vector subscript: Amethod of specifying an array section by means of a vector containing the subscripts of the elements of the parent array that are to constitute the array section. virtual function: A genetic function, with a specific return type, extended later for each new argument type. void subprogram: A C++ subprogram with an empty argument list and/or a subroutine with no returned argument. work array: A temporary array used for the storage of intermediate results during processing.
Question Bank with Answer UNIT – I PART - A 1. What is the output of the following program, if it is correct? Otherwise indicate the mistake: [May 2006] int l=10; Void main [] {int l=20; {int l=30; cout<
Class is the ADT where as structure is udt. Class needs access specifier such as private, public & private where as structure members can be accessed by public by default & don’t need any accessfiers. Class is oops where structure is borrowed from traditional structured [pop] concept.
3. What is abstract Class? [Nov-2009] An abstract class is a class that is designed to be specifically used as a base class.
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An abstract class contains at least one pure virtual function. You declare a pure virtual function by using a pure specifier [= 0] in the declaration of a virtual member function in the class declaration 4. List out the advantages of new operator over malloc[] [Dec-2012]
It automatically computes the size of the data object. It automatically returns the correct pointer type It is possible to initialize the objects while creating_ the memory space. It can be overloaded.
5. What are the basic concepts of OOS? [ April -2011] 1. 2. 3. 4. 5. 6. 7.
Objects. Classes. Data abstraction and Encapsulation. Inheritance. Polymorphism. Dynamic binding. Message passing
6. What is the difference between local variable and data member? [Nov-2011]
A data member belongs to an object of a class whereas local variable belongs to its current scope. A local variable is declared within the body of a function and can be used only from the point at which it is declared to the immediately following closing brace. A data member is declared in a class definition, but not in the body of any of the class member functions. Data members are accessible to all member function of the class.
7. What is the function parameter? Difference between parameter and Argument. [Nov 2011]
A function parameter is a variable declared in the prototype or declaration of a function: o void foo[int x]; // prototype -- x is a parameter o void foo[int x] // declaration -- x is a parameter o { o } An argument is the value that is passed to the function in place of a parameter
8. What is data hiding? [April -2011,Nov-2010]
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The insulation of data from direct access by the program is called as data hiding or information binding. The data is not accessible to the outside world and only those functions, which are wrapped in the class, can access it.
9. What are the advantages of Default Arguments? [Nov-2010] The function assigns a default value to the parameter which does not have a matching argument in the function call. They are useful in situations where some arguments always have the same value. e.g., float amt [float P, float n, float r = 0.15]; 10. List out the basic concepts of Object Oriented Programming. [Nov-2009]
Objects Classes Data Abstraction and Encapsulation Inheritance Polymorphism Dynamic Binding Message Passing
11. What are abstract classes? [Nov 2009, Apr 2013] o Classes containing at least one pure virtual function become abstract classes. o Classes inheriting abstract classes must redefine the pure virtual functions; otherwise the derived classes also will become abstract. Abstract classes cannot be instantiated. 12. Define abstraction and Encapsulation [Apr 2011] Data Abstraction Abstraction refers to the act of representing the essential features without including the background details or explanations. Data Encapsulation The wrapping up of data and functions into a single unit is known as data encapsulation. 13. What is the Need for Static Members [April 2011]
Class members can be declared using the storage class specifier static in the class member list. Only one copy of the static member is shared by all objects of a class in a program. When you declare an object of a class having a static member, the static member is not part of the class object.
14. Define Polymorphism. [Apr 2013] 109
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Polymorphism is another important oops concept. Polymorphism means the ability to take more than one form. For example, an operation may exhibit different behavior in different instances, behavior depends upon the types of data used in the operation.
15. What do you mean by pure virtual functions? [Dec2008] 1. A pure virtual member function is a member function that the base class forces derived classes to provide. 2. Any class containing any pure virtual function cannot be used to create object of its own type. 16. Write a C++ program to check the given integer is prime or composite number. [Apr2010] #include #include int main[] { int num,d,ctr; clrscr[]; printf["\n Enter a number="]; scanf["%d",&num]; d=1; ctr=0; while[d<=num] { if[num%d==0] ctr++; d=d+1; } if[ctr==2] printf["\n %d is a prime number",num]; else printf["\n %d is a composite number",num]; getch[]; return[0]; } 17. What is function Prototype? [DEC 2011] A function prototype or function interface in C, Perl, PHP or C++ is a declaration of a function that omits the function body but does specify the function's return type, name and argument types. While a function definition specifies what a function does, a function prototype can be thought of as specifying its interface. 110
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18. List out four Storage Classes in C++ [Nov 2008] Storage classes are used to specify the lifetime and scope of variables. How storage is allocated for variables and how variable is treated by complier depends on these storage classes. These are basically divided into 5 different types : 1. Global variablES 2. Local variables 3. Register variables 4. Static variables 5. Extern variables 19. What is an identifier?
Identifiers are names for various programming elements in c++ program. such as variables, arrays, function, structures, union, labels ect., An identifier can be Composed only of uppercase, lower case letter, underscore and digits, but should start only with an alphabet or an underscore.
20. What is a keyword? Keywords are word whose meanings have been already defined in the c compiler. They are also called as reserved words. (ex) main(), if, else, else, if, scanf, printf, switch, for, goto, while ect., 21. List out the benefits of oops. • Can create new programs faster because we can reuse code • Easier to create new data types • Easier memory management • Programs should be less bug-prone, as it uses a stricter syntax and type checking. • `Data hiding', the usage of data by one program part while other program parts cannot access the data Will whiten your teeth 22. List out the application of oops. • Client server computing • Simulation such as flight simulations. • Object-oriented database applications. • Artificial intelligence and expert system • Computer aided design and manufacturing systems. 23. Define data hiding.
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The purpose of the exception handling mechanism is to provide a means to detect and report an “exceptional circumstance” so that appropriate action can be taken.
24. What is the use of scope resolution operator? In C, the global version of the variable cannot be accessed from within the inner block. C++ resolves this problem by introducing a new operator :: called the scope resolution operator. It is used to uncover a hidden variable. Syntax: :: variable name 25. When will you make a function inline? When the function definition is small, we can make that function an inline function and we can mainly go for inline function to eliminate the cost of calls to small functions. 26. What is overloading? Overloading refers to the use of the same thing for different purposes. There are 2 types of overloading: • Function overloading • Operator overloading 27. What is the difference between normal function and a recursive function?
A recursive function is a function, which call it whereas a normal function does not. Recursive function can’t be directly invoked by main function
28. What are objects? How are they created? Objects are basic run-time entities in an object-oriented programming system. The class variables are known as objects. Objects are created by using the syntax: classname obj1,obj2,…,objn; (or) during definition of the class: class classname { ------}obj1,obj2,…,objn; 29. List some of the special properties of constructor function. • They should be declared in the public section. • They are invoked automatically when the objects are created. 112
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• They do not have return types, not even void and cannot return values. • Constructors cannot be virtual. Like other C++ functions, they can have default arguments 30. Describe the importance of destructor. A destructor destroys the objects that have been created by a constructor upon exit from the program or block to release memory space for future use. It is a member function whose name is the same as the class name but is preceded by a tilde. Syntax: ~classname() {} 31. What do you mean by friend functions? C++ allows some common functions to be made friendly with any number of classes, thereby allowing the function to have access to the private data of thse classes. Such a function need not be a member of any of these classes. Such common functions are called friend functions. 32. What are member functions? Functions that are declared within the class definition are referred as member function. 33. Define dynamic binding. Dynamic binding means that the code associated with a given procedure call is not known until the time of the call at run-time. 34. Write any four properties of constructor.(DEC 2010)
Constructors should be declared in the public section. They are invoked automatically when the objects are created. They do not have return types They cannot be inherited
35. List any four Operators that cannot be overloaded.(DEC 2010) (DEC 2009) (DEC 2011) Class member access operator (. , .*) Scope resolution operator (::) Size operator ( sizeof ) Conditional operator (?:) 36. What is a Destructor? (DEC 2012) 113
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A destructor is used to destroy the objects that have been created by a constructor. It is a special member function whose name is same as the class and is preceded by a tilde ‘~’ symbol. When an object goes out from object creation, automatically destructor will be executed. Example: class File { public: ~File(); //destructor declaration }; File::~File() { close(); // destructor definition } 37. What is the Need for initialization of object using Constructor? (DEC 2012) If we fails to create a constructor for a class, then the compiler will create a constructor by default in the name of class name without having any arguments at the time of compilation and provides the initial values to its data members. So we have to initialize the objects using constructor
38. What is a Copy Constructor (DEC 2009) A copy constructor is used to declare and initialize an object from another object. It takes a reference to an object of the same class as an argument Eg: integer i2(i1); would define the object i2 at the same time initialize it to the values of i1. Another form of this statement is Eg: integer i2=i1; The process of initializing through a copy constructor is known as copy initialization. 39. Give an example for a Copy Constructor (JUNE 2013) #include #include using namespace std; class Example { // Variable Declaration int a,b; public: 114
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//Constructor with Argument Example(int x,int y) { // Assign Values In Constructor a=x; b=y; cout<<"\nIm Constructor"; } void Display() { cout<<"\nValues :"<
40. What is the Need for Destructors? (June 2013)
Destructor is used to destroy an object. By destroying the object memory occupied by the object is released.
41. Explain the functions of Default Constructor(MAY 2011) The main function of the constructor is, if the programmer fails to create a constructor for a class, then the compiler will create a constructor by default in the name of class name without having any arguments at the time of compilation and provides the initial values to its data members. Since it is created by the compiler by default, the no argument constructor is called as default constructor. 42. What is the need for Overloading an operator(MAY 2011)
To define a new relation task to an operator, we must specify what it means in relation to the class to which the operator is applied. This is done with the help of a special function called operator function. It allows the developer to program using notation closer to the target domain and allow user types to look like types built into the language. 115
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The ability to tell the compiler how to perform a certain operation when its corresponding operator is used on one or more variables.
43. What is the function of get and put function (MAY 2010) Cin.get(ch) reads a character from cin and stores what is read in ch. Cout.put(ch) reads a character and writes to cout
UNIT -I PART – B 1. State the merits and demerits of object oriented methodology. Merits: • Can create new programs faster because we can reuse code • Easier to create new data types • Easier memory management • Programs should be less bug-prone, as it uses a stricter syntax and type checking. • `Data hiding', the usage of data by one program part while other program parts cannot access the data Will whiten your teeth Demerits: • disadvantages of C++ over Java: • Java protects you from making mistakes that C/C++ don’t, as you’ve • C++ has many concepts and possibilities so it has a steep learning curve • extensive use of operator overloading, function overloading and virtual • functions can very quickly make C++ programs very complicated • shortcuts offered in C++ can often make it completely unreadable, just like in C 2. Explain the basic concepts of object oriented programming in detail with example. BASIC CONCEPTS OF OBJECT ORIENTED PROGRAMMING These include: Objects Classes Data abstraction and encapsulation Inheritance Polymorphism Dynamic binding Message passing Objects:
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Objects are the basic run-time entities in an object oriented programming. They may representa person, a place, a bank account or any item that the program has to handle. They may represent user-defined data such as vectors, time and lists. Programming problem is analyzed in terms of objects and the nature of communication b/n them. When a program is executed, the objects interact by sending messages to another. Each object contains data and code to manipulate the data. Objects can interact without having to know the etails of each others data or code. It is sufficient to know the type of message accepted, and the type of message accepted and the type of response returned by the objects. Classes: The entire set of data and code of an object can made a user defined data type with the help of a class. In fact the objects are variable of the type class. Once class has been defined we can create any number of objects belonging to that class. In short, a class serves as a blueprint or a plan or a template. It specifies what data and what functions will be included in objects of that class. Defining the class doesn’t create any objects, just as the mere existence of a type int doesn’t create any variables. Data Abstraction and Encapsulation: The wrapping up of data and functions into a single unit is known as encapsulation. It is the most striking feature of the class. The data is not accessible to the outside world and only those functions which are wrapped in the class can access it. These functions provide interface b/n the object’s data and the program. This insulation of the data from direct access by the program is called data hiding or information hiding. Abstraction represents the act of representing the essential features without including the background details or explanations. Classes use the concept of abstraction and are defined as a list of abstract attributes such as size, weight and cost and functions to operate on these attributes. The attributes are called data members and functions are called member functions or methods. Since the classes use the concept of data abstraction, they are known as Abstract Data Types (ADT). Inheritance: It is the process by which objects of one class acquire the properties of objects of another class. It supports the concept of hierarchical classification. For example, the bird ‘robin’ is a part of the class ‘flying bird’ which is again a part of the class ‘bird’. This concept provides the idea of reusability. This means that we can add additional features to an existing class without modifying it. This is possible by a deriving a new class from an existing one. The new class will have the combined features of both the classes. Polymorphism: It means the ability to take more than one form. An operation may exhibit different behavior in different instances. The behavior depends upon the types of data used in the 117
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operation. For example the operation addition will generate sum if the operands are numbers whereas if the operands are strings then the operation would produce a third string by concatenation. The process of making an operator to exhibit different behaviors in different instances is known as operator overloading. A single function name can be used to handle different types of tasks based on the number and types of arguments. This is known as function overloading. It allows objects to have different internal structures to share the same external interface. Dynamic Binding: Binding refers to the linking of a procedure call to the code to be executed in response to the call. Dynamic Binding (late binding) means the code associated with the given procedure call is not known until the time of the call at run-time. It is associated with the polymorphism and inheritance. Message Passing: The process of programming in OOP involves the following basic steps: Creating classes that define objects and their behavior Creating objects from class definitions Establishing communication among objects A message for an object is request for execution of a procedure and therefore will invoke a function (procedure) in the receiving object that generates the desired result. Message passing involves specifying the name of the object, the name of the function (message) and the information to be sent. E.g.: employee.salary(name); Object: employee Message: salary Information: name
3. State the rules to be followed while overloading an operator.write a program to illustrate overloading. OPERATOR OVERLOADING: • Operator overloading means giving additional meaning to existing operators • By operator overloading an existing operator can be made to perform different operations than the stipulated one. • It doesn’t change the meaning and precedence of the original operator. • Almost all the operators in c++ can be overloaded except the following 1) 2) 3) 4)
Sizeof () Conditional operator (?:) Scope resolution operator (::) Class member access operator (.,.*) 118
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example the operation addition will generate sum if the operands are numbers whereas if the operands are strings then the operation would produce a third string by concatenation. The process of making an operator to exhibit different behaviors in different instances is known as operator overloading. A single function name can be used to handle different types of tasks based on the number and types of arguments. This is known as function overloading. It allows objects to have different internal structures to share the same external interface. Dynamic Binding: Binding refers to the linking of a procedure call to the code to be executed in response to the call. Dynamic Binding (late binding) means the code associated with the given procedure call is not known until the time of the call at run-time. It is associated with the polymorphism and inheritance. Message Passing: The process of programming in OOP involves the following basic steps: Creating classes that define objects and their behavior Creating objects from class definitions Establishing communication among objects A message for an object is request for execution of a procedure and therefore will invoke a function (procedure) in the receiving object that generates the desired result. Message passing involves specifying the name of the object, the name of the function (message) and the information to be sent. E.g.: employee.salary(name); Object: employee Message: salary Information: name 3. State the rules to be followed while overloading an operator.write a program to illustrate overloading. OPERATOR OVERLOADING: • Operator overloading means giving additional meaning to existing operators • By operator overloading an existing operator can be made to perform different operations than the stipulated one. • It doesn’t change the meaning and precedence of the original operator. • Almost all the operators in c++ can be overloaded except the following o Sizeof () o Conditional operator (?:) o Scope resolution operator (::) 119
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o Class member access operator (.,.*) SYNTAX: Return-type operator op-symbol(argument list) { body of the function; } Generally there are three general classifications of operator namely Operator Unary binary ternary Among the above unary and binary operators can be overloaded and ternary operator cannot be overloaded. OVERLOADING UNARY OPERATOR: Unary operators like unary + , Unary - ….. can be overloaded as follows EXAMPLE: #include #include class unary { int a; public: void get() { a=10; } void show() { cout <<"\n The value of the object is\n"< } void operator - () { a=-a; } }; void main() { clrscr(); unary u; u.get(); u.show(); -u; //unary operator - called u.show(); getch(); } 120
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O/P: The value of the object is 10 The value of the object is -10 • In the above program, the unary operator minus is overloaded. • In this an object ‘u’ is created and given the value 10 • When the unary operator – is called the operator function is invoked and the value of the member data of the object ‘u’ is negated. • The negated value is then displayed.
4. (i) Describe the application of oop technology
Applications of OOP: Real time systems Simulation and modeling AI and expert systems Neural networks and parallel programming. Decision support and office automation systems
(ii) What is an inline function? INLINE FUNCTIONS : An inline function is a function that is expanded in line when it is invoked. That is , the complier replaces the function call with the corresponding function code.The inline function are defined as follows: inline function header { function body } Example : inline int cube(int a) { return (a*a*a); } Program : #include 121
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inline float mul(float x, float y) { return (x*y); } inline float div(double p, double q) { return( p / q ) } int main() { float a=12.35; float b=9.32; cout<< mul(a,b); cout< return 0; } 5. (i). Explain copy constructor with suitable c++ coding. Constructor: A constructor is a special member function whose task is to initialize the objects of its class. It is special because its name is the same as the class name. The constructor is invoked whenever an object of its associated class it’s created. A constructor is declared and defined as follows: class sample { int m,n; public: sample() { m = n = 0; } // some code }; void main() { sample s; // object is created // some code } During the object creation, it also initializes the data member’s m and n to 0. Default Constructor: A constructor that accepts no parameters is called the default constructor. 122
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Characteristics of a constructor:
They should be declared in the public section They are invoked automatically when the objects are created They do not have return types They cannot be inherited They can have default arguments It cannot be virtual We cannot refer to their addresses An object with a constructor or destructor can not be used as a member of a union They make ‘implicit calls’ to the operators new and delete when memory allocation is required
Copy constructor: A copy constructor takes a reference to an object of the same class as itself as an argument. Example: It sets the value of every data element of s3 to the value of the corresponding data element of s2 Constructors with default arguments: It is possible to define constructors with default arguments. Example: Inside the class definition: sample(int a, int b = 10) Inside the main(): sample s2(20); assigns 20 to x and 10 to y. where as sample s5(25,35) ; assigns 25 to x and 35 to y (ii).List out the rules for overloading operator. OPERATOR OVERLOADING: • Operator overloading means giving additional meaning to existing operators • By operator overloading an existing operator can be made to perform different operations than the stipulated one. • It doesn’t change the meaning and precedence of the original operator. • Almost all the operators in c++ can be overloaded except the following o Sizeof () o Conditional operator (?:) o Scope resolution operator (::) 123
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o Class member access operator (.,.*) SYNTAX: Return-type operator op-symbol(argument list) { body of the function; } Generally there are three general classifications of operator namely Operator Unary binary ternary Among the above unary and binary operators can be overloaded and ternary operator cannot be overloaded. 6. Compare and contrast the following control structure with example: (i). break statement & continue statement. Break continue a) Used to terminate the loops or to Used to transfer the control to the Exit loop from a switch. Start of loop b) The break statement when executed The continue statement when causes Immediate termination of loop executed caused immediate containing it. termination of the current iteration of the loop. (ii). Do – while and the while statement. While loop do-while loop c) The while loop tests the condition The do-while loop tests the condition before each iteration after the first iteration d) If the condition fails initially the loop Even if the condition fails initially Is skipped entirely even in the first the loop is executed once in a Iteration.
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UNIT – II PAERT – A 1. What are templates? (AUC DEC 2009)
Template is one of the features added to C++. It is new concepts which enable us to define generic classes and functions and thus provides support for generic programming. A template can be used to create a family of classes or functions.
2. Illustrate the exception handling mechanism. (AUC DEC 2009) C++ exception handling mechanism is basically upon three keywords, namely, try, throw, and catch. try – is used to preface a block of statements which may generate exceptions. throw - When an exception is detected, it is thrown using a throw statement in the try block. Catch- A catch block defined by the keyword catch ‘catches’ the exception ‘thrown’ by the thrown statement in the try block and handles its appropriately. 3. What happens when a raised exception is not caught by catch block? (AUC MAY 2010)
If the type of object thrown matches the arg type in the catch statement, then catch block is executed for handling the exception. If they do not match the program is aborted with the help of abort() function which is invoked by default. When no exception is detected and thrown, the control goes to the statement immediately after the catch block. That is the catch block is skipped.
4. Give the syntax of a pointer to a function which returns an integer and takes arguments one of integer type and 2 of float type. What is the difference between a class and a structure? (AUC MAY 2010) int (X_fun) (int, float); 5. What is a template? What are their advantages (AUC DEC 2010/JUN 2012/DEC 2012)
A template can be used to create a family of classes or functions. A template is defined with a parameter that would be replaced by a specified data type at the time of actual use of the class or functions. Supporting different data types in a single framework. The template are sometimes called parameterized classes or functions.
6. How is an exception handled in C++? (AUC DEC 2010)
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Exceptions are run time anomalies or unusual conditions that a program may encounter while executing. 1. Find the problem (Hit the exception) 2. Inform that an error has occurred.( Throw the exception) 3. Receive the error information. ( Catch the exception) 4. Take corrective actions.( Handle the exception) 7. What is function template? Explain. (AUC MAY 2011)
Like class template, we can also define function templates that could be used to create a family of functions with different argument types. The general format of a function template is: template returntypefunctionname ( arguments of type T) { // ……… //……….Body of function with type T wherever appropriate //……….. }
8. List five common examples of exceptions. (AUC MAY 2011)
Division by zero Access to an array outside of its bounds Running out of memory or disk space.
9. What is class template? (AUC DEC 2011)
Templates allows to define generic classes. It is a simple process to create a generic class using a template with an anonymous type. The general format of class template is: template classclassname { // ………class member specification. //………. with anonymous type T wherever appropriate //……,….. }
10. What are 3 basic keywords of exception handling mechanism? (AUC DEC 2011) C++ exception handling mechanism is basically built upon three keywords try throw catch 126
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11. What are the c++ operators that cannot be overloaded? Size operator (sizeof) Scope resolution operator (::) member access operators(. , .*) Conditional operator (?:) 12. What is a virtual base class? When a class is declared as virtual c++ takes care to see that only copy of that class is inherited, regardless of how many inheritance paths exist between the virtual base class and a derived class. 13. What is the difference between base class and derived class? The biggest difference between the base class and the derived class is that the derived class contains the data members of both the base and its own data members. The other difference is based on the visibility modes of the data members. 14. What are the rules governing the declaration of a class of multiple inheritance? • More than one class name should be specified after the : symbol. • Visibility modes must be taken care of. If several inheritance paths are employed for a single derived class the base class must be appropriately declared 15. Mention the types of inheritance. 1.Single inheritance. 2. Multiple inheritance. 3. Hierarchical inheritance. 4. Multilevel inheritance. 5. Hybrid inheritance. 6. Define dynamic binding. APRIL AMY 2010 Dynamic binding means that the code associated with a given procedure call is not known until the time of the call at run-time. 17. What do u mean by pure virtual functions? A pure virtual function is a function declared in a base class that has no definition relative to the base class. In such cases, the compiler requires each derived class to either define the function or redeclare it as a pure virtual function. A class containing pure virtual functions cannot be used to declare any objects of its own. 18. Mention the key words used in exception handling. 127
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The keywords used in exception handling are • throw • try • catch 19. List the ios format function. The ios format functions are as follows: • width() • precision() • fill() • setf() • unsetf() 20. List the manipulators. The manipulators are: • setw() • setprecision() • setfill() • setiosflags() • resetiosflags() 21. Mention the equicalent ios function for manipulators. Manipulator Equivalent ios function setw(int w) width() setprecision(int d) precision() setfill(int c) fill() setiosflags(long f) setf() resetiosflags(long f) unsetf() endl “\n” 22. Define fill functions. The fill( ) function can be used to fill the unused positions of the field by any desired character rather than by white spaces (by default). It is used in the following form: cout.fill(ch); where ch represents the character which is used for filling the unused positions. For example, the statements cout.fill(‘*’); cout.width(10); cout<<5250<<”\n”; 23 .Give the syntax of exception handling mechanism. The syntax of exception handling mechanism is as follows: 128
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try { --------------------throw exception --------------------} catch(type arguments) { ----------------------------------------} ------------------------------------------UNIT – II PART – B 1. Explain hybrid inheritance with suitable C++ coding. 2. Explain multiple inheritances with suitable c++ coding. INHERITANCE: • Inheritance is a mechanism of deriving a new class from a old class. • It provides the concept of reusability • By inheritance some or all the properties of a class can be derived in to another class. • The class which provides the properties is called as base class and the class which derives the properties is called as derived class. Multiple inheritance: It is a type of inheritance in which a class can inherit properties from more than one class. Syntax: Class derivedclass name : visibility mode baseclass1,visibilitmode baseclass2 { body of the derived class; }; visibility mode can be either private or public. Example : #include #include class bc1 { protected: int a; public : void get() 129
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{ cout <<”\n enter the value for a\n”; cin >>a; } }; class bc2 { protected: int b; public; void get1() { cout <<” \n enter the value for b \n”; cin>>b; } }; class dc : public bc1, public bc2 { public : void show() { cout <<”The values of a and b are” ; cout <<<”\n”< } };
void main() { clrscr(); dc d; d.get(); d.get1(); d.show(); } 3. Define polymorphism. Explain the different types of polymorphism. Polymorphism Run time compile time Or Dynamic binding static binding Or late binding early binding 130
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Virtual fuctions operator overloading function overloading • Linking a function call to the function definition is called as binding. • If the binding is done at compile time then it is called as compile time polymorphism. •Compile time polymorphism is achieved by using function overloading and operator overloading. • If the binding is done at run time then it is called as run time polymorphism. It is achieved by using virtual functions. VIRTUAL FUNCTIONS: • When the same function is used in both the base class and derived class and if a pointer of base class is used to access the members of the derived class , then the members appropriate to the base class is called. Example: #include #include class base { public: void show() { cout <<”\n This is a base class\n”; } }; class derived : public base { public: void show() { cout <<”\n This is a derived class\n”; } }; void main() { base b,*bptr; bptr=&b; bptr->show(); derived d; bptr=&d; bptr->show(); getch(); } 131
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o/p This is a base class This is a base class • This can be overcome by using virtual functions. • The base class member functions should be preceeded by a keyword virtual. Example: #include #include class base { public: virtual void show() { cout <<”\n This is a base class\n”; } }; class derived : public base { public: void show() { cout <<”\n This is a derived class\n”; } }; void main() { base b,*bptr; bptr=&b; bptr->show(); derived d; bptr=&d; bptr->show(); getch(); }
o/p This is a base class This is a derived class 132
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133
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4. Explain multiple catch statement with help of suitable C++ coding. EXCEPTION HANDLING Exceptions are run time anomalies or unusual conditions that a program may encounter while executing. Anomalies might include conditions such as division by zero, access to an array outside of its bounds, or running out of memory or disk space. When a program encounters an exceptional condition, it is important that it is identified and dealt with effectively. Exceptions are of two kinds, namely, synchronous exceptions and asynchronous exceptions. Errors such as “out-of-range index” and “over flow” belong to the synchronous exceptions. The errors that are caused by events beyond the control of the program are called asynchronous exceptions. The proposed exception handling mechanism is designed to handle only synchronous exceptions.
The mechanism performs following tasks: Find the problem (Hit the exception). Inform that an error has occurred (Throw the exception). Receive the error information (Catch the expression). Take corrective actions (Handle the exceptions). The error handling code basically consists of two segments one to detect errors and to throw exceptions, and other to catch the exceptions and to take appropriate actions.
Exception Handling Mechanism: It is built upon three keywords, namely, try, throw and catch. The keyword try is used to preface a block of statements which may generate exceptions. This block of statements is known as try block. When an exception is detected, it is thrown using a throw statement in the try block. A catch block is defined by the keyword catch ‘catches’ the exception ‘thrown’ by the throw statement in the try block, and handles it appropriately. If the type of object thrown matches the arg type in the catch statement, then catch block is executed for handling the exception. If they do not match the program is aborted with the help of the abort() function is invoked by default. When no exception is detected and thrown, the control goes to the statement immediately after the catch block. Most often exceptions are thrown by the functions that are invoked from within the try blocks. The point at which the throw is executed is called the throw point. The general format of code for this kind of relationship is shown below
Multiple catch statements: It is possible that a program segment has more than one condition to throw an exception. In such cases, we can associate more than one catch statement with a try as shown below: try { // try block } catch(type1 arg) 134
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{ // catch block1 } catch(type2 arg) { // catch block2 } … … catch(typeN arg) { // catch blockN } Catch All Exceptions: In some situations we may not be able to anticipate all possible types of exceptions we can force a catch statement to catch all exceptions instead of a certain type alone. This is achieved as follows: catch (…) { // statement of processing all exceptions }
5. Describe the various file modes and its syntax. FILE To handle large volumes of data, we need to use some devices such as floppy disk or hard disk to store the data. The data is stored in these devices using the concept of files. A file is a collection of related data stores in a particular area on the disk. Programs can be designed to perform the read and write operations on these files. A program involves either or both of the following kinds of data communication: 1. Data transfer between the console unit and the program. 2. Data transfer between the program and a disk file. The I/O system of C++ uses file stream as an interface b/n the programs and the files. The stream that supplies data to the program is known as input stream. The stream that receives data from the program is known as output stream. In other words, the input stream reads data from the file and the output stream writes data to the file. Classes for File Stream Operations: The I/O system of C++ contains a set of classes that define the file handling methods. These include ifstream, ofstream and fstream. These classes are contained in the header file fstream. This file should be included for performing file operations. The filename is a string of characters that make up a valid filename for the operating system. It may contain two parts, a primary name and an optional period with extension. Examples: Input.txt Student For opening a file, we must create a file stream and then link it to the filename. There are two ways of opening a file: Using the constructor function of the class. Using the member function open() of the class. 135
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The first method is useful when only one file in the stream is used. The second method is useful when multiple files are managed using one stream. File Modes: The two methods that we discussed can also take two arguments instead of one. The second argument will specify the file-mode. The general form of the function open() with two arguments is: stream-object.open (“filename”, mode); Parameter Meaning ios::app Append to end of file ios::ate Go to end of file on opening ios::binary Binary file ios::in Open file for reading only ios::nocreate Open fails if the file does not exist ios::noreplace Open fails if the file already exists ios::out Open file for writing only ios::trunc Delete the contents of the file if it exists File pointers and their manipulations: Each file has two associated pointers known as the file pointers. They are input pointer and output pointer. The input pointer is used for reading the contents of a given file location and the output pointer is used for writing to a given file location. Read only mode: Input pointer is automatically set at the beginning so that we can read the file from start. Write only mode: Existing contents are deleted and the output pointer is set at the beginning. Append mode: The output pointer is set to the end of file. Functions for manipulations of file pointers: seekg() – Moves input pointer to a specified location seekp() – Moves output pointer to a specified location tellg() – Gives the current position of the input pointer tellp() – Gives the current position of the output pointer Example: infile.seekg(10); moves file pointer to the byte number 10. The bytes are numbered from zero hence it points to the 11th byte in the file. ofstream out out.open(“filename”,ios::app); int p = out.tellp(); The above program will give the number of bytes in the file, since the file is opened in the append mode. 136
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6. Discuss the need for exception with try, catch and throw keywords. Exceptions are run time anomalies or unusual conditions that a program may encounter while executing. Anomalies might include conditions such as division by zero, access to an array outside of its bounds, or running out of memory or disk space. When a program encounters an exceptional condition, it is important that it is identified and dealt with effectively. Exceptions are of two kinds, namely, synchronous exceptions and asynchronous exceptions. Errors such as “out-of-range index” and “over flow” belong to the synchronous exceptions. The errors that are caused by events beyond the control of the program are called asynchronous exceptions. The proposed exception handling mechanism is designed to handle only synchronous exceptions. The mechanism performs following tasks: Find the problem (Hit the exception). Inform that an error has occurred (Throw the exception). Receive the error information (Catch the expression). Take corrective actions (Handle the exceptions). The error handling code basically consists of two segments one to detect errors and to throw exceptions, and other to catch the exceptions and to take appropriate actions. Exception Handling Mechanism: It is built upon three keywords, namely, try, throw and catch. The keyword try is used to preface a block of statements which may generate exceptions. This block of statements is known as try block. When an exception is detected, it is thrown using a throw statement in the try block.
A catch block is defined by the keyword catch ‘catches’ the exception ‘thrown’ by the throw statement in the try block, and handles it appropriately. If the type of object thrown matches the arg type in the catch statement, then catch block is executed for handling the exception. If they do not match the program is aborted with the help of the abort() function is invoked by default. When no exception is detected and thrown, the control goes to the statement immediately after the catch block. Most often exceptions are thrown by the functions that are invoked from within the try blocks. The point at which the throw is executed is called the throw point. The general format of code for this kind of relationship is shown below: Example: #include void divide(int a, int b) 137
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{ if(b!=0) cout << “Result = “ << a/b; else throw(b); } void main() { cout << “Enter two numbers “; int x,y; cin >> x >> y; try { divide(x,y); } catch(int i) { cout << “Error! Dividing by Zero “; } 7. Explain the various forms of inheritance in C++ with necessary coding. INHERITANCE: • Inheritance is a mechanism of deriving a new class from a old class. • It provides the concept of reusability • By inheritance some or all the properties of a class can be derived in to another class. • The class which provides the properties is called as base class and the class which derives the properties is called as derived class. Types: There are five types of inheritance viz 1. Single level inheritance 2. Multiple inheritance 3. Multilevel inheritance 4. Hybrid inheritance and 5. Hierarchical inheritance Multiple inheritance: It is a type of inheritance in which a class can inherit properties from more than one class. Syntax: Class derivedclass name : visibility mode baseclass1,visibilitmode baseclass2 { body of the derived class; }; 138
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visibility mode can be either private or public. Example : #include #include class bc1 { protected: int a; public : void get() { cout <<”\n enter the value for a\n”; cin >>a; } }; class bc2 { protected: int b; public; void get1() { cout <<” \n enter the value for b \n”; cin>>b; } }; class dc : public bc1, public bc2 { public : void show() { cout <<”The values of a and b are” ; cout <<<”\n”< } }; void main() { clrscr(); dc d; d.get(); 139
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d.get1(); d.show(); }
output: Enter the value for a 20 Enter the value for b 30 The values of a and b are 20 30
140
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UNIT-III PART-A 1. Write down the definition of data structures? NOV DEC 2012 A data structure is a mathematical or logical way of organizing data in the memory that consider not only the items stored but also the relationship to each other and also it is characterized by accessing functions. 2. Binary Heap NOV DEC 2012 ,APRIL MAY 2009 The implementation we will use is known as a binary heap. Its use is so common for priority queue implementations that when the word heap is used without a qualifier Structure Property A heap is a binary tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right. Such a tree is known as a complete binary tree 3. Define Algorithm? Algorithm is a solution to a problem independent of programming language. It consist of set of finite steps which, when carried out for a given set of inputs, produce the corresponding output and terminate in a finite time. 4. What are the features of an efficient algorithm? • Free of ambiguity • Efficient in execution time • Concise and compact • Completeness • Definiteness • Finiteness 5. List down any four applications of data structures?
Compiler design Operating System Database Management system Network analysis
6. What is meant by an abstract data type (ADT)?
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An ADT is a set of operation. A useful tool for specifying the logical properties of a datatype is the abstract data type.ADT refers to the basic mathematical concept that defines the datatype. Eg.Objects such as list, set and graph along their operations can be viewed as ADT's. 7. What are the operations of ADT? Union, Intersection, size, complement and find are the various operations of ADT. 8. What is meant by list ADT? List ADT is a sequential storage structure. General list of the form a1, a2, a3.…., an and the size of the list is 'n'. Any element in the list at the position I is defined to be ai, ai+1 the successor of ai and ai-1 is the predecessor of ai. 9. What are the two parts of ADT? • Value definition • Operator definition 10. What is a Sequence? A sequence is simply an ordered set of elements.A sequence S is sometimes written as the enumeration of its elements,such as S =If S contains n elements,then length of S is n. 11. Define len(S),first(S),last(S),nilseq ? len(S) is the length of the sequence S. first(S) returns the value of the first element of S last(S) returns the value of the last element of S nilseq :Sequence of length 0 is nilseq .ie., contains no element. 12. What are the two basic operations that access an array? Extraction: Extraction operation is a function that accepts an array, a ,an index,i,and returns an element of the array. Storing: Storing operation accepts an array , a ,an index i , and an element x. 13. Define Structure? A Structure is a group of items in which each item is identified by its own identifier ,each of which is known as a member of the structure. 14. Define Union ? 142
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Union is collection of Structures ,which permits a variable to be interpreted in several different ways.
15. Define Automatic and External variables? Automatic variables are variables that are allocated storage when the function is invoked. External variables are variables that are declared outside any function and are allocated storage at the point at which they are first encountered for the remeinder of the program’s execution. 16. What is a Stack? NOV DEC 2008 A Stack is an ordered collection of items into which new items may be inserted and from which items may be deleted at one end, called the top of the stack. The other name of stack is Last-in -First-out list. 17. What are the two operations of Stack? • _ PUSH • _ POP 18. What is a Queue? A Queue is an ordered collection of items from which items may be deleted at one end called the front of the queue and into which tems may be inserted at the other end called rear of the queue.Queue is called as First–in-First-Out(FIFO). 19. What is a Priority Queue? NOV DEC 2010 Priority queue is a data structure in which the intrinsic ordering of the elements does determine the results of its basic operations. Ascending and Descending priority queue are the two types of Priority queue. 20. What is a linked list? Linked list is a kind of series of data structures, which are not necessarily adjacent in memory. Each structure contain the element and a pointer to a record containing its successor. 21. What is a doubly linked list? In a simple linked list, there will be one pointer named as 'NEXT POINTER' to point the next element, where as in a doubly linked list, there will be two pointers one to point the next element and the other to point the previous element location. 143
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22. Define double circularly linked list? In a doubly linked list, if the last node or pointer of the list, point to the first element of the list,then it is a circularly linked list. 23. What is a circular queue? The queue, which wraps around upon reaching the end of the array is called as circular queue. 24. Define max and min heap? A heap in which the parent has a larger key than the child's is called a max heap. A heap in which the parent has a smaller key than the child is called a min heap. 25. Write postfix from of the expression –A+B-C+D? A-B+C-D+ 26. Define Recursion? Recursion is a function calling itself again and again. 27. What is a Fibonacci sequence? Fibonacci sequence is the number of integers 0,1,1,2,3,5,8,13,21,34,………. Each element in this sequence is the sum of the two preceding elements. 28.Name the two fields of Linked list? • Info field • Next field 29. What is a doubly linked list? In a simple linked list, there will be one pointer named as 'NEXT POINTER' to point the next element, where as in a doubly linked list, there will be two pointers one to point the next element and the other to point the previous element location. 30. Name the three fields of Doubly Linked list? • Info field • Left field • Right field 31. Define double circularly linked list? In a doubly linked list, if the last node or pointer of the list, point to the first element of the list,then it is a circularly linked list. 32. What is the need for the header? 144
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Header of the linked list is the first element in the list and it stores the number of elements in the list. It points to the first data element of the list. 33. List three examples that uses linked list? • Polynomial ADT • Radix sort • Multi lists 34. Give some examples for linear data structures? • Stack • Queue 35. How do you test for an empty queue? To test for an empty queue, we have to check whether READ=HEAD where REAR is a pointer pointing to the last node in a queue and HEAD is a pointer that pointer to the dummy header. In the case of array implementation of queue, the condition to be checked for an empty queue is READ 36. What are the postfix and prefix forms of the expression? A+B*(C-D)/(P-R) Postfix form: ABCD-*PR-/+ Prefix form: +A/*B-CD-PR
37. Explain the usage of stack in recursive algorithm implementation? In recursive algorithms, stack data structures is used to store the return address when a recursive call is encountered and also to store the values of all the parameters essential to the current state of the procedure. 38. Write down the operations that can be done with queue data structure? Queue is a first - in -first out list. The operations that can be done with queue are insert and remove. 39. What is a circular queue? The queue, which wraps around upon reaching the end of the array is called as circular queue. 40. Define max heap? A heap in which the parent has a larger key than the child's is called a max heap. 41. Define min heap? A heap in which the parent has a smaller key than the child is called a min heap.
UNIT-III PART - B 145
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1. How do you analyses an algorithm? Algorithm analysis refers to the process of determining how much computing time and storage that algorithms will require. In other words, it’s a process of predicting the resource requirement of algorithms in a given environment. In order to solve a problem, there are many possible algorithms. One has to be able to choose the best algorithm for the problem at hand using some scientific method. To classify some data structures and algorithms as good, we need precise ways of analyzing them in terms of resource requirement. The main resources are: • Running Time • Memory Usage • Communication Bandwidth Running time is usually treated as the most important since computational time is the most precious resource in most problem domains. There are two approaches to measure the efficiency of algorithms: • Empirical: Programming competing algorithms and trying them on different instances. • Theoretical: Determining the quantity of resources required mathematically (Execution time, memory space, etc.) needed by each algorithm. However, it is difficult to use actual clock-time as a consistent measure of an algorithm’s efficiency, because clock-time can vary based on many things. For example, • Specific processor speed • Current processor load • Specific data for a particular run of the program o Input Size o Input Properties • Operating Environment Accordingly, we can analyze an algorithm according to the number of operations required, rather than according to an absolute amount of time involved. This can show how an algorithm’s efficiency changes according to the size of the input. Complexity Analysis Complexity Analysis is the systematic study of the cost of computation, measured either in time units or in operations performed, or in the amount of storage space required. The goal is to have a meaningful measure that permits comparison of algorithms independent of operating platform. There are two things to consider: • Time Complexity: Determine the approximate number of operations required to solve a problem of size n. • Space Complexity: Determine the approximate memory required to solve a problem of size n. Complexity analysis involves two distinct phases: • Algorithm Analysis: Analysis of the algorithm or data structure to produce a function T (n) that describes the algorithm in terms of the operations performed in order to measure the complexity of the algorithm. 146
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• Order of Magnitude Analysis: Analysis of the function T (n) to determine the general complexity category to which it belongs. There is no generally accepted set of rules for algorithm analysis. However, an exact count of operations is commonly used.
Analysis Rules: 1. We assume an arbitrary time unit. 2. Execution of one of the following operations takes time 1: • Assignment Operation • Single Input/Output Operation • Single Boolean Operations • Single Arithmetic Operations • Function Return 3. Running time of a selection statement (if, switch) is the time for the condition evaluation + the maximum of the running times for the individual clauses in the selection. 4. Loops: Running time for a loop is equal to the running time for the statements inside the loop * number of iterations. The total running time of a statement inside a group of nested loops is the running time of the statements multiplied by the product of the sizes of all the loops. For nested loops, analyze inside out. • Always assume that the loop executes the maximum number of iterations possible. 5. Running time of a function call is 1 for setup + the time for any parameter calculations + the time required for the execution of the function body. Examples: 1. int count(){ int k=0; cout<< “Enter an integer”; cin>>n; for (i=0;i k=k+1; return 0;} Time Units to Compute ------------------------------------------------1 for the assignment statement: int k=0 1 for the output statement. 1 for the input statement. In the for loop: 1 assignment, n+1 tests, and n increments. n loops of 2 units for an assignment, and an addition. 1 for the return statement. ------------------------------------------------------------------147
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T (n)= 1+1+1+(1+n+1+n)+2n+1 = 4n+6 = O(n) 2. int total(int n) { int sum=0; for (int i=1;i<=n;i++) sum=sum+1; return sum; } Time Units to Compute ------------------------------------------------1 for the assignment statement: int sum=0 In the for loop: 1 assignment, n+1 tests, and n increments. n loops of 2 units for an assignment, and an addition. 1 for the return statement. ------------------------------------------------------------------T (n)= 1+ (1+n+1+n)+2n+1 = 4n+4 = O(n) 3. void func() { int x=0; int i=0; int j=1; cout<< “Enter an Integer value”; cin>>n; while (i x++; i++; } while (j { j++; } } Time Units to Compute ------------------------------------------------1 for the first assignment statement: x=0; 1 for the second assignment statement: i=0; 1 for the third assignment statement: j=1; 1 for the output statement. 1 for the input statement. In the first while loop: n+1 tests n loops of 2 units for the two increment (addition) operations In the second while loop: 148
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n tests n-1 increments ------------------------------------------------------------------T (n)= 1+1+1+1+1+n+1+2n+n+n-1 = 5n+5 = O(n) 4. int sum (int n) { int partial_sum = 0; for (int i = 1; i <= n; i++) partial_sum = partial_sum +(i * i * i); return partial_sum; } Time Units to Compute ------------------------------------------------1 for the assignment. 1 assignment, n+1 tests, and n increments. n loops of 4 units for an assignment, an addition, and two multiplications. 1 for the return statement. ------------------------------------------------------------------T (n)= 1+(1+n+1+n)+4n+1 = 6n+4 = O(n) Formal Approach to Analysis In the above examples we have seen that analysis so complex. However, it can be simplified by using some formal approach in which case we can ignore initializations, loop control, and book keeping. For Loops: Formally • In general, a for loop translates to a summation. The index and bounds of the summation are the same as the index and bounds of the for loop. • Suppose we count the number of additions that are done. There is 1 addition per iteration of the loop, hence N additions in total. Nested Loops: Formally • Nested for loops translate into multiple summations, one for each for loop. • Again, count the number of additions. The outer summation is for the outer for loop. Consecutive Statements: Formally • Add the running times of the separate blocks of your code Conditionals: Formally • If (test) s1 else s2: Compute the maximum of the running time for s1 and s2.
2. Explain how pointer are used to implement linked list structure. A linked list is a data structure that is built from structures and pointers. It forms a chain of"nodes" with pointers representing the links of the chain and holding the entire thing together. 149
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A linked list can be represented by a diagram like this one: This linked list has four nodes in it, each with a link to the next node in the series. The last node has a link to the special value NULL, which any pointer (whatever its type) can point to, to show that it is the last link in the chain. There is also another special pointer, called Start (also called head), which points to the first link in the chain so that we can keep track of it. Defining the data structure for a linked list The key part of a linked list is a structure, which holds the data for each node (the name, address, age or whatever for the items in the list), and, most importantly, a pointer to the next node. Here we have given the structure of a typical node: struct node { char name[20]; // Name of up to 20 letters int age float height; // In metres node *nxt;// Pointer to next node }; struct node *start_ptr = NULL; The important part of the structure is the line before the closing curly brackets. This gives a pointer to the next node in the list. This is the only case in C++ where you are allowed to refer to a data type (in this case node) before you have even finished defining it! We have also declared a pointer called start_ptr that will permanently point to the start of the list. To start with, there are no nodes in the list, which is why start_ptr is set to NULL. 3. Explain various operation performed on the doubly linked list. Doubly Linked Lists That sounds even harder than a linked list! Well, if you've mastered how to do singly linked lists, then it shouldn't be much of a leap to doubly linked lists A doubly linked list is one where there are links from each node in both directions: You will notice that each node in the list has two pointers, one to the next node and one to the previous one - again, the ends of the list are defined by NULL pointers. Also there is no pointer to the start of the list. Instead, there is simply a pointer to some position in the list that can be moved left or right. The reason we needed a start pointer in the ordinary linked list is because, having moved on from one node to another, we can't easily move back, so without the start pointer, we would lose track of all the nodes in the list that we have already passed. With the doubly linked list, we can move the current pointer backwards and forwards at will. Creating Doubly Linked Lists The nodes for a doubly linked list would be defined as follows: struct node{ char name[20]; node *nxt; // Pointer to next node node *prv; // Pointer to previous node }; node *current; 150
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current = new node; current->name = "Fred"; current->nxt = NULL; current->prv = NULL; We have also included some code to declare the first node and set its pointers to NULL. It gives the following situation: We still need to consider the directions 'forward' and 'backward', so in this case, we will need to define functions to add a node to the start of the list (left-most position) and the end of the list (right-most position). Adding a Node to a Doubly Linked List void add_node_at_start (string new_name) { // Declare a temporary pointer and move it to the start node *temp = current; while (temp->prv != NULL) temp = temp->prv; // Declare a new node and link it in node *temp2; temp2 = new node; temp2->name = new_name; // Store the new name in the node temp2->prv = NULL; // This is the new start of the list temp2->nxt = temp; // Links to current list temp->prv = temp2; } void add_node_at_end () { // Declare a temporary pointer and move it to the end node *temp = current; while (temp->nxt != NULL) temp = temp->nxt; // Declare a new node and link it in node *temp2; temp2 = new node; temp2->name = new_name; // Store the new name in the node temp2->nxt = NULL; // This is the new start of the list temp2->prv = temp; // Links to current list temp->nxt = temp2; } Here, the new name is passed to the appropriate function as a parameter. We'll go through the function for adding a node to the right-most end of the list. The method is similar for adding a node at the other end. Firstly, a temporary pointer is set up and is made to march along the list until it points to last node in the list. After that, a new node is declared, and the name is copied into it. The nxt pointer of this new node is set to NULL to indicate that this node will be the new end of the list. The prv pointer of the new node is linked into the last node of the existing list. The nxt pointer of the current end of the list is set to the new node. 151
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4. Give linked list implementation of stack operation. Linked List Implementation of Stacks: the PUSH operation It’s very similar to the insertion operation in a dynamic singly linked list. The only difference is that here you'll add the new element only at the end of the list, which means addition can happen only from the TOP. Since a dynamic list is used for the stack, the Stack is also dynamic, means it has no prior upper limit set. So, we don't have to check for the Overflow condition at all! In Step [1] we create the new element to be pushed to the Stack. In Step [2] the TOP most element is made to point to our newly created element. In Step [3] the TOP is moved and made to point to the last element in the stack, which is our newly added element. Linked List Implementation of Stacks: the POP Operation This is again very similar to the deletion operation in any Linked List, but you can only delete from the end of the list and only one at a time; and that makes it a stack. Here, we'll have a list pointer, "target", which will be pointing to the last but one element in the List (stack). Every time we POP, the TOP most element will be deleted and "target" will be made as the TOP most element. In step[1] we got the "target" pointing to the last but one node. In step[2] we freed the TOP most element. In step[3] we made the "target" node as our TOP most element. Supposing you have only one element left in the Stack, then we won't make use of "target" rather we'll take help of our "bottom" pointer. See how... Algorithm: Step-1: If the Stack is empty then give an alert message "Stack Underflow" and quit; or else proceed Step-2: If there is only one element left go to step-3 or else step-4 Step-3: Free that element and make the "stack", "top" and "bottom" pointers point to NULL and quit Step-4: Make "target" point to just one element before the TOP; free the TOP most element; make "target" as your TOP most element Implementation: struct node { int nodeval; struct node *next; } struct node *stack = NULL; /*stack is initially empty*/ struct node *top = stack; main() 152
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{ int newvalue, delval; .. push(newvalue); .. delval = pop(); /*POP returns the deleted value from the stack*/ } int pop( ) { int pop_val = 0; struct node *target = stack; if(stack == NULL) /*step-1*/ cout<<"Stack Underflow"; else { if(top == bottom) /*step-2*/ { pop_val = top -> nodeval; /*step-3*/ delete top; stack = NULL; top = bottom = stack; } else /*step-4*/ { while(target->next != top) target = target ->next; pop_val = top->nodeval; delete top; top = target; target ->next = NULL; } } return(pop_val); }
5. What is a stack? Explain any two operations performed on a stack with required algorithm. Stacks A simple data structure in which insertion and deletion occur at the same end, is termed (called) a stack. It is a LIFO (Last In First Out) structure. The operations of insertion and deletion are called PUSH and POP Push - push (put) item onto stack 153
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Pop - pop (get) item from stack Initial Stack Push(8) Pop TOS=> 4 1 3 6 TOS=> 8 4 1 3 6 TOS=> 4 1 3 6 Our Purpose: To develop a stack implementation that does not tie us to a particular data type or to a particular implementation. Implementation: Stacks can be implemented both as an array (contiguous list) and as a linked list. We want a set of operations that will work with either type of implementation: i.e. the method of implementation is hidden and can be changed without affecting the programs that use them. The Basic Operations: Push() { if there is room { put an item on the top of the stack else give an error message } } Pop() { if stack not empty { return the value of the top item remove the top item from the stack } else { give an error message } 154
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} CreateStack() { remove existing items from the stack initialise the stack to empty } Array Implementation of Stacks: The PUSH operation Here, as you might have noticed, addition of an element is known as the PUSH operation. So, if an array is given to you, which is supposed to act as a STACK, you know that it has to be a STATIC Stack; meaning, data will overflow if you cross the upper limit of the array. So, keep this in mind. Algorithm: Step-1: Increment the Stack TOP by 1. Check whether it is always less than the Upper Limit of the stack. If it is less than the Upper Limit go to step-2 else report -"Stack Overflow" Step-2: Put the new element at the position pointed by the TOP Implementation: static int stack[UPPERLIMIT]; int top= -1; /*stack is empty*/ .. .. main() { .. .. push(item); .. .. } push(int item) { top = top + 1; if(top < UPPERLIMIT) stack[top] = item; /*step-1 & 2*/ else cout<<"Stack Overflow"; } Note:- In array implementation,we have taken TOP = -1 to signify the empty stack, as this simplifies the implementation. Array Implementation of Stacks: the POP operation POP is the synonym for delete when it comes to Stack. So, if you're taking an array as the stack, remember that you'll return an error message, "Stack underflow", if an attempt is made to Pop an item from an empty Stack. OK. Algorithm 155
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Step-1: If the Stack is empty then give the alert "Stack underflow" and quit; or else go to step-2 Step-2: a) Hold the value for the element pointed by the TOP b) Put a NULL value instead c) Decrement the TOP by 1 Implementation: static int stack[UPPPERLIMIT]; int top=-1; .. .. main() { .. .. poped_val = pop(); .. .. } int pop() { int del_val = 0; if(top == -1) cout<<"Stack underflow"; /*step-1*/ else { del_val = stack[top]; /*step-2*/ stack[top] = NULL; top = top -1; } return(del_val); } Note: - Step-2:(b) signifies that the respective element has been deleted. Algorithm Step-1: If the Stack is empty go to step-2 or else go to step-3 Step-2: Create the new element and make your "stack" and "top" pointers point to it and quit. Step-3: Create the new element and make the last (top most) element of the stack to point to it Step-4: Make that new element your TOP most element by making the "top" pointer point to it. Implementation: struct node{ int item; struct node *next; } struct node *stack = NULL; /*stack is initially empty*/ struct node *top = stack; main() { 156
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.. .. push(item); .. } push(int item) { if(stack == NULL) /*step-1*/ { newnode = new node /*step-2*/ newnode -> item = item; newnode -> next = NULL; stack = newnode; top = stack; } else { newnode = new node; /*step-3*/ newnode -> item = item; newnode -> next = NULL; top ->next = newnode; top = newnode; /*step-4*/ } } 6. State and explain the priority queue with example. Priority Queue - is a queue where each data has an associated key that is provided at the time of insertion. - Dequeue operation deletes data having highest priority in the list - One of the previously used dequeue or enqueue operations has to be modified Example: Consider the following queue of persons where females have higher priority than males (gender is the key to give priority). Dequeue()- deletes Aster Dequeue()- deletes Meron Now the queue has data having equal priority and dequeue operation deletes the front element like in the case of ordinary queues. Dequeue()- deletes Abebe Dequeue()- deletes Alemu Thus, in the above example the implementation of the dequeue operation need to be modified. 7. Explain, with example the basic heap operations and write the algorithms for the same. Heap Sort Heap sort operates by first converting the list in to a heap tree. Heap tree is a binary tree in which each node has a value greater than both its children (if any). It uses a process called "adjust to accomplish its task (building a heap tree) whenever a value is larger than its parent. 157
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The time complexity of heap sort is O(nlogn). Algorithm: 1. Construct a binary tree • The root node corresponds to Data[0]. • If we consider the index associated with a particular node to be i, then the left child of this node corresponds to the element with index 2*i+1 and the right child corresponds to the element with index 2*i+2. If any or both of these elements do not exist in the array, then the corresponding child node does not exist either. 2. Construct the heap tree from initial binary tree using "adjust" process. 3. Sort by swapping the root value with the lowest, right most value and deleting the lowest, right most value and inserting the deleted value in the array in it proper position. Example: Sort the following list using heap sort algorithm. 5 8 2 4 1 3 9 7 6 0
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UNIT - IV PART – A 1. Define non-linear data structure? Data structure which is capable of expressing more complex relationship than that of physical adjacency is called non-linear data structure. 2. Define tree? A tree is a data structure, which represents hierarchical relationship between individual Data items. 3. Define child and parent of a tree. The root of each subtree is said to be a child of ‘r’ and ‘r’ is the parent of each subtree root. 4. Define leaf? In a directed tree any node which has out degree o is called a terminal node or a leaf. 5. What is a Binary tree? A Binary tree is a finite set of elements that is either empty or is partitioned into three disjoint subsets. The first subset contains a single element called the root of the tree. The other two subsets are themselves binary trees called the left and right sub trees. 6. What are the applications of binary tree? Binary tree is used in data processing. a. File index schemes b. Hierarchical database management system 7. What is meant by traversing? Traversing a tree means processing it in such a way, that each node is visited only once. 8. What are the different types of traversing? The different types of traversing are a.Pre-order traversal-yields prefix form of expression. b. In-order traversal-yields infix form of expression. c. Post-order traversal-yields postfix form of expression. 159
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9. What are the two methods of binary tree implementation? Two methods to implement a binary tree are, a. Linear representation. b. Linked representation 10. Define Graph? A graph G consist of a nonempty set V which is a set of nodes of the graph, a set E which is the set of edges of the graph, and a mapping from the set for edge E to a set of pairs of elements of V. It can also be represented as G=(V, E). 11. Define adjacent nodes? Any two nodes which are connected by an edge in a graph are called adjacent nodes. For Example, if and edge xÎE is associated with a pair of nodes (u,v) where u, v Î V, then we say that the edge x connects the nodes u and v. 12.Name the different ways of representing a graph? a. Adjacency matrix b. Adjacency list 13. What are the two traversal strategies used in traversing a graph? a. Breadth first search b. Depth first search 14. What is an acyclic graph? A simple diagram which does not have any cycles is called an acyclic graph. 15. Give some example of NP complete problems. Hamiltonian circuit. Travelling salesmen problems 16. What are AVL trees?
An AVL tree is a binary search tree with a balancing condition. For every node in the tree the heigh of the left and right subtrees can differ at most by 1. 160
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The height of an empty tree is defined to be -1.It ensures that the depth of the tree is O(log N)1
7. What is topological sort? A topological sort is an ordering of vertices in a directed acyclic graph, such that if there is a path from vi then vj appears after vi in the ordering. 18. What is single source shortest path problem? Given as an input a weighted graph, G=(V,E) and a distinguished vertex, ’s’ find the shortest weighted path from ‘s’ to every other vertex in G. 19. Mention some shortest –path problems.
20. What are the algorithms used to find the minimum spanning tree?
Prim’s algorithm Kruskal’s algorit
21. Define complete binary tree. It is a complete binary tree only if all levels, except possibly the last level have the maximum number of nodes maximum. A complete binary tree of height ‘h’ has between 2h and 2h+1 – 1 node 22. Define binary search tree. Why it is preferred rather than the sorted linear array and linked list? Binary search tree is a binary tree in which key values of the left sub trees are lesser than the root value and the key values of the right sub tree are always greater than the root value. In linear array or linked list the values are arranged in the form of increasing or decreasing order. If we want to access any element means, we have to traverse the entire list. But if we use BST, the element to be accessed is greater or smaller than the root element means we can traverse either the right or left sub tree and can access the element irrespective of searching the entire tree. 23. Give various implementations of trees.
Linear implementation 161
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Linked list implementation
24. List out the application of trees.
Ordered tree “C” – representation of tree
25. What is the difference between binary tree and binary search tree?
Binary Tree Binary Search Tree A tree is said to be a binary tree if it A BST is binary tree in which the key values in the left sub tree is lesser than the has at most two children root and key values of the right sub tree is greater than the root value. It doesn’t have any order. It should be in order.
26. Show the maximum number of nodes in a binary tree of height H is 2H+1 – 1. Consider H = 3 No. of nodes in a full binary tree = 2H+1 – 1 = 23+1 – 1 = 24 – 1 = 15 nodes We know that a full binary tree with height h=3 has maximum 15 nodes. Hence proved. 27. List out the cases involved in deleting a node from a binary search tree. Case 1: Node to be deleted is a Leaf node Case 2: Node to be deleted has one child Case:3: Node to be deleted has two children.
28. A + (B-C)*D+(E*F), if the above arithmetic expression is represented using a binary tree, Find the number of non-leaf nodes in the tree. Expression tree is a binary tree in which non – leaf nodes are operators and the leaf nodes are operands. In the above example, we have 5 operators. Therefore the number of non-leaf nodes in the tree is 5. 29. What is a BST – binary search tree? (AUC NOV/ DEC 2009) 162
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Binary search tree is a binary tree in which key values of the left sub trees are lesser than the root value and the key values of the right sub tree are always greater than the root value.
30. Define threaded Binary Tree. (AUC NOV/ DEC 2010) A binary tree is threaded by making all right child pointers that would normally be null point to the inorder successor of the node, and all left child pointers that would normally be null point to the inorder predecessor of the node. 31 Write the advantages of threaded binary tree. (AUC NOV/ DEC 2009) 1. By doing threading we avoid the recursive method of traversing a Tree , which makes use of stack and consumes a lot of memory and time. 2. The node can keep record of its root 32. Write an algorithm to declare nodes of a tree structure. (AUC APR / MAY 2010) Struct tree node { int element; Struct tree *left; Struct tree *right; } UNIT - IV PART – B 1. Describe in detail about the implementation of trees One way to implement a tree would be to have in each node, besides its data, a link to each child of the node. However, since the number of children per node can vary so greatly and is not known in advance, it might be infeasible to make the children direct links in the data Node declarations for trees: 1 struct TreeNode 2{ 3 Object element; 4 TreeNode *firstChild; 5 TreeNode *nextSibling; 6 }; 163
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structure, because there would be too much wasted space. The solution is simple: Keep the children of each node in a linked list of tree nodes. The declaration is typical. Figure 4.4 shows how a tree might be represented in this implementation. Horizontal arrows that point downward are firstChild links. Arrows that go left to right are nextSibling links. Null links are not drawn, because there are too many. In the tree of Figure 4.4, node E has both a link to a sibling (F) and a link to a child (I), while some nodes have neither. Tree Traversals with an Application There are many applications for trees. One of the popular uses is the directory structure in many common operating systems, including UNIX and DOS. Figure 4.5 is a typical directory in the UNIX file system. The root of this directory is /usr. (The asterisk next to the name indicates that /usr is itself a directory.) /usr has three children, mark, alex, and bill, which are themselves directories. Thus, /usr contains three directories and no regular files. The filename /usr/mark/book/ch1.r is obtained by following the leftmost child three times. Each / after the first indicates an edge; the result is the full pathname. This hierarchical file system is very popular because it allows users to organize their data logically. Furthermore, two files in different directories can share the same name, because they must have different paths from the root and thus have different pathnames. A directory in the UNIX file system is just a file with a list of all its children, so the directories are structured almost exactly in accordance
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with the type declaration above.1 Indeed, on some versions of UNIX, if the normal command to print a file is applied to a directory, then the names of the files in the directory can be seen in the output (along with other non-ASCII information). Suppose we would like to list the names of all of the files in the directory. Our output format will be that files that are depth di will have their names indented by di tabs. Our algorithm is given in Figure 4.6 as pseudocode. The recursive function listAll needs to be started with a depth of 0 to signify no indenting for the root. This depth is an internal bookkeeping variable, and is hardly a parameter that a calling routine should be expected to know about. Thus, the default value of 0 is provided for depth. The logic of the algorithm is simple to follow. The name of the file object is printed out with the appropriate number of tabs. If the entry is a directory, then we process all children recursively, one by one. These children are one level deeper, and thus need to be indented an extra space. This traversal strategy is known as a preorder traversal. In a preorder traversal, work at a node is performed before (pre) its children are processed. When this program is run, it is clear that line 1 is executed exactly once per node, since each name is output once. Since line 1 is executed at most once per node, line 2 must also be executed once per node. Furthermore, line 4 can be executed at most once for each child of each node. But the number of children is exactly one less than the number of nodes. Finally, the for loop iterates once per execution of line 4 plus once each time the loop ends. Thus, the total amount of work is constant per node. If there are N file names to be output, then the running time is O(N). Another common method of traversing a tree is the postorder traversal. In a postorder traversal, the work at a node is performed after (post) its children are evaluated. As an example, Figure 4.8 represents the same directory structure as before, with the numbers in parentheses representing the number of disk blocks taken up by each 165
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file. Since the directories are themselves files, they have sizes too. Suppose we would like to calculate the total number of blocks used by all the files in the tree. The most natural way to do this would be to find the number of blocks contained in the subdirectories /usr/mark (30), /usr/alex (9), and /usr/bill (32). The total number of blocks is then the total in
the subdirectories plus the one block used by /usr, for a total of 72. The pseudocode method size in Figure 4.9 implements this strategy. If the current object is not a directory, then size merely returns the number of blocks it uses in the current object. Otherwise, the number of blocks used by the directory is added to the number of blocks (recursively) found in all the children. 2.What is a Binary Tree? Explain the implementation of a Binary Tree with an expression tree A binary tree is a tree in which no node can have more than two children. Figure 4.11 shows that a binary tree consists of a root and two subtrees, TL and TR, both of which could possibly be empty. A property of a binary tree that is sometimes important is that the depth of an average binary tree is considerably smaller than N. An analysis shows that the average depth is O(√N), and that for a special type of binary tree, namely the binary search tree, the average value of the depth is O(logN). Unfortunately, the depth can be as large as N − 1, as the example in Figure 4.12 shows. ch1.r 3 166
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ch2.r 2 ch3.r 4 book 10 syl.r 1 fall 2 syl.r 5 spr 6 syl.r 2 sum 3 cop3530 12 course 13 junk 6 mark 30 junk 8 alex 9 work 1 grades 3 prog1.r 4 prog2.r 1 fall 9 prog2.r 2 prog1.r 7 grades 9 fall 19 cop3212 29 course 30 bill 32 /usr 72 Figure 4.10 Trace of the size function
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Implementation Because a binary tree node has at most two children, we can keep direct links to them. The declaration of tree nodes is similar in structure to that for doubly linked lists, in that a node is a structure consisting of the element information plus two pointers (left and right) to other nodes(Figure 4.13). We could draw the binary trees using the rectangular boxes that are customary for linked lists, but trees are generally drawn as circles connected by lines, because they are actually graphs. We also do not explicitly draw nullptr links when referring to trees, because every binary tree with N nodes would require N + 1 nullptr links. Binary trees have many important uses not associated with searching. One of the principal uses of binary trees is in the area of compiler design, which we will now explore. Example: Expression Trees Figure 4.14 shows an example of an expression tree. The leaves of an expression tree are operands, such as constants or variable names, and the other nodes contain operators. This particular tree happens to be binary, because all the operators are binary, and although this is the simplest case, it is possible for nodes to have more than two children. It is also possible for a node to have only one child, as is the case with the unary minus operator. We can evaluate an expression tree, T, by applying the operator at the root to the values struct BinaryNode { Object element; // The data in the node BinaryNode *left; // Left child BinaryNode *right; // Right child };
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Figure 4.13 Binary tree node class (pseudocode)
obtained by recursively evaluating the left and right subtrees. In our example, the left subtree evaluates to a + (b * c) and the right subtree evaluates to ((d * e) + f) * g. The entire tree therefore represents (a + (b * c)) + (((d * e) + f) * g). We can produce an (overly parenthesized) infix expression by recursively producing a parenthesized left expression, then printing out the operator at the root, and finally recursively producing a parenthesized right expression. This general strategy (left, node, right) is known as an inorder traversal; it is easy to remember because of the type of expression it produces. An alternate traversal strategy is to recursively print out the left subtree, the right subtree, and then the operator. If we apply this strategy to our tree above, the output is a b c * + d e * f + g * +, which is easily seen to be the postfix representation. This traversal strategy is generally known as a postorder traversal. A third traversal strategy is to print out the operator first and then recursively print out the left and right subtrees. The resulting expression, + + a * b c * + * d e f g, is the less useful prefix notation, and the traversal strategy is a preorder traversal 3. Explain in detail about Breadth First Search This strategy for searching a graph is known as breadth-first search. It operates by processing vertices in layers: The vertices closest to the start are evaluated first, and the most distant vertices are evaluated last. This is much the same as a level-order traversal for trees. Given this strategy, we must translate it into code. Figure 9.15 shows the initial configuration of the table that our algorithm will use to keep track of its progress. For each vertex, we will keep track of three pieces of information. First, we will keep its distance from s in the entry dv. Initially all vertices are unreachable except for s, whose path length is 0. The entry in pv is the bookkeeping variable, which will allow us to print the actual paths. The entry known is set to true after a vertex is processed. Initially, all entries are not known, including the start vertex. When a vertex is marked known, we have
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Figure 9.14 Final Shortest Path a guarantee that no cheaper path will ever be found, and so processing for that vertex is essentially complete. The basic algorithm can be described in Figure 9.16. The algorithm n below mimics the diagrams by declaring as known the vertices at distance d = 0, then d = 1, then d = 2, and so on, and setting all the adjacent vertices w that still have dw = ∞to a distance dw = d + 1. Pseudocode for unweighted shortest-path algorithm void Graph::unweighted( Vertex s ) { for each Vertex v { v.dist = INFINITY; v.known = false; } s.dist = 0; for( int currDist = 0; currDist < NUM_VERTICES; currDist++ ) for each Vertex v if( !v.known && v.dist == currDist ) { v.known = true; for each Vertex w adjacent to v if( w.dist == INFINITY ) { w.dist = currDist + 1; w.path = v; 170
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} } }
Figure 9.15 Initial configuration of table used in unweighted shortest-path computation
Figure 9.17 A bad case for unweighted shortest-path algorithm using the above algorithmBy tracing back through the pv variable, the actual path can be printed. We will seehow when we discuss the weighted case. The running time of the algorithm is O(|V|2), because of the doubly nested for loops. An obvious inefficiency is that the outside loop continues until NUM_VERTICES-1, even if all the vertices become known much earlier. Although an extra test could be made to avoid this, it does not affect the worst-case running time, as can be seen by generalizing what happens when the input is the graph in Figure 9.17 with start vertex v9. We can remove the inefficiency in much the same way as was done for topological sort. At any point in time, there are only two types of unknown vertices that have dv _=∞. Some have dv = currDist, and the rest have dv = currDist + 1. Because of this extra structure, it is very wasteful to search through the entire table to find a proper vertex. A very simple but abstract solution is to keep two boxes. Box #1 will have the unknown vertices with dv = currDist, and box #2 will have dv = currDist + 1. The test to find an appropriate vertex v can be replaced by finding any vertex in box #1. After updating w (inside the innermost if block), we can add w to box #2. After the outermost for loop erminates, box #1 is empty, and box #2 can be transferred to box #1 for the next pass of the for loop. We can refine this idea even further by using just one queue. At the start of the pass, the 171
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queue contains only vertices of distance currDist. When we add adjacent vertices of distance currDist + 1, since they enqueue at the rear, we are guaranteed that they will not be processed until after all the vertices of distance currDist have been processed. After the last vertex at distance currDist dequeues and is processed, the queue only contains vertices of distance currDist + 1, so this process perpetuates. We merely need to begin the process by placing the start node on the queue by itself. The refined algorithm is shown in Figure 9.18. In the pseudocode, we have assumed that the start vertex, s, is passed as a parameter. Also, it is possible that the queue might empty prematurely, if some vertices are unreachable from the start node. In this case, a distance of INFINITY will be reported for these nodes, which is perfectly reasonable. Finally, the known data member is not used; once a vertex is processed it can never enter the queue again, so the fact that it need not be reprocessed is implicitly marked. Thus, the known data member can be discarded. Figure 9.19 shows how the values on the graph we have been using are changed during the algorithm (it includes the changes that would occur to known if we had kept it). Using the same analysis as was performed for topological sort, we see that the running time is O(|E| + |V|), as long as adjacency lists are used. 4. Give the application of Depth First Search Depth-first search is a generalization of preorder traversal. Starting at some vertex, v, we process v and then recursively traverse all vertices adjacent to v. If this process is performed on a tree, then all tree vertices are systematically visited in a total of O(|E|) time, since |E| = _(|V|). If we perform this process on an arbitrary graph, we need to be careful to avoid cycles. To do this, when we visit a vertex, v, we mark it visited, since now we have been there, and recursively call depth-first search on all adjacent vertices that are not already marked. We implicitly assume that for undirected graphs every edge (v, w) appears twice in the adjacency lists: once as (v, w) and once as (w, v). The procedure in Figure 9.61 performs a depth-first search (and does absolutely nothing else) and is a template for the general style. For each vertex, the data member visited is initialized to false. By recursively calling the procedures only on nodes that have not been visited, we guarantee that we do not loop indefinitely. If the graph is undirected and not connected, or directed and not strongly connected, this strategy might fail to visit some nodes. We then search for an unmarked node, void Graph::dfs( Vertex v ) { v.visited = true; for each Vertex w adjacent to v if( !w.visited ) dfs( w ); } Template for depth-first search (pseudocode) apply a depth-first traversal there, and continue this process until there are no unmarked nodes.2 Because this strategy guarantees that each edge is encountered only once, the total time to perform the traversal is O(|E| + |V|), as long as adjacency lists are used. 172
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Implementation: Undirected Graphs An undirected graph is connected if and only if a depth-first search starting from any node visits every node. Because this test is so easy to apply, we will assume that the graphs we deal with are connected. If they are not, then we can find all the connected components and apply our algorithm on each of these in turn. As an example of depth-first search, suppose in the graph of Figure 9.62 we start at vertex A. Then we mark A as visited and call dfs(B) recursively. dfs(B) marks B as visited and calls dfs(C) recursively. dfs(C) marks C as visited and calls dfs(D) recursively. dfs(D) sees both A and B, but both of these are marked, so no recursive calls are made. dfs(D) also sees that C is adjacent but marked, so no recursive call is made there, and dfs(D) returns back to dfs(C). dfs(C) sees B adjacent, ignores it, finds a previously unseen vertex E adjacent, and thus calls dfs(E). dfs(E) marks E, ignores A and C, and returns to dfs(C). dfs(C) returns to dfs(B). dfs(B) ignores both A and D and returns. dfs(A) ignores both D and E and returns. (We have actually touched every edge twice, once as (v, w) and again as (w, v), but this is really once per adjacency list entry.) We graphically illustrate these steps with a depth-first spanning tree. The root of the tree is A, the first vertex visited. Each edge (v, w) in the graph is present in the tree. If, when we process (v, w), we find that w is unmarked, or if, when we process (w, v), we find that v is unmarked, we indicate this with a tree edge. If, when we process (v, w), we find that w is already marked, and when processing (w, v), we find that v is already marked, we draw a dashed line, which we will call a back edge, to indicate that this “edge” is not really part of the tree. The depth-first search of the graph in Figure 9.62 is shown in Figure 9.63. The tree will simulate the traversal we performed. A preorder numbering of the tree, using only tree edges, tells us the order in which the vertices were marked. If the graph is not connected, then processing all nodes (and edges) requires several calls to dfs, and each generates a tree. This entire collection is a depth-first spanning forest.
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UNIT - V PART A 1. What is maxheap? Apr/May,2010 If we want the elements in the more typical increasing sorted order, we can change the ordering property so that the parent has a larger key than the child. it is called max heap. 2. What is divide and conquer strategy? In divide and conquer strategy the given problem is divided into smaller problems and solved recursively. The conquering phase consists of patching together the answers. Divide and conquer is a very powerful use of recursion that we will see many times. 3. Differentiate between merge sort and quick sort? Apr/May,2011 Mergesort 1.Divide and conquer strategy 2.Partition by position Quicksort 1. Divide and conquer strategy 2. Partition by value 4. Mention some methods for choosing the pivot element in quicksort? 1. Choosing first element 2. Generate random number 3. Median of three 5. What are the three cases that arise during the left to right scan in quicksort? I and j cross each other I and j do not cross each other I and j points the same position 6. What is the need of external sorting? External sorting is required where the input is too large to fit into memory. So external sorting is necessary where the program is too large. It is a basic external sorting in which there are two inputs and two outputs tapes. 7. Define multi way merge? Apr/May,2011 If we have extra tapes then we can expect to reduce the number of passes required to sort 175
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8. Define polyphase merge? The k-way merging strategy requires the use of 2 k tapes. This could be prohibitive for some applications. It is possible to get 9. What is replacement selection? We read as many records as possible and sort them. Writing the result to some tapes. This seems like the best approach possible until one realizes that as soon as the first record is written to a output tape the memory it used becomes available for another record. If the next record on the input tape is larger than the record we have just output then it can be included in the item. Using this we can give algorithm. This is called replacement selection. 10. What is sorting? Sorting is the process of arranging the given items in a logical order. Sorting is an example where the analysis can be precisely performed. 11. What is mergesort? The mergesort algorithm is a classic divide and conquer strategy. The problem is divided into two arrays and merged into single array 12. What are the properties involved in heapsort? Apr/May,2010 1.Structure property 2.Heap order property 13. Define articulation points. If a graph is not biconnected, the vertices whose removal would disconnect the graph are known as articulation points. An expression tree is a binary tree in which the operands are attached as leaf nodes and operators become the internal nodes.
14. What is an acyclic graph? A simple diagram which does not have any cycles is called an acyclic graph. 15. Give some example of NP complete problems.
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Hamiltonian circuit. Travelling salesmen problems
16. What are AVL trees? An AVL tree is a binary search tree with a balancing condition.For every node in the tree the heigh of the left and right subtrees can differ at most by 1.The height of an empty tree is defined to be -1.It ensures that the depth of the tree is O(log N) 17. What is topological sort? A topological sort is an ordering of vertices in a directed acyclic graph, such that if there is a path from vi then vj appears after vi in the ordering. 18.What is single source shortest path problem? Given as an input a weighted graph, G=(V,E) and a distinguished vertex,’s’ find the shortest weighted path from ‘s’ to every other vertex in G. 19.Mention some shortest –path problems.
20. Define threaded Binary Tree. (AUC NOV/ DEC 2010) A binary tree is threaded by making all right child pointers that would normally be null point to the inorder successor of the node, and all left child pointers that would normally be null point to the inorder predecessor of the node. UNIT – V PART – B 1. Discuss in detail about Insertion Sort One of the simplest sorting algorithms is the insertion sort. Insertion sort consists of N−1 passes. For pass p=1 through N−1, insertion sort ensures that the elements in positions 0 through p are in sorted order. Insertion sort makes use of the fact that elements in positions 0 through p−1 are already known to be in sorted order. Figure below shows a sample array after each pass of insertion sort. Figure belowshows the general strategy. In pass p, we move the element in position p left until its correct place is found among the first p+1 elements. The code implements this strategy. Lines 11 to 14 implement that data movement without the explicit use of swaps. 177
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The element in position p is moved to tmp, and all larger elements (prior to position p) are moved one spot to the right. Then tmp is moved to the correct spot. This is the same technique that was used in the implementation of binary heaps.
Insertion Sort After each Pass 1 /** 2 * Simple insertion sort. 3 */ 4 template 5 void insertionSort( vector & a ) 6{ 7 for( int p = 1; p < a.size( ); ++p ) 8{ 9 Comparable tmp = std::move( a[ p ] ); 10 11 int j; 12 for( j = p; j > 0 && tmp < a[ j - 1 ]; --j ) 13 a[ j ] = std::move( a[ j - 1 ] ); 14 a[ j ] = std::move( tmp ); 15 } 16 } Insertion sort routine Implementation of Insertion Sort In the STL, instead of having the sort routines take an array of comparable items as a single parameter, the sort routines receive a pair of iterators that represent the start and endmarker of a range. A two-parameter sort routine uses just that pair of iterators and presumes that the items can be ordered, while a three-parameter sort routine has a function object as a third parameter. Converting the algorithm in Figure 7.2 to use the STL introduces several issues. The obvious issues are 1. We must write a two-parameter sort and a three-parameter sort. Presumably, the two parameter sort invokes the three-parameter sort, with less
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virtual function: A genetic function, with a specific return type, extended later for each new argument. type. ... work array: A temporary array used for the storage of intermediate results during processing. Question Bank with ... Class needs access
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EC6301 Object Oriented Programming and Data Structure 123- By EasyEngineering.net.pdf. EC6301 Object Oriented Programming and Data Structure 123- By ...
EC6301 Object Oriented Programming and Data Structure 123- By EasyEngineering.net.pdf. EC6301 Object Oriented Programming and Data Structure 123- By ...
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List some of various object oriented features supported by C++. 6. What are differences between structures and classes in C++?. 7. Explain the client-server model of object communication. 8. Explain built-in and user defined data types. 9. Explain th
Dr. R. Balasubramanian. Associate Professor. Department of Computer Science and Engineering. Indian Institute of Technology Roorkee. Roorkee 247 667 [email protected] https://sites.google.com/site/balaiitr/. CSN- 103. Page 2. 2. Assembly Languages.
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