PPT-Quicksort

CIS 606 Spring 2010 Quicksort Worstcase running time Θ n 2 Expected running time Θ n lg n Constants hidden in Θ n lg n are small Sorts in place. work on single-pivot quicksort to be: !Then, the number of swaps to partition around pivots p and r is: !! AndrewRosenberg LastTime IntroductiontoRecursion Fibonacci BinarySearch MergeSort QuickSort Today MathematicalAnalysisofRecurrenceRelations MathematicalRecurrences SeriesoftheformSn=Sn1+1,S1=1 Mathem 1. Outline. More pattern matching. Function values and anonymous functions. Higher-order functions and currying. Predefined higher-order functions. 2. More Pattern-Matching. Last time we saw pattern-matching in function definitions:. 27 . – Feb 3, . 2010. Multicore. (and Shared Memory) Programming with . Cilk. ++. Multicore and NUMA architectures. Multithreaded Programming. Cilk++ as a concurrency platform. Divide and conquer paradigm for Cilk++. Artur Laksberg. arturl@microsoft.com. Visual C++ Team, Microsoft. September 17, . 2014. Agenda. Parallel Fundamentals. Task regions. Parallel Algorithms. Parallelization. Vectorization. Part 1: The Fundamentals. Quicksort. . [CLRS, kapitel 7]. Gerth Stølting Brodal. Sandsynligheden for at slå krone. 1/2. Quicksort:. Sorter . A. [. p. ... r. ]. Hoare, 1961. Worst-case tid . O(. n. 2. ). A. p. r. x. A. p. r. Selection Sort. Insertion Sort. Merge Sort. Quick Sort. Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order.. Worst and Average Case Time Complexity: . To seal: moisten flap,. fold over, and seal. 1. Three recursive algorithms. Sorting. GCD (greatest common divisor). Exponentiation. Used in cryptography, which protects information and communication. Quicksort. Haidong. . Xue. Summer 2012, at GSU. Review of insertion sort and merge sort. Insertion sort. Algorithm. Worst case number of comparisons = O(?). Merge sort. Algorithm. Worst case number of comparisons = O(?). Cost to interview (low . C. i. ). Cost to fire/hire . … (expensive . C. h. ). n. number of candidates. m. hired. O . (. c. i. n. + c. h. m. ). Independent of order of candidates. depends on order of candidates. Outline In this topic we will look at quicksort: The idea behind the algorithm The run time and worst-case scenario Strategy for avoiding the worst-case: median-of-three Implementing quicksort in place CS 179: GPU Programming Lecture 7 Week 3 Goals: Advanced GPU- accelerable algorithms CUDA libraries and tools This Lecture GPU- accelerable algorithms: Reduction Prefix sum Stream compaction Sorting (quicksort) Lecture 7. Last Week. Memory optimizations using different GPU caches. Atomic operations. Synchronization with __. syncthreads. (). Week 3. Advanced GPU-accelerable algorithms. “Reductions” to parallelize problems that don’t seem intuitively parallelizable. Roadmap. 2. Last time. Path problems. Shortest-distance problem. Started on concrete semantics. Showing you the “how,” but not the “why”. Today: the “why”. Via an optimization example. 3.