其实这个解决问题的思路就是算法中常用的divide and conquer, 这篇日志通过解决矩阵的乘法,来了解另外一个基本divide and conque思想的strassen算法。 矩阵A乘以B等于X, 则Xij = 注意左乘右乘的区别,AB 与BA是不同的。 如果r = 1, 直接就是两个数的相乘。 如果r = 2, 例如 X = [ 1, 2; 3, 4]; Y...
1.Introduction2.Thedivideandconquerparadigm3.Binarysearch4.Mergesort5.Multiplicationoflargeintegers6.Matrixmultiplication7.Linear-timeselectionproblem NorthChinaElectricPowerUniversity §1Introduction Thenameof“divideandconquer”hasbeengiventoapowerfulalgorithmdesigntechniquethatisusedtosolveavarietyofproblems.Initssimplest...
切割與征服 Divide-and-Conquer 國立聯合大學資訊管理學系陳士杰老師 國立聯合大學資訊管理學系 演算法課程(陳士杰)2 ▓Outlines 本章重點 Divide-and-Conquer策略的描述BinarySearchMergeSortTheDivide-and-ConquerApproachQuickSortStrassen'sMatrixMultiplicationAlgorithmWhenNottoUseDivide-...
Divide-and-conquerparallel architecturesparallel matrix multiplicationparallel sortingRecent advances in the development of modern satellite sensors have increased the need for image coding, because of the huge volume of such collected data. It is well-known that the Karhunen-Lo锚ve transform provides ...
Conquer: multiply 8 n/2-by-n/2 recursively. Combine: add appropriate products using 4 matrix additions. Runnig time Key Idea Key idea. multiply 2-by-2 block matrices with only 7 multiplications. where Fast Matrix multiply Fast matrix multiplication. [Strassen, 1969] Divide: partition X and ...
A divide-and-conquer algorithm for integer multiplication (3次乘法) functionmultiply(x,y)Input:Positive integers xandy,in binary Output:Their product/n=max(size of x,size of y)ifn=1:returnxy/xL,xR=leftmost ⌈n/2⌉,rightmost ⌊n/2⌋ bits of x ...
Divide and Conquer 目录 Merge Sort Counting Inversions Closest Pair 场景 算法 Karatsuba Multiplication FFT and Inverse FFT 场景 FFT Inverse FFT Merge Sort 持续将序列分成两半,直到不可再分,然后合并 T(n) = 2T(\frac{n}{2}) + O(n) Counting Inversions...
Multiplication of large integers Matrix multiplication: Strassen’s algorithm Closest-pair and convex-hull algorithms General Divide-and-Conquer Recurrence T(n) = aT(n/b) + f (n) where f(n) ? ?(nd), d ? 0 Master Theorem: If a bd, T(n) ? ?(nd) If a = bd, T(n) ? ?(nd ...
conquertechnology Zouquan(PhD)computersciencedepartment Thefeed 33.233.3divide-and-conquerprincipleDivide-and-Conquer principleintegermultiplicationmatrixmultiplication Findingtheclosestpairofpoints 3.1divide-and-conquerprincipleofdivide-and-conquer principle Divide-and-conqueralgorithmdesignofdivide-and-conquer ...
【3】分治法(divide-and-conquer) 文章目录 分治法 举例 归并排序(Merge sort) 二分查找方法(Binary search) 乘方问题(Powering a number) 斐波那契数(Fibonacci numbers) 传统的Naive算法 朴素平方递归式 矩阵乘法(Matrix multiplication) 朴素算法 分治法 分治法 Strassen’s idea 超大规模集成电路(VLSI layo......