Coding Interview Preparation
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
An Alternative to Fibonacci Heaps with Worst Case Rather Than Amortized Time Bounds∗
Relaxed Fibonacci heaps: An alternative to Fibonacci heaps with worst case rather than amortized time bounds¤ Chandrasekhar Boyapati C. Pandu Rangan Department of Computer Science and Engineering Indian Institute of Technology, Madras 600036, India Email: [email protected] November 1995 Abstract We present a new data structure called relaxed Fibonacci heaps for implementing priority queues on a RAM. Relaxed Fibonacci heaps support the operations find minimum, insert, decrease key and meld, each in O(1) worst case time and delete and delete min in O(log n) worst case time. Introduction The implementation of priority queues is a classical problem in data structures. Priority queues find applications in a variety of network problems like single source shortest paths, all pairs shortest paths, minimum spanning tree, weighted bipartite matching etc. [1] [2] [3] [4] [5] In the amortized sense, the best performance is achieved by the well known Fibonacci heaps. They support delete and delete min in amortized O(log n) time and find min, insert, decrease key and meld in amortized constant time. Fast meldable priority queues described in [1] achieve all the above time bounds in worst case rather than amortized time, except for the decrease key operation which takes O(log n) worst case time. On the other hand, relaxed heaps described in [2] achieve in the worst case all the time bounds of the Fi- bonacci heaps except for the meld operation, which takes O(log n) worst case ¤Please see Errata at the end of the paper. 1 time. The problem that was posed in [1] was to consider if it is possible to support both decrease key and meld simultaneously in constant worst case time. -
Skip Lists: a Probabilistic Alternative to Balanced Trees
Skip Lists: A Probabilistic Alternative to Balanced Trees Skip lists are a data structure that can be used in place of balanced trees. Skip lists use probabilistic balancing rather than strictly enforced balancing and as a result the algorithms for insertion and deletion in skip lists are much simpler and significantly faster than equivalent algorithms for balanced trees. William Pugh Binary trees can be used for representing abstract data types Also giving every fourth node a pointer four ahead (Figure such as dictionaries and ordered lists. They work well when 1c) requires that no more than n/4 + 2 nodes be examined. the elements are inserted in a random order. Some sequences If every (2i)th node has a pointer 2i nodes ahead (Figure 1d), of operations, such as inserting the elements in order, produce the number of nodes that must be examined can be reduced to degenerate data structures that give very poor performance. If log2 n while only doubling the number of pointers. This it were possible to randomly permute the list of items to be in- data structure could be used for fast searching, but insertion serted, trees would work well with high probability for any in- and deletion would be impractical. put sequence. In most cases queries must be answered on-line, A node that has k forward pointers is called a level k node. so randomly permuting the input is impractical. Balanced tree If every (2i)th node has a pointer 2i nodes ahead, then levels algorithms re-arrange the tree as operations are performed to of nodes are distributed in a simple pattern: 50% are level 1, maintain certain balance conditions and assure good perfor- 25% are level 2, 12.5% are level 3 and so on. -
Skip B-Trees
Skip B-Trees Ittai Abraham1, James Aspnes2?, and Jian Yuan3 1 The Institute of Computer Science, The Hebrew University of Jerusalem, [email protected] 2 Department of Computer Science, Yale University, [email protected] 3 Google, [email protected] Abstract. We describe a new data structure, the Skip B-Tree that combines the advantages of skip graphs with features of traditional B-trees. A skip B-Tree provides efficient search, insertion and deletion operations. The data structure is highly fault tolerant even to adversarial failures, and allows for particularly simple repair mechanisms. Related resource keys are kept in blocks near each other enabling efficient range queries. Using this data structure, we describe a new distributed peer-to-peer network, the Distributed Skip B-Tree. Given m data items stored in a system with n nodes, the network allows to perform a range search operation for r consecutive keys that costs only O(logb m + r/b) where b = Θ(m/n). In addition, our distributed Skip B-tree search network has provable polylogarithmic costs for all its other basic operations like insert, delete, and node join. To the best of our knowledge, all previous distributed search networks either provide a range search operation whose cost is worse than ours or may require a linear cost for some basic operation like insert, delete, and node join. ? Supported in part by NSF grants CCR-0098078, CNS-0305258, and CNS-0435201. 1 Introduction Peer-to-peer systems provide a decentralized way to share resources among machines. An ideal peer-to-peer network should have such properties as decentralization, scalability, fault-tolerance, self-stabilization, load- balancing, dynamic addition and deletion of nodes, efficient query searching and exploiting spatial as well as temporal locality in searches. -
On the Cost of Persistence and Authentication in Skip Lists*
On the Cost of Persistence and Authentication in Skip Lists⋆ Micheal T. Goodrich1, Charalampos Papamanthou2, and Roberto Tamassia2 1 Department of Computer Science, University of California, Irvine 2 Department of Computer Science, Brown University Abstract. We present an extensive experimental study of authenticated data structures for dictionaries and maps implemented with skip lists. We consider realizations of these data structures that allow us to study the performance overhead of authentication and persistence. We explore various design decisions and analyze the impact of garbage collection and virtual memory paging, as well. Our empirical study confirms the effi- ciency of authenticated skip lists and offers guidelines for incorporating them in various applications. 1 Introduction A proven paradigm from distributed computing is that of using a large collec- tion of widely distributed computers to respond to queries from geographically dispersed users. This approach forms the foundation, for example, of the DNS system. Of course, we can abstract the main query and update tasks of such systems as simple data structures, such as distributed versions of dictionar- ies and maps, and easily characterize their asymptotic performance (with most operations running in logarithmic time). There are a number of interesting im- plementation issues concerning practical systems that use such distributed data structures, however, including the additional features that such structures should provide. For instance, a feature that can be useful in a number of real-world ap- plications is that distributed query responders provide authenticated responses, that is, answers that are provably trustworthy. An authenticated response in- cludes both an answer (for example, a yes/no answer to the query “is item x a member of the set S?”) and a proof of this answer, equivalent to a digital signature from the data source. -
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. -
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 -
Optimizing Systems for Byte-Addressable NVM by Reducing Bit Flipping
Optimizing Systems for Byte-Addressable NVM by Reducing Bit Flipping Daniel Bittman Peter Alvaro Darrell D. E. Long Ethan L. Miller FAST ‘19 2019-02-26 1 Byte-addressable Non-volatile Memory BNVM is coming, and with it, new optimization targets CRSS Confidential 2 Byte-addressable Non-volatile Memory 0 1 0 1 0 0 0 1 It’s not just writes... ...it’s the bits flipped by those writes 0 1 1 0 0 1 0 1 CRSS Confidential 3 BNVM power usage 4 Can we take advantage of this? Software vs. hardware? 5 Can we take advantage of this? Software vs. hardware? How hard is it to reason about bit flips? 6 Can we take advantage of this? Software vs. hardware? How hard is it to reason about bit flips? How do we design data structures to reduce bit flips? 7 8 Reducing Bit ● Flips in Software ● ● 9 XOR linked lists Traditional doubly linked list value value value next next next prev prev prev XOR linked list value value value xptr xptr xptr xptr = next ⊕ prev 10 Pointers! Some actual pointers A = 0x000055b7bda8f260 B = 0x000055b7bda8f6a0 A ⊕ B = 0x4C0 = 0b10011000000 11 Using XOR in hash tables key value xnext ... key key value value xnext xnext ... key value xnext 12 Using XOR in hash tables key value xnext D key key value value 00000 0 xxxxx 1 Both indicate “entry is empty” 13 From XOR linked lists to Red Black Trees L P R Standard 3-pointer red-black tree design 14 From XOR linked lists to Red Black Trees ⊕ RX = R P L P R LX RX ⊕ LX = L P Now 2-pointer, and XOR pointers 15 Evaluation ● ● 16 Experimental framework , at the memory controller Test different data -
Advanced Data Structures
Advanced Data Structures PETER BRASS City College of New York CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521880374 © Peter Brass 2008 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2008 ISBN-13 978-0-511-43685-7 eBook (EBL) ISBN-13 978-0-521-88037-4 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface page xi 1 Elementary Structures 1 1.1 Stack 1 1.2 Queue 8 1.3 Double-Ended Queue 16 1.4 Dynamical Allocation of Nodes 16 1.5 Shadow Copies of Array-Based Structures 18 2 Search Trees 23 2.1 Two Models of Search Trees 23 2.2 General Properties and Transformations 26 2.3 Height of a Search Tree 29 2.4 Basic Find, Insert, and Delete 31 2.5ReturningfromLeaftoRoot35 2.6 Dealing with Nonunique Keys 37 2.7 Queries for the Keys in an Interval 38 2.8 Building Optimal Search Trees 40 2.9 Converting Trees into Lists 47 2.10 -
Programmer's Guide
Programmer’s Guide Release 2.2.0 January 16, 2016 CONTENTS 1 Introduction 1 1.1 Documentation Roadmap...............................1 1.2 Related Publications..................................2 2 Overview 3 2.1 Development Environment..............................3 2.2 Environment Abstraction Layer............................4 2.3 Core Components...................................4 2.4 Ethernet* Poll Mode Driver Architecture.......................6 2.5 Packet Forwarding Algorithm Support........................6 2.6 librte_net........................................6 3 Environment Abstraction Layer7 3.1 EAL in a Linux-userland Execution Environment..................7 3.2 Memory Segments and Memory Zones (memzone)................ 11 3.3 Multiple pthread.................................... 12 3.4 Malloc.......................................... 14 4 Ring Library 19 4.1 References for Ring Implementation in FreeBSD*................. 20 4.2 Lockless Ring Buffer in Linux*............................ 20 4.3 Additional Features.................................. 20 4.4 Use Cases....................................... 21 4.5 Anatomy of a Ring Buffer............................... 21 4.6 References....................................... 28 5 Mempool Library 31 5.1 Cookies......................................... 31 5.2 Stats.......................................... 31 5.3 Memory Alignment Constraints............................ 31 5.4 Local Cache...................................... 32 5.5 Use Cases....................................... 33 6 -
Podcast Ch23a
Podcast Ch23a • Title: Bit Arrays • Description: Overview; bit operations in Java; BitArray class • Participants: Barry Kurtz (instructor); John Helfert and Tobie Williams (students) • Textbook: Data Structures for Java; William H. Ford and William R. Topp Bit Arrays • Applications such as compiler code generation and compression algorithms create data that includes specific sequences of bits. – Many applications, such as compilers, generate specific sequences of bits. Bit Arrays (continued) • Java binary bit handling operators |, &, and ^ act on pairs of bits and return the new value. The unary operator ~ inverts the bits of its operand. BitBit OperationsOperations x y ~x x | y x & y x ^ y 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 Bit Arrays (continued) Bit Arrays (continued) • Operator << shifts integer or char values to the left. Operators >> and >>> shift values to the right using signed or unsigned arithmetic, respectively. Assume x and y are 32-bit integers. x = 0...10110110 x << 2 = 0...1011011000 x = 101...11011100 x >> 3 = 111101...11011 x = 101...11011100 x >>> 3 = 000101...11011 Bit Arrays (continued) Before performing the bitwise operator |, &, or ^, Java performs binary numeric promotion on the operands. The type of the bitwise operator expression is the promoted type of the operands. The rules of promotion are as follows: • If either operand is of type long, the other is converted to long. • Otherwise, both operands are converted to type int. In the case of the unary operator ~, Java converts a byte, char, short to int before applying the operator, and the resulting value is an int.