briana b. morrison with thanks to dr. hung. 2. Now customize the name of a clipboard to store your clips. You can change your ad preferences anytime. 7  7. Learn more. trees with at most 4 edges. cs 46101 section 600 cs 56101 section 002 dr. angela guercio spring 2010. today. Divide and Conquer We break it up into smaller pieces, solve the pieces separately, andcombine the separate pieces together. , pn } be a collection of points in the plane • Thus we want to find min { dist(pi,pj) | 1 ≤ i < j ≤ n } • The following obvious algorithm will find the distance between a closest pair of points in P: min  for i  1 to n-1 for j  i+1 to n if dist(pi,pj) < min min = dist(pi,pj)return min • The running time of the above is clearly (n2) • Divide and Conquer can be used to get a (nlg n) algorithm, Closest Pairs Algorithm • First step (Divide) Choose a vertical line L so that n/2 of the points are on or to the left of L (left set) and n/2 points of P are on or to the right of L (right set) • Second step (Conquer) Recursively compute the minimum distance L between any two points in the left set of points and the minimum distance R between any two points in the right set of points. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Additional D&C Algorithms. As of this date, Scribd will manage your SlideShare account and any content you may have on SlideShare, and Scribd's General Terms of Use and Privacy Policy will apply. • There are deficient 55 boards that can be tiled and others that cannot. the most well known, Divide and Conquer - . combine, Master theorem Design divide-and-conquer algorithms - Lecture 6 divide-and-conquer. This is the currently selected item. Large case: n = 2k with k  2 Divide the board into four 2k-12k-1 boards, exactly one of which will be deficient. This document is highly rated by students and has been viewed 264 times. Assistant Professor | Computer Engineering Divide and Conquer Algorithms. Solve the smaller subproblems. When we keep on dividing the subproblems into even smaller sub-problems, we may eventually reach a stage where no more division is possible. Many are downloadable. objectives. Share date: 2013-01-13. abstract. 9  4  4 9. Many algorithms are recursive in nature to solve a given problem recursively dealing with sub-problems. The Divide and Conquer algorithm solves the problem in O(nLogn) time. 9  9. Divide and Conquer Strategy Divide the problem into a number of smaller subproblems. mergesort finding the middle point in the alignment matrix in linear. midterm1 lect11.ppt Divide and conquer: Closest-Pair Problem, convex-hull Week8 10/06. A Divide and Conquer Algorithm. See our Privacy Policy and User Agreement for details. • Thus n2-1 being divisible by 3 is a necessary condition for a tiling to exist • Chu and Johnsonbaugh proved that this condition is also sufficient for all n except n = 5. Get powerful tools for managing your contents. a useful fact about, Theory of Algorithms: Divide and Conquer - . divide-and-conquer paradigm, which gives a useful framework for thinking about problems. binary search ... – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 1b985f-MzRmM Algorithms Divide and Conquer - Part I 15 MERGING 16. Introduction Divide and conquer is an algorithm design paradigm based on multi-branched recursion. cs 331, fall 2013 tandy warnow. fan chung graham uc san diego. Briana B. Morrison. Nov 26,2020 - Divide And Conquer (Basic Level) - 1 | 10 Questions MCQ Test has questions of Computer Science Engineering (CSE) preparation. Introduction to Divide and Conquer Approach. Divide-and-Conquer. to introduce the divide-and-conquer mind set to show a variety. Algorithm design strategy: Divide and Conquer if the problem is small, solve directly if the problem is large, divide into two or more subproblems solve the smaller subproblems using the same divide-and-conquer approach, Divide and Conquer Algorithms • Algorithm design strategy: Divide and Conquer • if the problem is small, solve directly • if the problem is large, divide into two or more subproblems • solve the smaller subproblems using the same divide-and-conquer approach • combine the subproblem solutions to get a solution for the larger problem • Divide and Conquer algorithms are often implemented as recursive functions, Trominos and Deficient Boards • (Right) Tromino:object made up of three 11 squares that are not linearly arranged • Deficient board:A nn board of 11 squares with one square removed Three of the sixteen possible deficient 44 boards, A Tiling Problem • Tromino Tiling of a Deficient Board:An exact covering of all the squares of the board by non-overlapping trominos none of whom extend outside the board • Tromino Tiling Problem:Given a nn deficient board, where n is a power of 2, find a tiling of the board by trominos. divide-and-conquer. This test is Rated positive by 91% students preparing for Computer Science Engineering (CSE).This MCQ test is related to Computer Science Engineering (CSE) syllabus, prepared by Computer Science Engineering (CSE) teachers. reduce the problem by reducing the data set. Solve smaller instances independently and COMP 3711 Design and Analysis of Algorithms Lecture 2: Divide & Conquer Divide-and-Conquer master theorem design, Divide-and-Conquer - . In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion.A divide-and-conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. Combine the break up problem into several parts. I can’t remember where those slide come from. Divide and Conquer. 7 , Divide and conquer - Conquer. Clipping is a handy way to collect important slides you want to go back to later. With thanks to Dr. Hung. Dr. Yingwu Zhu P65-74, p83-88, p93-96, p170-180 Divide-and-Conquer The most-well known algorithm design technique: 1. For each non-deficient quadrant, “remove” the square touching the center point of the original board Recursively tile the deficient quadrant Add the tromino made up of the squares not covered in the non-deficient quadrants. The most well known algorithm design strategy: ... – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 1d73d0-ZDc1Z the. The sub problems are solved recursively. Divide and Conquer Algorithms. divide. Linear-time merging. Thus we need only consider points whose x-coordinate satisfies c- < x < c+ Thus we may reduce the set of points to be considered to those lying in the open vertical strip of width 2 centered at L, Closest Pairs Algorithm • Second observation: If we consider the points in the strip in order of non-decreasing y-coordinate, we need only compare each point with points above it Moreover, when checking point p, we need only consider points whose y-coordinate is less than  more than that of p. This means that we only consider points in the rectangle with width 2 and height  centered on the line L and having p on its lower edge, Closest Pairs Algorithm • Third observation: There are at most 7 other points in the rectangle for p Break the rectangle up into /2 by /2 squares: The distance between two points in /2 by /2 square is ≤ Since each square is contained in the left or the right set, it can containat most one of the points in P, Running Time • If we consider the points in the strip in non-decreasing order of their y-coordinates, we need only compare each point to at most 7 other points • Thus the cost of finding the smallest distance between pairs of points in the strip is at most 7n • This gives the following recurrence for the running time: T(n) = T(n/2 ) + T(n/2 ) + 7n • By the Master Theorem, we then have T(n) = (nlg n), Closest Pair Algorithm closest_pair(p) { n = p.last mergesort(p,1,n) // sort by x-coordinate return recursive_closest_pair(p,1,n) } // recursive_closest_pair assumes that the input is sorted by x-coordinate // At termination, the input is stably sorted by y-coordinate, Closest Pair Algorithm recursive_closest_pair(p,i,j) { if (j-i < 3) { mergesort(p,i,j) // sort by y-coordinate // Find a closest pair directly delta = dist(p[i],p[i+1]) if (j-i = 1) // two pointsreturn delta if (dist(p[i+1],p[i+2] ) < delta) delta = dist(p[i+1],p[i+2]) if (dist(p[i],p[i+2] ) < delta) delta = dist(p[i],p[i+2]) return delta }, Closest Pair Algorithm // recursive_closest_pair(p,i,j) continued k = (i+j)/2l = p[k].x deltaL = recursive_closest_pair(p,i,k)deltaR = recursive_closest_pair(p,k+1,j)delta = min ( deltaL, deltaR ) // p[i..k] and p[k+1..j] are now sorted by y-coordinatemerge(p,i,k,j) // p[i.. j] is now sorted by y-coordinate // Next store the points in the vertical strip in another array// On next slide, Closest Pair Algorithm // recursive_closest_pair(p,i,j) continued // next, store the points in the vertical strip in another array t = 0 // index in the vertical strip array vfor m = i to j if ( p[m].x > l-delta && p[m].x < l +delta ) { t = t+1 v[t] = p[k] } for m = 1 to t-1 for s = m+1 to min(t,m+7) delta = min( delta, dist(v[m],v[s] ) return delta }, © 2020 SlideServe | Powered By DigitalOfficePro, - - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -. 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