Push Vs. Pull: Data Movement for Linked Data Structures

Total Page:16

File Type:pdf, Size:1020Kb

Push Vs. Pull: Data Movement for Linked Data Structures Push vs. Pull: Data Movement for Linked Data Structures Chia-Lin Yang and Alvin R. Lebeck Department of Computer Science Duke University Durham, NC 27708 USA fyangc,[email protected] y are essential to build a high p er- Abstract the e ect of this disparit formance computer system. The use of caches b etween the As the performance gap between the CPU and main mem- CPU and main memory is recognized as an e ective metho d ory continues to grow, techniques to hide memory latency to bridge this gap [21]. If programs exhibit go o d temp oral are essential to deliver a high performance computer sys- and spatial lo cality, the ma jority of memory requests can b e tem. Prefetching can often overlap memory latency with satis ed by caches without having to access main memory. computation for array-based numeric applications. How- However, a cache's e ectiveness can b e limited for programs ever, prefetching for pointer-intensive applications stil l re- with p o or lo cality. mains a chal lenging problem. Prefetching linked data struc- Prefetching is a common technique that attempts to hide tures LDS is dicult because the address sequence of LDS memory latency by issuing memory requests earlier than de- traversal does not present the same arithmetic regularity as mand fetching a cache blo ck when a miss o ccurs. Prefetching array-based applications and the data dependenceofpointer works very well for programs with regular access patterns. dereferences can serialize the address generation process. Unfortunately, many applications create sophisticated data In this paper, we propose a cooperative hardware/software structures using p ointers, and do not exhibit sucient reg- mechanism to reduce memory access latencies for linked data ularity for conventional prefetch techniques to exploit. Fur- structures. Instead of relying on the past address history to thermore, prefetching p ointer-intensive data structures can predict futureaccesses, we identify the load instructions that be limited by the serial nature of p ointer dereferences| traverse the LDS, and execute them ahead of the actual com- known as the p ointer chasing problem|since the address of putation. To overcome the serial nature of the LDS address the next no de is not known until the contents of the current generation, we attach a prefetch control ler to each level of no de is accessible. the memory hierarchy and push, rather than pul l, data to the CPU. Our simulations, using four pointer-intensive ap- For these applications, p erformance may improveiflower plications, show that the push model can achieve between 4 levels of the memory hierarchy could dereference p ointers and 30 larger reductions in execution time compared to the and pro-actively push data up to the pro cessor rather than pul l model. requiring the pro cessor to fetch each no de b efore initiating the next request. An oracle could accomplish this by know- yout and traversal order of the p ointer-based data 1. INTRODUCTION ing the la structure, and thus overlap the transfer of consecutively ac- Since 1980, micropro cessor p erformance has improved cessed no des up the memory hierarchy. The challenge is to 60 p er year, however, memory access time has improved develop a realizable memory hierarchy that can obtain these only 10 p er year. As the p erformance gap b etween pro- b ene ts. cessors and memory continues to grow, techniques to reduce This pap er presentsanovel memory architecture to p er- This work supp orted in part byDARPA GrantDABT63- form p ointer dereferences in the lower levels of the memory 98-1-0001, NSF Grants CDA-97-2637, CDA-95-12356, and hierarchy and push data up to the CPU. In this architec- EIA-99-72879, Career Award MIP-97-02547, Duke Univer- ture, if the cache blo ck containing the data corresp onding sity, and an equipment donation through Intel Corp oration's to p ointer p *p is found at a particular level of the mem- Technology for Education 2000 Program. The views and conclusions contained herein are those of the authors and ory hierarchy, the request for the next element *p+o set should not b e interpreted as representing the ocial p olicies is issued from that level. This allows the access for the next or endorsements, either expressed or implied, of DARPAor no de to overlap with the transfer of the previous element. In the U.S. Government. this way, a series of p ointer dereferences b ecomes a pip elined pro cess rather than a serial pro cess. In this pap er, we present results using sp ecialized hard- ware to supp ort the ab ove push mo del for data movement in list-based programs. Our simulations using four p ointer- intensive b enchmarks show that conventional prefetching us- ing the pull mo del can achieve sp eedups of 0 to 223, while the new push mo del achieves sp eedups from 6 to More sp eci cally, the push mo del reduces execution Copyright ACM 2000, Appears in International Conference on Supercom- 227. y 4 to 30 more than the pull mo del. puting (ICS) 2000 time b The rest of this pap er is organized as follows. Section 2 list = head; provides background information and motivation for the push whilelist != NULL { mo del. Section 3 describ es the basic push mo del and details p = list->patient; /* 1 traversal load */ of a prop osed architecture. Section 4 presents our simula- x = p->data; /* 2 data load */ tion results. Related work is discussed in Section 5 and we list = list->forward; /* 3 recurrent load */ conclude in Section 6. } 2. BACKGROUND AND MOTIVATION a source co de Pointer-based data structures, often called linked data 1: lw $15, o1$24 structures LDS, presenttwochallenges to any prefetching 2: lw $4, o2$15 technique: address irregularity and data dep endencies. To 3: lw $24, o3$24 improve the memory system p erformance of many p ointer- based applications, b oth of these issues must b e addressed. b LDS Traversal Kernel 2.1 Address Irregularity hing LDS is unlike array-based numeric applica- Prefetc 3a tions since the address sequence from LDS accesses do es ve arithmetic regularity. Consider traversing a linear not ha 1b 3b arrayofintegers versus traversing a linked-list. For linear ys, the address of array elements accessed at iteration arra 2b i is A +4i, where A is the base address of ar- addr addr c Data Dep endencies ray A and i is the iteration numb er. Using this formula, the address of elementA[i]atany iteration i is easily com- Figure 1: Linked Data Structure LDS Traversal puted. Furthermore, the ab ove formula pro duces a compact representation of array accesses, thus making it easier to predict future addresses. In contrast, LDS elements are al- lo cated dynamically from the heap and adjacent elements p endencies. In LDS traversal a series of p ointer dereferences are not necessarily contiguous in memory. Therefore, tra- is required to generate future element addresses. If the ad- ditional array-based address prediction techniques are not dress of no de i is stored in the p ointer p, then the address of applicable to LDS accesses. no de i+1 is *p+x, where x is the o set of the next eld. Instead of predicting the future LDS addresses based on The address *p+x is not known until the value of p is address regularity, Roth et. al [19] observed that the load known. This is commonly called the p ointer-chasing prob- instructions Program Counters that access LDS elements lem. In this scenario, the serial nature of the memory access are themselves a compact representation of LDS accesses| can make it dicult to hide memory latencies longer than called a traversal kernel. Consider the linked-list traversal one iteration of computation. example shown in Figure 1, the structure list is the LDS The primary contribution of this pap er is the develop- b eing traversed. Instructions 1 and 3 access list itself, while ment of a new mo del for data movement in linked data instruction 2 accesses another p ortion of the LDS through structures that reduces the impact of data dep endencies. p ointer p. These three instructions make up the list traversal By abandoning the conventional pul l approach of initiat- kernel. Assembly co de for this kernel is shown in Figure 1b. ing all memory requests demand fetch or prefetch by the Consecutive iterations of the traversal kernel create data pro cessor or upp er level of the memory hierarchy, we can dep endencies. Instruction 3 at iteration a pro duces an ad- eliminate some of the delay in traversing linked data struc- dress consumed by itself and instruction 1 in the next it- tures. The following section elab orates on the new mo del eration b. Instruction 1 pro duces an address consumed by and a prop osed implementation. instruction 2 in the same iteration. This relation can b e rep- resented as a dep endency tree, shown in Figure 1c. Loads in versal kernels can b e classi ed into three typ es: re- LDS tra 3. THE PUSH MODEL Most existing prefetch techniques issue requests from the current, traversal, and data. Instruction 3 list=list!forward CPU level to fetch data from the lower levels of the mem- generates the address of the next element of the list struc- ory hierarchy. Since p ointer-dereferences are required to ture, and is classi ed as a recurrent load.
Recommended publications
  • Device Tree 101
    Device Tree 101 Device Tree 101 Organized in partnership with ST February 9, 2021 Thomas Petazzoni embedded Linux and kernel engineering [email protected] © Copyright 2004-2021, Bootlin. Creative Commons BY-SA 3.0 license. Corrections, suggestions, contributions and translations are welcome! - Kernel, drivers and embedded Linux - Development, consulting, training and support - https://bootlin.com 1/56 Who is speaking ? I Thomas Petazzoni I Chief Technical Officer at Bootlin I Joined in 2008, employee #1 I Embedded Linux & Linux kernel engineer, open-source contributor I Author of the Device Tree for Dummies talk in 2013/2014 I Buildroot co-maintainer I Linux kernel contributor: ≈ 900 contributions I Member of Embedded Linux Conference (Europe) program committee I Based in Toulouse, France - Kernel, drivers and embedded Linux - Development, consulting, training and support - https://bootlin.com 2/56 Agenda I Bootlin introduction I STM32MP1 introduction I Why the Device Tree ? I Basic Device Tree syntax I Device Tree inheritance I Device Tree specifications and bindings I Device Tree and Linux kernel drivers I Common properties and examples - Kernel, drivers and embedded Linux - Development, consulting, training and support - https://bootlin.com 3/56 Bootlin I In business since 2004 I Team based in France I Serving customers worldwide I 18% revenue from France I 44% revenue from EU except France I 38% revenue outside EU I Highly focused and recognized expertise I Embedded Linux I Linux kernel I Embedded Linux build systems I Activities
    [Show full text]
  • Slide Set 17 for ENCM 339 Fall 2015
    Slide Set 17 for ENCM 339 Fall 2015 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 2015 SN's ENCM 339 Fall 2015 Slide Set 17 slide 2/46 Contents Data structures Abstract data types Linked data structures A singly-linked list type in C++ Operations and implementation of SLListV1 The Big 3 for a linked-list class Ordered linked lists SN's ENCM 339 Fall 2015 Slide Set 17 slide 3/46 Outline of Slide Set 17 Data structures Abstract data types Linked data structures A singly-linked list type in C++ Operations and implementation of SLListV1 The Big 3 for a linked-list class Ordered linked lists SN's ENCM 339 Fall 2015 Slide Set 17 slide 4/46 Data structures In discussion of programming, the term data structure means a collection of data items, organized to support some of the following goals: I fast insertion or removal of data items I fast access to data items I fast searching for the location of a particular data item, if the item is in the collection I maintaining items in some kind of sorted order I keeping the memory footprint of the collection as small as possible There are design trade-offs|no single data structure design is best for all of the above goals. SN's ENCM 339 Fall 2015 Slide Set 17 slide 5/46 Here are two kinds of data structures that everybody in this course should be familiar with: I arrays I C and C++ structure objects We're about to study a kind of data structure called a linked list.
    [Show full text]
  • Fast Sequential Summation Algorithms Using Augmented Data Structures
    Fast Sequential Summation Algorithms Using Augmented Data Structures Vadim Stadnik [email protected] Abstract This paper provides an introduction to the design of augmented data structures that offer an efficient representation of a mathematical sequence and fast sequential summation algorithms, which guarantee both logarithmic running time and logarithmic computational cost in terms of the total number of operations. In parallel summation algorithms, logarithmic running time is achieved by high linear computational cost with a linear number of processors. The important practical advantage of the fast sequential summation algorithms is that they do not require supercomputers and can run on the cheapest single processor systems. Layout 1. Motivation 2. Parallel Summation Algorithms 3. Choice of Data Structure 4. Geometric Interpretation 5. Representation of Sequence 6. Fast Sequential Summation Algorithms 7. Mean Value and Standard Deviation 8. Other Data Structures 1. Motivation The original version of the fast sequential summation algorithms described here was implemented in C++ using data structures that support interfaces of STL containers [1]. These interesting and important algorithms can be implemented in many other programming languages. This discussion provides an introduction to the design of data structures, which significantly improve performance of summation algorithms. The fast summation algorithms have been developed by applying the method of augmenting data structures [2]. This powerful method can be used to solve a wide range of problems. It helps design advanced data structures that support more efficient algorithms than basic data structures. The main disadvantage of this method is its complexity, which makes the use of this method difficult in practice.
    [Show full text]
  • Linked List Data Structure
    Linked List Data Structure Static and Dynamic data structures A static data structure is an organization of collection of data that is fixed in size. as memory ,(مسبقا") This results in the maximum size needing to be known in advance cannot be reallocated at a later. Arrays are example of static data structure. A dynamic data structure , where in with the latter the size of the structure can dynamically grow or shrink in size as needed. Linked lists are example of dynamic data structure. Linked Lists Like arrays, Linked List is a linear data structure. Unlike arrays, linked list elements are not stored at contiguous location; the elements are linked using pointers. It consists of group of nodes in a sequence which is divided in two parts. Each node consists of its own data and the address of the next node and forms a chain. Linked Lists are used to create trees and graphs. What are different between linked lists and arrays? Arrays Linked lists Have a pre-determined fixed No fixed size; grow one element at a time size Array items are store Element can be stored at any place contiguously Easy access to any element in No easy access to i-th element , need to hop through all previous constant time elements start from start Size = n x sizeof(element) Size = n x sizeof (element) + n x sizeof(reference) Insertion and deletion at Insertion and deletion are simple and faster particular position is complex(shifting) Only element store Each element must store element and pointer to next element (extra memory for storage pointer).
    [Show full text]
  • Trees • Binary Trees • Traversals of Trees • Template Method Pattern • Data
    TREES • trees • binary trees • traversals of trees • template method pattern • data structures for trees Trees 1 Trees •atree represents a hierarchy - organization structure of a corporation Electronics R’Us R&D Sales Purchasing Manufacturing Domestic International TV CD Tuner Canada S. America Overseas Africa Europe Asia Australia - table of contents of a book student guide overview grading environment programming support code exams homeworks programs Trees 2 Another Example • Unix or DOS/Windows file system /user/rt/courses/ cs016/ cs252/ grades grades homeworks/ programs/ projects/ hw1 hw2 hw3 pr1 pr2 pr3 papers/ demos/ buylow sellhigh market Trees 3 Terminology • A is the root node. • B is the parent of D and E. • C is the sibling of B • D and E are the children of B. • D, E, F, G, I are external nodes, or leaves. • A, B, C, H are internal nodes. • The depth (level) of E is 2 • The height of the tree is 3. • The degree of node B is 2. A B C D E F G H I Property: (# edges) = (#nodes) − 1 Trees 4 Binary Trees • Ordered tree: the children of each node are ordered. • Binary tree: ordered tree with all internal nodes of degree 2. • Recursive definition of binary tree: •Abinary tree is either -anexternal node (leaf), or -aninternal node (the root) and two binary trees (left subtree and right subtree) Trees 5 Examples of Binary Trees • arithmetic expression + × × + 5 4 + × + 7 2 3 + 2 8 1 + 4 6 ((((3 × (1 + (4 + 6))) + (2 + 8)) × 5) + ( 4 × (7 + 2))) •river Trees 6 Properties of Binary Trees •(# external nodes ) = (# internal nodes) + 1 •(#
    [Show full text]
  • Verifying Linked Data Structure Implementations
    Verifying Linked Data Structure Implementations Karen Zee Viktor Kuncak Martin Rinard MIT CSAIL EPFL I&C MIT CSAIL Cambridge, MA Lausanne, Switzerland Cambridge, MA [email protected] viktor.kuncak@epfl.ch [email protected] Abstract equivalent conjunction of properties. By processing each conjunct separately, Jahob can use different provers to es- The Jahob program verification system leverages state of tablish different parts of the proof obligations. This is the art automated theorem provers, shape analysis, and de- possible thanks to formula approximation techniques[10] cision procedures to check that programs conform to their that create equivalent or semantically stronger formulas ac- specifications. By combining a rich specification language cepted by the specialized decision procedures. with a diverse collection of verification technologies, Jahob This paper presents our experience using the Jahob sys- makes it possible to verify complex properties of programs tem to obtain full correctness proofs for a collection of that manipulate linked data structures. We present our re- linked data structure implementations. Unlike systems that sults using Jahob to achieve full functional verification of a are designed to verify partial correctness properties, Jahob collection of linked data structures. verifies the full functional correctness of the data structure implementation. Not only do our results show that such full functional verification is feasible, the verified data struc- 1 Introduction tures and algorithms provide concrete examples that can help developers better understand how to achieve similar results in future efforts. Linked data structures such as lists, trees, graphs, and hash tables are pervasive in modern software systems. But because of phenomena such as aliasing and indirection, it 2 Example has been a challenge to develop automated reasoning sys- tems that are capable of proving important correctness prop- In this section we use a verified association list to demon- erties of such data structures.
    [Show full text]
  • 8.1 Doubly Linked List
    CMSC 132, Object-Oriented Programming II Summer 2017 Lecture 8: Lecturer: Anwar Mamat Disclaimer: These notes may be distributed outside this class only with the permission of the Instructor. 8.1 Doubly Linked List Like a singly linked list, a doubly-linked list is a linked data structure that consists of a set of sequentially linked records called nodes. Unlike a singly linked list, each node of the doubly singly list contains two fields that are references to the previous and to the next node in the sequence of nodes. The beginning and ending nodes' previous and next links, respectively, point to some kind of terminator, typically a sentinel node or null, to facilitate traversal of the list. Listing 1: Doubly Linked List Node Class 1 class Node<E>{ 2 E data; 3 Node previous; 4 Node next; 5 Node(E item){ 6 data = item; 7 } 8 } Usually Node class is nested inside the LinkedList class, and members of Node are private. 8.1.1 Create a simple linked list Now, let us create a simple linked list. 1 Node<String> n1 = new Node("Alice"); 2 Node<String> n2 = new Node("Bob"); 3 Node<String> n3 = new Node("Cathy"); 4 n1.next = n2; 5 n2.previous = n1; 6 n2.next = n3; 7 n3.previous = n2; This linked list represents this: Alice Bob Cathy 8.1.2 Display the Linked List We can display all the linked list: 8-1 8-2 Lecture 8: 1 Node<String> current = first; 2 while(current != null){ 3 System.out.println(current.data); 4 current = current.next; 5 } We can also display all the linked list in reverse order: 1 Node<String> current = tail; 2 while(current != null){ 3 System.out.println(current.data); 4 current = current.previous; 5 } 8.1.3 Insert a node Now, let us insert a node between \Bob" and \Cathy".
    [Show full text]
  • Linked Data Structures 17
    Linked Data Structures 17 17.1 NODES AND LINKED LISTS 733 Efficiency of Hash Tables 783 Nodes 733 Example: A Set Template Class 784 Linked Lists 738 Efficiency of Sets Using Linked Lists 790 Inserting a Node at the Head of a List 740 Pitfall: Losing Nodes 743 17.3 ITERATORS 791 Inserting and Removing Nodes Inside a List 743 Pointers as Iterators 792 Pitfall: Using the Assignment Operator with Dynamic Iterator Classes 792 Data Structures 747 Example: An Iterator Class 794 Searching a Linked List 747 17.4 TREES 800 Doubly Linked Lists 750 Tree Properties 801 Adding a Node to a Doubly Linked List 752 Example: A Tree Template Class 803 Deleting a Node from a Doubly Linked List 752 Example: A Generic Sorting Template Version of Linked List Tools 759 17.2 LINKED LIST APPLICATIONS 763 Example: A Stack Template Class 763 Example: A Queue Template Class 770 Tip: A Comment on Namespaces 773 Friend Classes and Similar Alternatives 774 Example: Hash Tables with Chaining 777 Chapter Summary 808 Answers to Self-Test Exercises 809 Programming Projects 818 MM17_SAVT071X_01_SE_C17.indd17_SAVT071X_01_SE_C17.indd 773131 22/8/12/8/12 33:53:53 PPMM 17 Linked Data Structures If somebody there chanced to be Who loved me in a manner true My heart would point him out to me And I would point him out to you. GILBERT AND SULLIVAN, Ruddigore Introduction A linked list is a list constructed using pointers. A linked list is not fixed in size but can grow and shrink while your program is running. A tree is another kind of data structure constructed using pointers.
    [Show full text]
  • MASTER of SCIENCE May,1995 DESIGN and IMPLEMENTATION of an EFFICIENT
    DESIGN AND IMPLEMENTATION OF AN EFFICIENT INDEX STRUCTURE AND A GUI FOR SPATIAL DATABASES USING VISUAL C++ By SUJATHA SAMADARSINI NEELAM Bachelor ofTechnology S. V. University Tirupathi, India 1986 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfIllment of the requirements for the Degree of MASTER OF SCIENCE May,1995 DESIGN AND IMPLEMENTATION OF AN EFFICIENT INDEX STRUCTURE AND A GUI FOR SPATIAL DATABASES USING VISUAL C++ Thesis Approved: Thesis Adviser ii ACKNOWLEDGMENTS I wish to express my sincere and special thanks to my major advisor, Dr. Huizhu Lu, for her expert guidance, constructive supervision and friendship. I would also like to thank my committee members Dr. George and Dr. Benjamin for their encouragement, guidance and advice. My sincere thanks to Dr. Mark Gregory ofthe Department of Agriculture, OSU, for providing the data for this project. I would also like to take this opportunity to show my appreciation to my brother Mr. VCS Reddy Kummetha for his encouragement, guidance and friendship and heartfelt thanks to our friend Mr. Siva Rama Krishna Kavuturu, for his guidance and help, all through my study at Stillwater, when I am away from my family. My special appreciation goes to my husband Mr. Chinnappa Reddy Neelam, and my daughter Ms. Pranu Neelam, for all their encouragement, love and understanding. My in depth gratitude goes to my parents Mr. and Mrs. K. Rama Krishna Reddy, for their love, support and encouragement without which I wouldn't have been what lam today and also for taking care ofmy daughter, so I can complete my studies successfully.
    [Show full text]
  • Efficient Run-Time Support for Global View Programming of Linked Data Structures on Distributed Memory Parallel Systems
    Efficient Run-time Support For Global View Programming of Linked Data Structures on Distributed Memory Parallel Systems DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Darrell Brian Larkins, M.S. Department of Computer Science and Engineering The Ohio State University 2010 Dissertation Committee: P. Sadayappan, Advisor Atanas Rountev Paul A. G. Sivilotti © Copyright by Darrell Brian Larkins 2010 ABSTRACT Developing high-performance parallel applications that use linked data structures on distributed-memory clusters is challenging. Many scientific applications use algo- rithms based on linked data structures like trees and graphs. These structures are especially useful in representing relationships between data which may not be known until runtime or may otherwise evolve during the course of a computation. Meth- ods such as n-body simulation, Fast Multipole Methods (FMM), and multiresolution analysis all use trees to represent a fixed space populated by a dynamic distribu- tion of elements. Other problem domains, such as data mining, use both trees and graphs to summarize large input datasets into a set of relationships that capture the information in a form that lends itself to efficient mining. This dissertation first describes a runtime system that provides a programming interface to a global address space representation of generalized distributed linked data structures, while providing scalable performance on distributed memory com- puting systems. This system, the Global Chunk Layer (GCL), provides data access primitives at the element level, but takes advantage of coarse-grained data movement to enhance locality and improve communication efficiency.
    [Show full text]
  • Lecture 8: 8.1 Doubly Linked List
    CMSC 132, Object-Oriented Programming II Summer 2016 Lecture 8: Lecturer: Anwar Mamat Disclaimer: These notes may be distributed outside this class only with the permission of the Instructor. 8.1 Doubly Linked List Like a singly linked list, a doubly-linked list is a linked data structure that consists of a set of sequentially linked records called nodes. Unlike a singly linked list, each node of the doubly singly list contains two fields that are references to the previous and to the next node in the sequence of nodes. The beginning and ending nodes' previous and next links, respectively, point to some kind of terminator, typically a sentinel node or null, to facilitate traversal of the list. Listing 1: Doubly Linked List Node Class 1 class Nodef 2 E data ; 3 Nodeprevious; 4 Node next ; 5 Node(Eitem)f 6 data=item; 7 next = null ; 8 previous = null ; 9 g 10 Node ( ) f 11 data = null ; 12 next = null ; 13 previous = null ; 14 g 15 g Usually Node class is nested inside the LinkedList class, and members of Node are private. 8.1.1 Create a simple linked list Now, let us create a simple linked list. 1 Node<String > n1 = new Node("Alice"); 2 Node<String > n2 = new Node("Bob" ); 3 Node<String > n3 = new Node("Cathy"); 4 n1.next = n2; 5 n2.previous = n1; 6 n2.next = n3; 7 n3.previous = n2; 8-1 8-2 Lecture 8: This linked list represents this: Alice Bob Cathy 8.1.2 Display the Linked List We can display all the linked list: 1 Node<String > current = first; 2 while ( current != null )f 3 System.out.println(current.data); 4 current=current.next; 5 g We can also display all the linked list in reverse order: 1 Node<String > current = tail; 2 while ( current != null )f 3 System.out.println(current.data); 4 current = current.previous; 5 g 8.1.3 Insert a node Now, let us insert a node between \Bob" and \Cathy".
    [Show full text]
  • 15. Symbol Tables
    COMPUTER SCIENCE SEDGEWICK/WAYNE 15. Symbol Tables Section 4.4 http://introcs.cs.princeton.edu COMPUTER SCIENCE SEDGEWICK/WAYNE 15.Symbol Tables •APIs and clients •A design challenge •Binary search trees •Implementation •Analysis http://introcs.cs.princeton.edu FAQs about sorting and searching Hey, Alice. That whitelist filter with mergesort and binary search is working great. Right, but it's a pain sometimes. Why? We have to sort the whole list whenever we add new customers. Also, we want to process transactions and associate all sorts of information with our customers. Bottom line. Need a more flexible API. 3 Why are telephone books obsolete? Unsupported operations • Change the number associated with a given name. • Add a new name, associated with a given number. • Remove a givne name and associated number Observation. Mergesort + binary search has the same problem with add and remove. see Sorting and Searching lecture 4 Associative array abstraction Imagine using arrays whose indices are string values. phoneNumber["Alice"] = "(212) 123-4567" legal code in some programming phoneNumber["Bob"] = "(609) 987-6543" languages (not Java) phoneNumber["Carl"] = "(800) 888-8888" phoneNumber["Dave"] = "(888) 800-0800" phoneNumber["Eve"] = "(999) 999-9999" transactions["Alice"] = "Dec 12 12:01AM $111.11 Amazon, Dec 12 1:11 AM $989.99 Ebay" ... A fundamental abstraction • Use keys to access associated values. URL["128.112.136.11"] = "www.cs.princeton.edu" • Keys and values could be any type of data. URL["128.112.128.15"] = "www.princeton.edu" URL["130.132.143.21"] = "www.yale.edu" • Client code could not be simpler. URL["128.103.060.55"] = "www.harvard.edu" IPaddr["www.cs.princeton.edu"] = "128.112.136.11" IPaddr["www.princeton.edu"] = "128.112.128.15" Q.
    [Show full text]