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The document discusses recursive definitions of sequences, functions, sets, and strings. It provides examples of recursively defining the Fibonacci sequence, factorial function, set of prices using quarters and dimes, and set of binary numbers. It also discusses recursively defining the length, empty string, concatenation, and reversal of strings.
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This document discusses recursive definitions, algorithms, and program correctness. It provides examples of recursively defining functions and sets using a basis step and recursive step. Examples of recursive algorithms are given for computing factorials and exponentials. The difference between recursion and iteration is explained. Program verification and correctness are defined, and examples are worked through to show initial and final assertions for program segments. The document concludes with an announcement about an upcoming exam.
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We dedicate this to all of you, the artists in Infopark, in Kochi at large and why not, to the entire wide world of art!!!
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C++ classes allow programmers to encapsulate data and functions into user-defined types called classes. A class defines the data attributes and functions that operate on those attributes. Classes support object-oriented programming by allowing objects to be created from a class which store and manipulate data private to the class through public member functions.
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This document provides an overview of different types of programming languages including:
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The document outlines an introduction to computers, C++ programming, and other programming languages. It discusses the history and components of computers, operating systems, programming languages like C, C++, Java, and concepts like structured programming. The chapters also introduce simple C++ programs, basic C syntax like data types, operators, control flow, and the typical development process for a C++ program.
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The document presents an overview of algorithms for inserting and deleting data from stacks, queues, and linked lists. It discusses:
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The document summarizes algorithms for inserting and deleting data from stacks, queues, and linked lists. It provides examples of:
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Editor's Notes
- A closed formula for C ( n,k ) is given by: C ( n,k ) = n !/( k ! ( n-k )! )
- 1 In other texts, including the text for computability the Greek letter epsilon is used instead.
- 1 In other texts, including the text for computability (CS3261) the Greek letter (epsilon) is used instead.
- 1 In other texts, including the text for computability the Greek letter is used instead.
- 1 In other texts, including the text for computability the Greek letter (epsilon) is used instead.
- 1 In other texts, including the text for computability the Greek letter (epsilon) is used instead.
- 1 In other texts, including the text for computability the Greek letter (epsilon) is used instead.
- n<=0 is used instead of n==0 because Java’s long is signed, and we don’t want the program to crash or enter an infinite loop for negative numbers. Exceptions handling would be more appropriate here, but this is well beyond the scope of 3203.
- Here we assume that the ranges are mutually disjoint and cover all possible input values. Strictly speaking, this code will not compile in Java because there is no default return value. This is fixed by changing the last clause: “ if ( n in range k ) return output k ” to a simple return statement which removes the conditional: “ return output k ”