Computational Complexity
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This document discusses computational complexity and analyzing the running time of algorithms. It defines big-O notation, which is used to classify algorithms according to their worst-case performance as the problem size increases. Examples are provided of algorithms with running times that are O(1), O(log N), O(N), O(N log N), O(N^2), O(N^3), and O(2^N). The growth rates of these functions from slowest to fastest are also listed.
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Data Structure - Lecture 1 - Introduction.pdf
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L12 complexity
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Getting Started with Visual Basic ProgrammingKasun Ranga Wijeweera This document is the first lesson of a 8 part series on Visual Basic programming. It introduces some basic concepts like what a computer program and programming language are. It then provides instructions on how to get started with the Visual Studio Integrated Development Environment, including how to create a new Windows Forms Application project by selecting options, specifying a name and location, and viewing various windows.
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Variables in Visual Basic Programming
Variables in Visual Basic ProgrammingKasun Ranga Wijeweera This document is a lesson on variables in Visual Basic programming. It defines a variable as a location in memory that holds information during program execution. It explains that variables are declared to create them in memory and initialized to assign them a value. Different data types like byte, integer, and long can be used to store different kinds of numeric values in variables. The document provides examples of declaring, initializing, and performing math operations on variables.
Loops in Visual Basic Programming
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Conditional Logic in Visual Basic Programming
Conditional Logic in Visual Basic ProgrammingKasun Ranga Wijeweera This document discusses conditional logic in Visual Basic programming. It provides examples of using If/Then statements to execute code based on whether a condition is true or false. Specifically, it demonstrates:
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Assignment for Variables
Assignment for VariablesKasun Ranga Wijeweera This document contains instructions for 3 Visual Basic programming assignments involving variables. The first assignment has the user declare integer variables, perform a sum calculation, and display the result. The second assignment declares string variables to store name fields, concatenates them into a full name, and displays it. The third assignment takes a user-entered integer, stores it in a variable, multiplies it by 10, and displays the result.
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Assignment for Factory Method Design Pattern in C# [ANSWERS]Kasun Ranga Wijeweera The document describes implementing a factory method design pattern to create different shape objects like circles, ellipses, rectangles and squares. It defines an interface IShape with methods to calculate area and perimeter. Classes are created for each shape inheriting the interface. A Creator class uses factory method to return the appropriate shape object based on user input character. Sample code demonstrates creating a circle object with radius 7 and computing its area and perimeter.
Assignment for Events
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Mastering Arrays Assignment
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1) Store values in an integer array and display them using message boxes. Try accessing an invalid index.
2) Populate an integer array from a user-input start value. Display the array in a list box.
3) Store user text inputs in a global string array. Concatenate and display the concatenated array.
4) Populate a dynamic integer array with random numbers. Display in a list box.
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Computational Complexity
- 1. Computational Complexity Kasun Ranga Wijeweera (Email: krw19870829@gmail.com)
- 2. Background • The running time of a program is proportional to some constant multiplied by one of these terms plus some smaller terms Leading Term + Smaller Terms (Negligible for larger N)
- 3. Examples • N3 + 5 * N2 – 3 * N + 7 N3 is the leading term • N = 108 3 * N2 and 2 * N3 Constant coefficients can be ignored
- 4. Computational Complexity • Here the worst case performance of algorithms is studied • Constant factors are ignored • Determine the functional dependence of the running time
- 5. Definition of Big-Oh Notation • A function g(N) is said to O(f(N)) if there exists constants c0 and N0 such that g(N) is less than c0 * f (N) for all N > N0
- 6. Examples • 7 * N - 2 7 *N – 2 is O (N) Take c0 = 7, N0 = 1 • 3 * N3 + 20 * N2 + 5 3 * N3 + 20 * N2 + 5 is O (N3) Take c0 = 4, N0 = 21 • 3 * log N + 5 3 * log N +5 is O (log N) Take c0 = 11, N0 = 2
- 7. Problem • 7 * N – 2 < N2 Take c0 = 7, N0 = 1 ?
- 8. Growth Rate • Functions in order of increasing growth rate is as follows 1 log N N N log N N2 N3 2N
- 9. Examples of Algorithm Running Times • Min element of an array: O (N) • Closest points in the plane, i.e. smallest distance pairs: N (N - 1)/2 O (N2)
- 10. Comparing Algorithms Experimentally • Implement each algorithm – Lots of work – Error prone • Run it with sample data • Count the time – Same hardware and software are used
- 11. A Sample C Program void main () { clrscr (); clock_t start, end; start = clock (); delay (1000); end = clock(); cout << “Time = ” << (end - start); getch(); }
- 12. Required Header Files # include <conio.h> # include <fstream.h> # include <dos.h> # include <time.h>
- 13. Reference
- 14. Any Questions?
- 15. Thank You!