERVISED LEARNING. Unsupervised learning. Supervised learning 11/25/13. Final project. No office hours today

Administrative UNSUPERVISED LEARNING. Unsupervised learning. Supervised learning 11/25/13. Final project. No office hours today Admiistrative Fial project No office hours today UNSUPERVISED LEARNING David Kauchak CS 451 Fall 2013 Supervised learig Usupervised learig label label 1 label 3 model/ predictor label 4 label 5 Supervised

More information

Weston Anniversary Fund

Weston Anniversary Fund Westo Olie Applicatio Guide 2018 1 This guide is desiged to help charities applyig to the Westo to use our olie applicatio form. The Westo is ope to applicatios from 5th Jauary 2018 ad closes o 30th Jue

More information

1.2 Binomial Coefficients and Subsets

1.2 Binomial Coefficients and Subsets 1.2. BINOMIAL COEFFICIENTS AND SUBSETS 13 1.2 Biomial Coefficiets ad Subsets 1.2-1 The loop below is part of a program to determie the umber of triagles formed by poits i the plae. for i =1 to for j =

More information

CSC165H1 Worksheet: Tutorial 8 Algorithm analysis (SOLUTIONS)

CSC165H1 Worksheet: Tutorial 8 Algorithm analysis (SOLUTIONS) CSC165H1, Witer 018 Learig Objectives By the ed of this worksheet, you will: Aalyse the ruig time of fuctios cotaiig ested loops. 1. Nested loop variatios. Each of the followig fuctios takes as iput a

More information

Last class. n Scheme. n Equality testing. n eq? vs. equal? n Higher-order functions. n map, foldr, foldl. n Tail recursion

Last class. n Scheme. n Equality testing. n eq? vs. equal? n Higher-order functions. n map, foldr, foldl. n Tail recursion Aoucemets HW6 due today HW7 is out A team assigmet Submitty page will be up toight Fuctioal correctess: 75%, Commets : 25% Last class Equality testig eq? vs. equal? Higher-order fuctios map, foldr, foldl

More information

COP4020 Programming Languages. Compilers and Interpreters Prof. Robert van Engelen

COP4020 Programming Languages. Compilers and Interpreters Prof. Robert van Engelen COP4020 mig Laguages Compilers ad Iterpreters Prof. Robert va Egele Overview Commo compiler ad iterpreter cofiguratios Virtual machies Itegrated developmet eviromets Compiler phases Lexical aalysis Sytax

More information