Euclidean algorithm In mathematics‚ the Euclidean algorithm‚ or Euclid’s algorithm‚ is a method for computing the greatest common divisor (GCD) of two (usually positive) integers‚ also known as the greatest common factor (GCF) or highest common factor (HCF). It is named after the Greek mathematician Euclid‚ who described it in Books VII and X of his Elements. The GCD of two positive integers is the largest integer that divides both of them without leaving a remainder (the GCD of two integers in
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2010 A Secure Steganography Method based on Genetic Algorithm Shen Wang‚ Bian Yang and Xiamu Niu School of Computer Science and Technology Harbin Institute of Technology 150080‚ Harbin‚ China shen.wang@ict.hit.edu.cn; bian.yang@ict.hit.edu.cn; xiamu.niu@hit.edu.cn Received April 2009; revised August 2009 Abstract. With the extensive application of steganography‚ it is challenged by steganalysis. The most notable steganalysis algorithm is the RS attack which detects the steg-message by the
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The Design & Analysis o f A lgorithms ~~ I_ND EDIIIQN ~ I ntroduction t o * The Design & Analysis o f Algorithms I ND EDITION " I ntroduction t o ~ ~ ~ Anany Levitin Villanova University B oston San Francisco N ew York L ondon T oronto S ydney Tokyo Singapore Madrid M exico City M unich Paris C ape Town H ong K ong M ontreal Publisher Acquisitions E ditor P roject E ditor P roduction Supervisor M arketing Manager P roject Management & Composition Technical
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Student Name Syed Haseeb Hashmi Registration # FA11-BCS-075 Course Title Design and Analysis of Algorithm Assignment # 1 Submitted To Sir Tanveer Ahmed Siddiqui Due Date 19-03-2013 For Odd Role Number Group Q1. How does a flowchart help a programmer in a program development? Ans. Flowcharts provide the visual representation of a concept and make it clear. A flow chart serves
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CPSC 413 Assignment 1 Asymptotic Notation and Summations Sample Analysis Goal This document will give a detailed analysis of Floyd-Warshall’s All-Pairs Shortest Path algorithm‚ which should give you an idea of the detail that is required in your own solution for assignment 1. Floyd’s Algorithm • Graph Problem: All-Pairs Shortest Path • Input: A weighted graph denoted by adjacency matrix W . (The vertices are assumed to be numbered from 1 to n) • Output: Matrix D containing the length
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Project 1 - Methodologies for Analyzing Algorithms Video games today are very detailed and very realistic. It is amazing how far video games have come in the last 30 years. Now you have new games like Gears of War 3 that is so graphically intense that there is plenty of coding involved. But just basic programming isn’t enough for these video games‚ you need algorithms. The more advanced the video game is‚ the more advanced the algorithm is as well. Algorithm in video games was not created recently
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THE THREE ELEMENTARY SORTING ALGORITHMS Bubble Sort Bubble Sort is probably one of the oldest‚ easiest‚ straight-forward‚ and inefficient sorting algorithms. It is the algorithm introduced as a sorting routine in most introductory courses on Algorithms. Bubble Sort works by comparing each element of the list with the element next to it and swapping them if required. With each pass‚ the largest of the list is "bubbled" to the end of the list whereas the smaller values sink to the bottom.
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60 LABEL A 70 END (i) Explain what is being achieved. [4] (ii) If you replaced the line LET Y = X/3 by the line LET Y = X/5‚ how would this change the outcome of the above? [1] 2. The following algorithm is to be applied to the positive integers from 1 to 12. Step 1: Cross out every even number. Step 2: Change the state of every multiple of 3 (including 3) – i.e. for every multiple of 3‚ if it is crossed out then remove the crossing
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This file contains the exercises‚ hints‚ and solutions for Chapter 5 of the book ”Introduction to the Design and Analysis of Algorithms‚” 2nd edition‚ by A. Levitin. The problems that might be challenging for at least some students are marked by ◃; those that might be difficult for a majority of students are marked by . Exercises 5.1 1. Ferrying soldiers A detachment of n soldiers must cross a wide and deep river with no bridge in sight. They notice two 12-year-old boys playing in a rowboat by the
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510.6401 Design and Analysis of Algorithms January 21‚ 2008 Problem Set 1 Due: February 4‚ 2008. 1. In the bin packing problem‚ the input consists of a sequence of items I = {1‚ . . . ‚ n} where each item i has a size‚ which is a real number 0 ≤ ai ≤ 1. The goal is to “pack” the items in the smallest possible number of bins of unit size. Formally‚ the items should be partitioned in disjoint subsets (bins)‚ such that the total size in each bin is at most 1. The first fit heuristic scans the items
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