算法课件全121301ADA12变治法高斯消去法与多项式计算
21页1、Transform and Conquer (I),Chapter 6,Introduction to Transform-and-Conquer Its Application to Numerical Problem Linear Equation Calculating Polynomials,2019/6/21,3,2012-2013-01 Design and Analysis of Algorithm SCUN,Goals of the Lecture,At the end of this lecture, you should Master the basic idea and all kinds of variations of transform and conquer technique Master the linear equation solving algorithm and its analysis Master the Polynomials calculating algorithm and its analysis,2019/6/21,4,2012-
2、2013-01 Design and Analysis of Algorithm SCUN,Transform and Conquer (basic idea),Second, the modified instance is solved, we call this as a conquering stage,Original instance,More amenable instance,Solution,transform,conquer,Transform and conquer deals with a group of design methods that are based on the idea of transformation,First, the original problems instance is modified to be more amenable to solve, we call this as a transformation stage,2019/6/21,5,2012-2013-01 Design and Analysis of Algo
3、rithm SCUN,3 Types of Transform and Conquer,Computing the least common multiple Linear programming,Instance simplification: Transform to a simpler/more convenient instance of the same problem,Presorting Solving linear equation,Representation change: Transform to a different representation of the same instance,Calculating polynomial Heap sort,Problem reduction: Transform to a different problem for which an algorithm is already available,2019/6/21,6,2012-2013-01 Design and Analysis of Algorithm SC
4、UN,Instance simplification - Presorting,Also: Presorting is used in many geometric algorithms.,Many problems involving lists are easier when list is sorted.,searching,computing a mode,checking if all elements are distinct (element uniqueness),a value that occurs most often in a given list of numbers,2012-2013-01 Design and Analysis of Algorithm SCUN,Instance simplification: Linear equation Examples and General form(p203-208),Standard method (cramer method),Example: How to solve the problem of ch
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