Meant to Provoke Thought Regarding the Current "Software Crisis" at the Time
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Overview of Sorting Algorithms
Unit 7 Sorting Algorithms Simple Sorting algorithms Quicksort Improving Quicksort Overview of Sorting Algorithms Given a collection of items we want to arrange them in an increasing or decreasing order. You probably have seen a number of sorting algorithms including ¾ selection sort ¾ insertion sort ¾ bubble sort ¾ quicksort ¾ tree sort using BST's In terms of efficiency: ¾ average complexity of the first three is O(n2) ¾ average complexity of quicksort and tree sort is O(n lg n) ¾ but its worst case is still O(n2) which is not acceptable In this section, we ¾ review insertion, selection and bubble sort ¾ discuss quicksort and its average/worst case analysis ¾ show how to eliminate tail recursion ¾ present another sorting algorithm called heapsort Unit 7- Sorting Algorithms 2 Selection Sort Assume that data ¾ are integers ¾ are stored in an array, from 0 to size-1 ¾ sorting is in ascending order Algorithm for i=0 to size-1 do x = location with smallest value in locations i to size-1 swap data[i] and data[x] end Complexity If array has n items, i-th step will perform n-i operations First step performs n operations second step does n-1 operations ... last step performs 1 operatio. Total cost : n + (n-1) +(n-2) + ... + 2 + 1 = n*(n+1)/2 . Algorithm is O(n2). Unit 7- Sorting Algorithms 3 Insertion Sort Algorithm for i = 0 to size-1 do temp = data[i] x = first location from 0 to i with a value greater or equal to temp shift all values from x to i-1 one location forwards data[x] = temp end Complexity Interesting operations: comparison and shift i-th step performs i comparison and shift operations Total cost : 1 + 2 + .. -
The Analysis and Synthesis of a Parallel Sorting Engine Redacted for Privacy Abstract Approv, John M
AN ABSTRACT OF THE THESIS OF Byoungchul Ahn for the degree of Doctor of Philosophy in Electrical and Computer Engineering, presented on May 3. 1989. Title: The Analysis and Synthesis of a Parallel Sorting Engine Redacted for Privacy Abstract approv, John M. Murray / Thisthesisisconcerned withthe development of a unique parallelsort-mergesystemsuitablefor implementationinVLSI. Two new sorting subsystems, a high performance VLSI sorter and a four-waymerger,werealsorealizedduringthedevelopment process. In addition, the analysis of several existing parallel sorting architectures and algorithms was carried out. Algorithmic time complexity, VLSI processor performance, and chiparearequirementsfortheexistingsortingsystemswere evaluated.The rebound sorting algorithm was determined to be the mostefficientamongthoseconsidered. The reboundsorter algorithm was implementedinhardware asasystolicarraywith external expansion capability. The second phase of the research involved analyzing several parallel merge algorithms andtheirbuffer management schemes. The dominant considerations for this phase of the research were the achievement of minimum VLSI chiparea,design complexity, and logicdelay. Itwasdeterminedthattheproposedmerger architecture could be implemented inseveral ways. Selecting the appropriate microarchitecture for the merger, given the constraints of chip area and performance, was the major problem.The tradeoffs associated with this process are outlined. Finally,apipelinedsort-merge system was implementedin VLSI by combining a rebound sorter -
Lecture 04 Linear Structures Sort
Algorithmics (6EAP) MTAT.03.238 Linear structures, sorting, searching, etc Jaak Vilo 2018 Fall Jaak Vilo 1 Big-Oh notation classes Class Informal Intuition Analogy f(n) ∈ ο ( g(n) ) f is dominated by g Strictly below < f(n) ∈ O( g(n) ) Bounded from above Upper bound ≤ f(n) ∈ Θ( g(n) ) Bounded from “equal to” = above and below f(n) ∈ Ω( g(n) ) Bounded from below Lower bound ≥ f(n) ∈ ω( g(n) ) f dominates g Strictly above > Conclusions • Algorithm complexity deals with the behavior in the long-term – worst case -- typical – average case -- quite hard – best case -- bogus, cheating • In practice, long-term sometimes not necessary – E.g. for sorting 20 elements, you dont need fancy algorithms… Linear, sequential, ordered, list … Memory, disk, tape etc – is an ordered sequentially addressed media. Physical ordered list ~ array • Memory /address/ – Garbage collection • Files (character/byte list/lines in text file,…) • Disk – Disk fragmentation Linear data structures: Arrays • Array • Hashed array tree • Bidirectional map • Heightmap • Bit array • Lookup table • Bit field • Matrix • Bitboard • Parallel array • Bitmap • Sorted array • Circular buffer • Sparse array • Control table • Sparse matrix • Image • Iliffe vector • Dynamic array • Variable-length array • Gap buffer Linear data structures: Lists • Doubly linked list • Array list • Xor linked list • Linked list • Zipper • Self-organizing list • Doubly connected edge • Skip list list • Unrolled linked list • Difference list • VList Lists: Array 0 1 size MAX_SIZE-1 3 6 7 5 2 L = int[MAX_SIZE] -
Cyclone: a Type-Safe Dialect of C∗
Cyclone: A Type-Safe Dialect of C∗ Dan Grossman Michael Hicks Trevor Jim Greg Morrisett If any bug has achieved celebrity status, it is the • In C, an array of structs will be laid out contigu- buffer overflow. It made front-page news as early ously in memory, which is good for cache locality. as 1987, as the enabler of the Morris worm, the first In Java, the decision of how to lay out an array worm to spread through the Internet. In recent years, of objects is made by the compiler, and probably attacks exploiting buffer overflows have become more has indirections. frequent, and more virulent. This year, for exam- ple, the Witty worm was released to the wild less • C has data types that match hardware data than 48 hours after a buffer overflow vulnerability types and operations. Java abstracts from the was publicly announced; in 45 minutes, it infected hardware (“write once, run anywhere”). the entire world-wide population of 12,000 machines running the vulnerable programs. • C has manual memory management, whereas Notably, buffer overflows are a problem only for the Java has garbage collection. Garbage collec- C and C++ languages—Java and other “safe” lan- tion is safe and convenient, but places little con- guages have built-in protection against them. More- trol over performance in the hands of the pro- over, buffer overflows appear in C programs written grammer, and indeed encourages an allocation- by expert programmers who are security concious— intensive style. programs such as OpenSSH, Kerberos, and the com- In short, C programmers can see the costs of their mercial intrusion detection programs that were the programs simply by looking at them, and they can target of Witty. -
REFPERSYS High-Level Goals and Design Ideas*
REFPERSYS high-level goals and design ideas* Basile STARYNKEVITCH† Abhishek CHAKRAVARTI‡ Nimesh NEEMA§ refpersys.org October 2019 - May 2021 Abstract REFPERSYS is a REFlexive and orthogonally PERsistent SYStem (as a GPLv3+ licensed free software1) running on Linux; it is a hobby2 but serious research project for many years, mostly aimed to experiment open science ideas close to Artificial General Intelligence3 dreams, and we don’t expect use- ful or interesting results before several years of hard work. audience : LINUX free software developers4 and computer scientists interested in an experimental open science approach to reflexive systems, orthogonal persistence, symbolic artificial intelligence, knowledge engines, etc.... Nota Bene: this report contains many hyperlinks to relevant sources so its PDF should rather be read on a computer screen, e.g. with evince. Since it describes a circular design (with many cycles [Hofstadter:1979:GEB]), we recommend to read it twice (skipping footnotes and references on the first read). This entire document is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. *This document has git commit fb17387fbbb7e200, was Lua-LATEX generated on 2021-May-17 18:55 MEST, see gitlab.com/bstarynk/refpersys/ and its doc/design-ideas subdirectory. Its draft is downloadable, as a PDF file, from starynkevitch.net/Basile/refpersys-design.pdf ... †See starynkevitch.net/Basile/ and contact [email protected], 92340 Bourg La Reine (near Paris), France. ‡[email protected], FL 3C, 62B PGH Shah Road, Kolkata 700032, India. -
Sorting Algorithms Correcness, Complexity and Other Properties
Sorting Algorithms Correcness, Complexity and other Properties Joshua Knowles School of Computer Science The University of Manchester COMP26912 - Week 9 LF17, April 1 2011 The Importance of Sorting Important because • Fundamental to organizing data • Principles of good algorithm design (correctness and efficiency) can be appreciated in the methods developed for this simple (to state) task. Sorting Algorithms 2 LF17, April 1 2011 Every algorithms book has a large section on Sorting... Sorting Algorithms 3 LF17, April 1 2011 ...On the Other Hand • Progress in computer speed and memory has reduced the practical importance of (further developments in) sorting • quicksort() is often an adequate answer in many applications However, you still need to know your way (a little) around the the key sorting algorithms Sorting Algorithms 4 LF17, April 1 2011 Overview What you should learn about sorting (what is examinable) • Definition of sorting. Correctness of sorting algorithms • How the following work: Bubble sort, Insertion sort, Selection sort, Quicksort, Merge sort, Heap sort, Bucket sort, Radix sort • Main properties of those algorithms • How to reason about complexity — worst case and special cases Covered in: the course book; labs; this lecture; wikipedia; wider reading Sorting Algorithms 5 LF17, April 1 2011 Relevant Pages of the Course Book Selection sort: 97 (very short description only) Insertion sort: 98 (very short) Merge sort: 219–224 (pages on multi-way merge not needed) Heap sort: 100–106 and 107–111 Quicksort: 234–238 Bucket sort: 241–242 Radix sort: 242–243 Lower bound on sorting 239–240 Practical issues, 244 Some of the exercise on pp. -
Spindle Documentation Release 2.0.0
spindle Documentation Release 2.0.0 Jorge Ortiz, Jason Liszka June 08, 2016 Contents 1 Thrift 3 1.1 Data model................................................3 1.2 Interface definition language (IDL)...................................4 1.3 Serialization formats...........................................4 2 Records 5 2.1 Creating a record.............................................5 2.2 Reading/writing records.........................................6 2.3 Record interface methods........................................6 2.4 Other methods..............................................7 2.5 Mutable trait...............................................7 2.6 Raw class.................................................7 2.7 Priming..................................................7 2.8 Proxies..................................................8 2.9 Reflection.................................................8 2.10 Field descriptors.............................................8 3 Custom types 9 3.1 Enhanced types..............................................9 3.2 Bitfields..................................................9 3.3 Type-safe IDs............................................... 10 4 Enums 13 4.1 Enum value methods........................................... 13 4.2 Companion object methods....................................... 13 4.3 Matching and unknown values...................................... 14 4.4 Serializing to string............................................ 14 4.5 Examples................................................. 14 5 Working -
Union Types for Semistructured Data
Edinburgh Research Explorer Union Types for Semistructured Data Citation for published version: Buneman, P & Pierce, B 1999, Union Types for Semistructured Data. in Union Types for Semistructured Data: 7th International Workshop on Database Programming Languages, DBPL’99 Kinloch Rannoch, UK, September 1–3,1999 Revised Papers. Lecture Notes in Computer Science, vol. 1949, Springer-Verlag GmbH, pp. 184-207. https://doi.org/10.1007/3-540-44543-9_12 Digital Object Identifier (DOI): 10.1007/3-540-44543-9_12 Link: Link to publication record in Edinburgh Research Explorer Document Version: Peer reviewed version Published In: Union Types for Semistructured Data General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 27. Sep. 2021 Union Typ es for Semistructured Data Peter Buneman Benjamin Pierce University of Pennsylvania Dept of Computer Information Science South rd Street Philadelphia PA USA fpeterbcpiercegcisupenn edu Technical -
An Evolutionary Approach for Sorting Algorithms
ORIENTAL JOURNAL OF ISSN: 0974-6471 COMPUTER SCIENCE & TECHNOLOGY December 2014, An International Open Free Access, Peer Reviewed Research Journal Vol. 7, No. (3): Published By: Oriental Scientific Publishing Co., India. Pgs. 369-376 www.computerscijournal.org Root to Fruit (2): An Evolutionary Approach for Sorting Algorithms PRAMOD KADAM AND Sachin KADAM BVDU, IMED, Pune, India. (Received: November 10, 2014; Accepted: December 20, 2014) ABstract This paper continues the earlier thought of evolutionary study of sorting problem and sorting algorithms (Root to Fruit (1): An Evolutionary Study of Sorting Problem) [1]and concluded with the chronological list of early pioneers of sorting problem or algorithms. Latter in the study graphical method has been used to present an evolution of sorting problem and sorting algorithm on the time line. Key words: Evolutionary study of sorting, History of sorting Early Sorting algorithms, list of inventors for sorting. IntroDUCTION name and their contribution may skipped from the study. Therefore readers have all the rights to In spite of plentiful literature and research extent this study with the valid proofs. Ultimately in sorting algorithmic domain there is mess our objective behind this research is very much found in documentation as far as credential clear, that to provide strength to the evolutionary concern2. Perhaps this problem found due to lack study of sorting algorithms and shift towards a good of coordination and unavailability of common knowledge base to preserve work of our forebear platform or knowledge base in the same domain. for upcoming generation. Otherwise coming Evolutionary study of sorting algorithm or sorting generation could receive hardly information about problem is foundation of futuristic knowledge sorting problems and syllabi may restrict with some base for sorting problem domain1. -
A Proposal for a Standard Systemverilog Synthesis Subset
A Proposal for a Standard Synthesizable Subset for SystemVerilog-2005: What the IEEE Failed to Define Stuart Sutherland Sutherland HDL, Inc., Portland, Oregon [email protected] Abstract frustrating disparity in commercial synthesis compilers. Each commercial synthesis product—HDL Compiler, SystemVerilog adds hundreds of extensions to the Encounter RTL Compiler, Precision, Blast and Synplify, to Verilog language. Some of these extensions are intended to name just a few—supports a different subset of represent hardware behavior, and are synthesizable. Other SystemVerilog. Design engineers must experiment and extensions are intended for testbench programming or determine for themselves what SystemVerilog constructs abstract system level modeling, and are not synthesizable. can safely be used for a specific design project and a The IEEE 1800-2005 SystemVerilog standard[1] defines specific mix of EDA tools. Valuable engineering time is the syntax and simulation semantics of these extensions, lost because of the lack of a standard synthesizable subset but does not define which constructs are synthesizable, or definition for SystemVerilog. the synthesis rules and semantics. This paper proposes a standard synthesis subset for SystemVerilog. The paper This paper proposes a subset of the SystemVerilog design reflects discussions with several EDA companies, in order extensions that should be considered synthesizable using to accurately define a common synthesis subset that is current RTL synthesis compiler technology. At Sutherland portable across today’s commercial synthesis compilers. HDL, we use this SystemVerilog synthesis subset in the training and consulting services we provide. We have 1. Introduction worked closely with several EDA companies to ensure that this subset is portable across a variety of synthesis SystemVerilog extensions to the Verilog HDL address two compilers. -
Presentation on Ocaml Internals
OCaml Internals Implementation of an ML descendant Theophile Ranquet Ecole Pour l’Informatique et les Techniques Avancées SRS 2014 [email protected] November 14, 2013 2 of 113 Table of Contents Variants and subtyping System F Variants Type oddities worth noting Polymorphic variants Cyclic types Subtyping Weak types Implementation details α ! β Compilers Functional programming Values Why functional programming ? Allocation and garbage Combinatory logic : SKI collection The Curry-Howard Compiling correspondence Type inference OCaml and recursion 3 of 113 Variants A tagged union (also called variant, disjoint union, sum type, or algebraic data type) holds a value which may be one of several types, but only one at a time. This is very similar to the logical disjunction, in intuitionistic logic (by the Curry-Howard correspondance). 4 of 113 Variants are very convenient to represent data structures, and implement algorithms on these : 1 d a t a t y p e tree= Leaf 2 | Node of(int ∗ t r e e ∗ t r e e) 3 4 Node(5, Node(1,Leaf,Leaf), Node(3, Leaf, Node(4, Leaf, Leaf))) 5 1 3 4 1 fun countNodes(Leaf)=0 2 | countNodes(Node(int,left,right)) = 3 1 + countNodes(left)+ countNodes(right) 5 of 113 1 t y p e basic_color= 2 | Black| Red| Green| Yellow 3 | Blue| Magenta| Cyan| White 4 t y p e weight= Regular| Bold 5 t y p e color= 6 | Basic of basic_color ∗ w e i g h t 7 | RGB of int ∗ i n t ∗ i n t 8 | Gray of int 9 1 l e t color_to_int= function 2 | Basic(basic_color,weight) −> 3 l e t base= match weight with Bold −> 8 | Regular −> 0 in 4 base+ basic_color_to_int basic_color 5 | RGB(r,g,b) −> 16 +b+g ∗ 6 +r ∗ 36 6 | Grayi −> 232 +i 7 6 of 113 The limit of variants Say we want to handle a color representation with an alpha channel, but just for color_to_int (this implies we do not want to redefine our color type, this would be a hassle elsewhere). -
Sorting Partnership Unless You Sign Up! Brian Curless • Homework #5 Will Be Ready After Class, Spring 2008 Due in a Week
Announcements (5/9/08) • Project 3 is now assigned. CSE 326: Data Structures • Partnerships due by 3pm – We will not assume you are in a Sorting partnership unless you sign up! Brian Curless • Homework #5 will be ready after class, Spring 2008 due in a week. • Reading for this lecture: Chapter 7. 2 Sorting Consistent Ordering • Input – an array A of data records • The comparison function must provide a – a key value in each data record consistent ordering on the set of possible keys – You can compare any two keys and get back an – a comparison function which imposes a indication of a < b, a > b, or a = b (trichotomy) consistent ordering on the keys – The comparison functions must be consistent • Output • If compare(a,b) says a<b, then compare(b,a) must say b>a • If says a=b, then must say b=a – reorganize the elements of A such that compare(a,b) compare(b,a) • If compare(a,b) says a=b, then equals(a,b) and equals(b,a) • For any i and j, if i < j then A[i] ≤ A[j] must say a=b 3 4 Why Sort? Space • How much space does the sorting • Allows binary search of an N-element algorithm require in order to sort the array in O(log N) time collection of items? • Allows O(1) time access to kth largest – Is copying needed? element in the array for any k • In-place sorting algorithms: no copying or • Sorting algorithms are among the most at most O(1) additional temp space.