# CSE 332: Data Structures & Parallelism Lecture 10:Hashing. Ruth Anderson Autumn 2018

Save this PDF as:

Size: px
Start display at page:

Download "CSE 332: Data Structures & Parallelism Lecture 10:Hashing. Ruth Anderson Autumn 2018"

## Transcription

1 CSE 332: Data Structures & Parallelism Lecture 10:Hashing Ruth Anderson Autumn 2018

2 Today Dictionaries Hashing 10/19/2018 2

3 Motivating Hash Tables For dictionary with n key/value pairs insert find delete Unsorted linked-list O(n) * O(n) O(n) Unsorted array O(n) * O(n) O(n) Sorted linked list O(n) O(n) O(n) Sorted array O(n) O(log n) O(n) Balanced tree O(log n) O(log n) O(log n) * Assuming we must check to see if the key has already been inserted. Cost becomes cost of a find operation, inserting itself is O(1). 10/19/2018 3

4 Hash Tables Aim for constant-time (i.e., O(1)) find, insert, and delete On average under some reasonable assumptions A hash table is an array of some fixed size Basic idea: hash table 0 hash function: h(key) index key space (e.g., integers, strings) TableSize 1 10/19/2018 4

5 Aside: Hash Tables vs. Balanced Trees In terms of a Dictionary ADT for just insert, find, delete, hash tables and balanced trees are just different data structures Hash tables O(1) on average (assuming few collisions) Balanced trees O(log n) worst-case Constant-time is better, right? Yes, but you need hashing to behave (must avoid collisions) Yes, but what if we want to findmin, findmax, predecessor, and successor, printsorted? Hashtables are not designed to efficiently implement these operations Your textbook considers Hash tables to be a different ADT Not so important to argue over the definitions 10/19/2018 5

6 Hash Tables There are m possible keys (m typically large, even infinite) We expect our table to have only n items n is much less than m (often written n << m) Many dictionaries have this property Compiler: All possible identifiers allowed by the language vs. those used in some file of one program Database: All possible student names vs. students enrolled AI: All possible chess-board configurations vs. those considered by the current player 10/19/2018 6

7 Hash functions An ideal hash function: Is fast to compute Rarely hashes two used keys to the same index Often impossible in theory; easy in practice Will handle collisions a bit later hash table 0 hash function: h(key) index key space (e.g., integers, strings) TableSize 1 10/19/2018 7

8 Who hashes what? Hash tables can be generic To store keys of type E, we just need to be able to: 1. Test equality: are you the E I m looking for? 2. Hashable: convert any E to an int When hash tables are a reusable library, the division of responsibility generally breaks down into two roles: client hash table library E int table-index collision? collision resolution We will learn both roles, but most programmers in the real world spend more time as clients while understanding the library 10/19/2018 8

9 More on roles Some ambiguity in terminology on which parts are hashing client hash table library E int table-index collision? collision resolution hashing? hashing? Two roles must both contribute to minimizing collisions (heuristically) Client should aim for different ints for expected items Avoid wasting any part of E or the 32 bits of the int Library should aim for putting similar ints in different indices conversion to index is almost always mod table-size using prime numbers for table-size is common 10/19/2018 9

10 What to hash? We will focus on two most common things to hash: ints and strings If you have objects with several fields, it is usually best to have most of the identifying fields contribute to the hash to avoid collisions Example: class Person { String first; String middle; String last; Date birthdate; } An inherent trade-off: hashing-time vs. collision-avoidance Use all the fields? Use only the birthdate? Admittedly, what-to-hash is often an unprincipled guess 10/19/

11 Hashing integers key space = integers Simple hash function: h(key) = key % TableSize Client: f(x) = x Library g(x) = f(x) % TableSize Fairly fast and natural Example: TableSize = 10 Insert 7, 18, 41, 34, 10 (As usual, ignoring corresponding data) /19/

12 Collision-avoidance With x % TableSize the number of collisions depends on the ints inserted (obviously) TableSize Larger table-size tends to help, but not always Example: 70, 24, 56, 43, 10 with TableSize = 10 and TableSize = 60 Technique: Pick table size to be prime. Why? Real-life data tends to have a pattern Multiples of 61 are probably less likely than multiples of 60 We ll see some collision strategies do better with prime size 10/19/

13 More arguments for a prime table size If TableSize is 60 and Lots of keys are multiples of 5, wasting 80% of table Lots of keys are multiples of 10, wasting 90% of table Lots of keys are multiples of 2, wasting 50% of table If TableSize is 61 Collisions can still happen, but 5, 10, 15, 20, will fill table Collisions can still happen but 10, 20, 30, 40, will fill table Collisions can still happen but 2, 4, 6, 8, will fill table In general, if x and y are co-prime (means gcd(x,y)==1), then (a * x) % y == (b * x) % y if and only if a % y == b % y Given table size y and keys as multiples of x, we ll get a decent distribution if x & y are co-prime So good to have a TableSize that has no common factors with any likely pattern x 10/19/

14 What if the key is not an int? If keys aren t ints, the client must convert to an int Trade-off: speed and distinct keys hashing to distinct ints Common and important example: Strings Key space K = s 0 s 1 s 2 s m-1 where s i are chars: s i [0,256] Some choices: Which avoid collisions best? 1. h(k) = s 0 2. h(k) = m 1 i 0 s i Then on the library side we typically mod by Tablesize to find index into the table 3. h(k) = m 1 s i i 0 37 i 10/19/

15 Specializing hash functions How might you hash differently if all your strings were web addresses (URLs)? 10/19/

16 Aside: Combining hash functions A few rules of thumb / tricks: 1. Use all 32 bits (careful, that includes negative numbers) 2. Use different overlapping bits for different parts of the hash This is why a factor of 37 i works better than 256 i 3. When smashing two hashes into one hash, use bitwise-xor bitwise-and produces too many 0 bits bitwise-or produces too many 1 bits 4. Rely on expertise of others; consult books and other resources 5. If keys are known ahead of time, choose a perfect hash 10/19/

17 Collision resolution Collision: When two keys map to the same location in the hash table We try to avoid it, but number-of-possible-keys exceeds table size So hash tables should support collision resolution Ideas? 10/19/

18 Flavors of Collision Resolution Separate Chaining Open Addressing Linear Probing Quadratic Probing Double Hashing 10/19/

19 Separate Chaining 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / Chaining: All keys that map to the same table location are kept in a list (a.k.a. a chain or bucket ) As easy as it sounds Example: insert 10, 22, 107, 12, 42 with mod hashing and TableSize = 10 10/19/

20 Separate Chaining 0 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / Chaining: All keys that map to the same table location are kept in a list (a.k.a. a chain or bucket ) As easy as it sounds Example: insert 10, 22, 107, 12, 42 with mod hashing and TableSize = 10 10/19/

21 Separate Chaining 0 1 / 2 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 22 / Chaining: All keys that map to the same table location are kept in a list (a.k.a. a chain or bucket ) As easy as it sounds Example: insert 10, 22, 107, 12, 42 with mod hashing and TableSize = 10 10/19/

22 Separate Chaining 0 1 / 2 3 / 4 / 5 / 6 / 7 8 / 9 / 10 / 22 / 107 / Chaining: All keys that map to the same table location are kept in a list (a.k.a. a chain or bucket ) As easy as it sounds Example: insert 10, 22, 107, 12, 42 with mod hashing and TableSize = 10 10/19/

23 Separate Chaining 0 1 / 2 10 / / Chaining: All keys that map to the same table location are kept in a list (a.k.a. a chain or bucket ) 3 / 4 / As easy as it sounds 5 / 6 / Example: insert 10, 22, 107, 12, 42 with mod hashing and TableSize = / 8 / 9 / 10/19/

24 Separate Chaining 0 1 / 2 3 / 4 / 5 / 6 / 7 8 / 9 / 10 / / / Chaining: All keys that map to the same table location are kept in a list (a.k.a. a chain or bucket ) As easy as it sounds Example: insert 10, 22, 107, 12, 42 with mod hashing and TableSize = 10 Worst case time for find? 10/19/

25 Thoughts on separate chaining Worst-case time for find? Linear But only with really bad luck or bad hash function So not worth avoiding (e.g., with balanced trees at each bucket) Keep # of items in each bucket small Overhead of AVL tree, etc. not worth it for small n Beyond asymptotic complexity, some data-structure engineering can improve constant factors Linked list vs. array or a hybrid of the two Move-to-front (part of Project 2) Leave room for 1 element (or 2?) in the table itself, to optimize constant factors for the common case A time-space trade-off 10/19/

26 Time vs. space (only makes a difference in constant factors) 0 1 / 2 3 / 4 / 5 / 6 / 7 8 / 9 / 10 / / / 0 10 / 1 / X / X 4 / X 5 / X 6 / X / 8 / X 9 / X / 10/19/

27 More rigorous separate chaining analysis Definition: The load factor,, of a hash table is N TableSize number of elements Under chaining, the average number of elements per bucket is So if some inserts are followed by random finds, then on average: Each unsuccessful find compares against items Each successful find compares against items How big should TableSize be?? 10/19/

28 Load Factor? 0 1 / 2 3 / 4 / 5 / 6 7 / 8 / 9 / 10 / / / λ = n TableSize =? 10/19/

29 Load Factor? / / / / / / 86 / / 99 / λ = n TableSize =? 10/19/

30 Separate Chaining Deletion? 10/19/

31 Separate Chaining Deletion Not too bad 0 10 / Find in table 1 / Delete from bucket Say, delete 12 Similar run-time as insert 2 3 / 4 / / 5 / 6 / / 8 / 9 / 10/19/

### B+ Tree Review. CSE332: Data Abstractions Lecture 10: More B Trees; Hashing. Can do a little better with insert. Adoption for insert

B+ Tree Review CSE2: Data Abstractions Lecture 10: More B Trees; Hashing Dan Grossman Spring 2010 M-ary tree with room for L data items at each leaf Order property: Subtree between keys x and y contains

### CSE373: Data Structures & Algorithms Lecture 6: Hash Tables

Lecture 6: Hash Tables Hunter Zahn Summer 2016 Summer 2016 1 MoCvaCng Hash Tables For a dic\$onary with n key, value pairs insert find delete Unsorted linked- list O(1) O(n) O(n) Unsorted array O(1) O(n)

### HASH TABLES. CSE 332 Data Abstractions: B Trees and Hash Tables Make a Complete Breakfast. An Ideal Hash Functions.

-- CSE Data Abstractions: B Trees and Hash Tables Make a Complete Breakfast Kate Deibel Summer The national data structure of the Netherlands HASH TABLES July, CSE Data Abstractions, Summer July, CSE Data

### CSE373: Data Structures & Algorithms Lecture 17: Hash Collisions. Kevin Quinn Fall 2015

CSE373: Data Structures & Algorithms Lecture 17: Hash Collisions Kevin Quinn Fall 2015 Hash Tables: Review Aim for constant-time (i.e., O(1)) find, insert, and delete On average under some reasonable assumptions

### Topic HashTable and Table ADT

Topic HashTable and Table ADT Hashing, Hash Function & Hashtable Search, Insertion & Deletion of elements based on Keys So far, By comparing keys! Linear data structures Non-linear data structures Time

### CMSC 341 Hashing (Continued) Based on slides from previous iterations of this course

CMSC 341 Hashing (Continued) Based on slides from previous iterations of this course Today s Topics Review Uses and motivations of hash tables Major concerns with hash tables Properties Hash function Hash

### CSE 373: Data Structures and Algorithms

CSE 373: Data Structures and Algorithms Lecture 6: Finishing Amortized Analysis; Dictionaries ADT; Introduction to Hash Tables Instructor: Lilian de Greef Quarter: Summer 2017 Today: Finish up Amortized

### CMSC 341 Lecture 16/17 Hashing, Parts 1 & 2

CMSC 341 Lecture 16/17 Hashing, Parts 1 & 2 Prof. John Park Based on slides from previous iterations of this course Today s Topics Overview Uses and motivations of hash tables Major concerns with hash

### General Idea. Key could be an integer, a string, etc e.g. a name or Id that is a part of a large employee structure

Hashing 1 Hash Tables We ll discuss the hash table ADT which supports only a subset of the operations allowed by binary search trees. The implementation of hash tables is called hashing. Hashing is a technique

### Understand how to deal with collisions

Understand the basic structure of a hash table and its associated hash function Understand what makes a good (and a bad) hash function Understand how to deal with collisions Open addressing Separate chaining

### COMP171. Hashing.

COMP171 Hashing Hashing 2 Hashing Again, a (dynamic) set of elements in which we do search, insert, and delete Linear ones: lists, stacks, queues, Nonlinear ones: trees, graphs (relations between elements

### CSE100. Advanced Data Structures. Lecture 21. (Based on Paul Kube course materials)

CSE100 Advanced Data Structures Lecture 21 (Based on Paul Kube course materials) CSE 100 Collision resolution strategies: linear probing, double hashing, random hashing, separate chaining Hash table cost

### HashTable CISC5835, Computer Algorithms CIS, Fordham Univ. Instructor: X. Zhang Fall 2018

HashTable CISC5835, Computer Algorithms CIS, Fordham Univ. Instructor: X. Zhang Fall 2018 Acknowledgement The set of slides have used materials from the following resources Slides for textbook by Dr. Y.

### Hash Tables Outline. Definition Hash functions Open hashing Closed hashing. Efficiency. collision resolution techniques. EECS 268 Programming II 1

Hash Tables Outline Definition Hash functions Open hashing Closed hashing collision resolution techniques Efficiency EECS 268 Programming II 1 Overview Implementation style for the Table ADT that is good

### Hash Open Indexing. Data Structures and Algorithms CSE 373 SP 18 - KASEY CHAMPION 1

Hash Open Indexing Data Structures and Algorithms CSE 373 SP 18 - KASEY CHAMPION 1 Warm Up Consider a StringDictionary using separate chaining with an internal capacity of 10. Assume our buckets are implemented

### Module 5: Hashing. CS Data Structures and Data Management. Reza Dorrigiv, Daniel Roche. School of Computer Science, University of Waterloo

Module 5: Hashing CS 240 - Data Structures and Data Management Reza Dorrigiv, Daniel Roche School of Computer Science, University of Waterloo Winter 2010 Reza Dorrigiv, Daniel Roche (CS, UW) CS240 - Module

### 1 CSE 100: HASH TABLES

CSE 100: HASH TABLES 1 2 Looking ahead.. Watch out for those deadlines Where we ve been and where we are going Our goal so far: We want to store and retrieve data (keys) fast 3 Tree structures BSTs: simple,

### HASH TABLES.

1 HASH TABLES http://en.wikipedia.org/wiki/hash_table 2 Hash Table A hash table (or hash map) is a data structure that maps keys (identifiers) into a certain location (bucket) A hash function changes the

### stacks operation array/vector linked list push amortized O(1) Θ(1) pop Θ(1) Θ(1) top Θ(1) Θ(1) isempty Θ(1) Θ(1)

Hashes 1 lists 2 operation array/vector linked list find (by value) Θ(n) Θ(n) insert (end) amortized O(1) Θ(1) insert (beginning/middle) Θ(n) Θ(1) remove (by value) Θ(n) Θ(n) find (by index) Θ(1) Θ(1)

### Cpt S 223. School of EECS, WSU

Hashing & Hash Tables 1 Overview Hash Table Data Structure : Purpose To support insertion, deletion and search in average-case constant t time Assumption: Order of elements irrelevant ==> data structure

### Lecture 16. Reading: Weiss Ch. 5 CSE 100, UCSD: LEC 16. Page 1 of 40

Lecture 16 Hashing Hash table and hash function design Hash functions for integers and strings Collision resolution strategies: linear probing, double hashing, random hashing, separate chaining Hash table

### Hash Tables. CS 311 Data Structures and Algorithms Lecture Slides. Wednesday, April 22, Glenn G. Chappell

Hash Tables CS 311 Data Structures and Algorithms Lecture Slides Wednesday, April 22, 2009 Glenn G. Chappell Department of Computer Science University of Alaska Fairbanks CHAPPELLG@member.ams.org 2005

### Algorithms with numbers (2) CISC4080, Computer Algorithms CIS, Fordham Univ.! Instructor: X. Zhang Spring 2017

Algorithms with numbers (2) CISC4080, Computer Algorithms CIS, Fordham Univ.! Instructor: X. Zhang Spring 2017 Acknowledgement The set of slides have used materials from the following resources Slides

### Algorithms with numbers (2) CISC4080, Computer Algorithms CIS, Fordham Univ. Acknowledgement. Support for Dictionary

Algorithms with numbers (2) CISC4080, Computer Algorithms CIS, Fordham Univ. Instructor: X. Zhang Spring 2017 Acknowledgement The set of slides have used materials from the following resources Slides for

### Hash[ string key ] ==> integer value

Hashing 1 Overview Hash[ string key ] ==> integer value Hash Table Data Structure : Use-case To support insertion, deletion and search in average-case constant time Assumption: Order of elements irrelevant

### The dictionary problem

6 Hashing The dictionary problem Different approaches to the dictionary problem: previously: Structuring the set of currently stored keys: lists, trees, graphs,... structuring the complete universe of

### 5. Hashing. 5.1 General Idea. 5.2 Hash Function. 5.3 Separate Chaining. 5.4 Open Addressing. 5.5 Rehashing. 5.6 Extendible Hashing. 5.

5. Hashing 5.1 General Idea 5.2 Hash Function 5.3 Separate Chaining 5.4 Open Addressing 5.5 Rehashing 5.6 Extendible Hashing Malek Mouhoub, CS340 Fall 2004 1 5. Hashing Sequential access : O(n). Binary

### CMSC 341 Hashing. Based on slides from previous iterations of this course

CMSC 341 Hashing Based on slides from previous iterations of this course Hashing Searching n Consider the problem of searching an array for a given value q If the array is not sorted, the search requires

### Introduction hashing: a technique used for storing and retrieving information as quickly as possible.

Lecture IX: Hashing Introduction hashing: a technique used for storing and retrieving information as quickly as possible. used to perform optimal searches and is useful in implementing symbol tables. Why

### Lecture 6: Hashing Steven Skiena

Lecture 6: Hashing Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.stonybrook.edu/ skiena Dictionary / Dynamic Set Operations Perhaps

### CSE 332 Winter 2015: Midterm Exam (closed book, closed notes, no calculators)

_ UWNetID: Lecture Section: A CSE 332 Winter 2015: Midterm Exam (closed book, closed notes, no calculators) Instructions: Read the directions for each question carefully before answering. We will give

### Hashing. Dr. Ronaldo Menezes Hugo Serrano. Ronaldo Menezes, Florida Tech

Hashing Dr. Ronaldo Menezes Hugo Serrano Agenda Motivation Prehash Hashing Hash Functions Collisions Separate Chaining Open Addressing Motivation Hash Table Its one of the most important data structures

### Lecture 7: Efficient Collections via Hashing

Lecture 7: Efficient Collections via Hashing These slides include material originally prepared by Dr. Ron Cytron, Dr. Jeremy Buhler, and Dr. Steve Cole. 1 Announcements Lab 6 due Friday Lab 7 out tomorrow

### Hash Tables: Handling Collisions

CSE 373: Data Structures and Algorithms Hash Tables: Handling Collisions Autumn 208 Shrirang (Shri) Mare shri@cs.washington.edu Thanks to Kasey Champion, Ben Jones, Adam Blank, Michael Lee, Evan McCarty,

### Fast Lookup: Hash tables

CSE 100: HASHING Operations: Find (key based look up) Insert Delete Fast Lookup: Hash tables Consider the 2-sum problem: Given an unsorted array of N integers, find all pairs of elements that sum to a

### CSE 332: Data Structures & Parallelism Lecture 3: Priority Queues. Ruth Anderson Winter 2019

CSE 332: Data Structures & Parallelism Lecture 3: Priority Queues Ruth Anderson Winter 201 Today Finish up Intro to Asymptotic Analysis New ADT! Priority Queues 1/11/201 2 Scenario What is the difference

### Acknowledgement HashTable CISC4080, Computer Algorithms CIS, Fordham Univ.

Acknowledgement HashTable CISC4080, Computer Algorithms CIS, Fordham Univ. Instructor: X. Zhang Spring 2018 The set of slides have used materials from the following resources Slides for textbook by Dr.

Introducing Hashing Chapter 21 Contents What Is Hashing? Hash Functions Computing Hash Codes Compressing a Hash Code into an Index for the Hash Table A demo of hashing (after) ARRAY insert hash index =

### csci 210: Data Structures Maps and Hash Tables

csci 210: Data Structures Maps and Hash Tables Summary Topics the Map ADT Map vs Dictionary implementation of Map: hash tables READING: GT textbook chapter 9.1 and 9.2 Map ADT A Map is an abstract data

### Lecture 12 Hash Tables

Lecture 12 Hash Tables 15-122: Principles of Imperative Computation (Spring 2018) Frank Pfenning, Rob Simmons Dictionaries, also called associative arrays as well as maps, are data structures that are

### HASH TABLES. Goal is to store elements k,v at index i = h k

CH 9.2 : HASH TABLES 1 ACKNOWLEDGEMENT: THESE SLIDES ARE ADAPTED FROM SLIDES PROVIDED WITH DATA STRUCTURES AND ALGORITHMS IN C++, GOODRICH, TAMASSIA AND MOUNT (WILEY 2004) AND SLIDES FROM JORY DENNY AND

### Open Addressing: Linear Probing (cont.)

Open Addressing: Linear Probing (cont.) Cons of Linear Probing () more complex insert, find, remove methods () primary clustering phenomenon items tend to cluster together in the bucket array, as clustering

### Dictionary. Dictionary. stores key-value pairs. Find(k) Insert(k, v) Delete(k) List O(n) O(1) O(n) Sorted Array O(log n) O(n) O(n)

Hash-Tables Introduction Dictionary Dictionary stores key-value pairs Find(k) Insert(k, v) Delete(k) List O(n) O(1) O(n) Sorted Array O(log n) O(n) O(n) Balanced BST O(log n) O(log n) O(log n) Dictionary

### Hashing. 1. Introduction. 2. Direct-address tables. CmSc 250 Introduction to Algorithms

Hashing CmSc 250 Introduction to Algorithms 1. Introduction Hashing is a method of storing elements in a table in a way that reduces the time for search. Elements are assumed to be records with several

### CSE 373 Autumn 2012: Midterm #2 (closed book, closed notes, NO calculators allowed)

Name: Sample Solution Email address: CSE 373 Autumn 0: Midterm # (closed book, closed notes, NO calculators allowed) Instructions: Read the directions for each question carefully before answering. We may

### Hashing. CptS 223 Advanced Data Structures. Larry Holder School of Electrical Engineering and Computer Science Washington State University

Hashing CptS 223 Advanced Data Structures Larry Holder School of Electrical Engineering and Computer Science Washington State University 1 Overview Hashing Technique supporting insertion, deletion and

### CSE 332 Autumn 2013: Midterm Exam (closed book, closed notes, no calculators)

Name: Email address: Quiz Section: CSE 332 Autumn 2013: Midterm Exam (closed book, closed notes, no calculators) Instructions: Read the directions for each question carefully before answering. We will

### Data Structures. Topic #6

Data Structures Topic #6 Today s Agenda Table Abstract Data Types Work by value rather than position May be implemented using a variety of data structures such as arrays (statically, dynamically allocated)

### Dynamic Dictionaries. Operations: create insert find remove max/ min write out in sorted order. Only defined for object classes that are Comparable

Hashing Dynamic Dictionaries Operations: create insert find remove max/ min write out in sorted order Only defined for object classes that are Comparable Hash tables Operations: create insert find remove

### UNIT III BALANCED SEARCH TREES AND INDEXING

UNIT III BALANCED SEARCH TREES AND INDEXING OBJECTIVE The implementation of hash tables is frequently called hashing. Hashing is a technique used for performing insertions, deletions and finds in constant

### CS 310 Advanced Data Structures and Algorithms

CS 310 Advanced Data Structures and Algorithms Hashing June 6, 2017 Tong Wang UMass Boston CS 310 June 6, 2017 1 / 28 Hashing Hashing is probably one of the greatest programming ideas ever. It solves one

### CSCI 104 Hash Tables & Functions. Mark Redekopp David Kempe

CSCI 104 Hash Tables & Functions Mark Redekopp David Kempe Dictionaries/Maps An array maps integers to values Given i, array[i] returns the value in O(1) Dictionaries map keys to values Given key, k, map[k]

### Table ADT and Sorting. Algorithm topics continuing (or reviewing?) CS 24 curriculum

Table ADT and Sorting Algorithm topics continuing (or reviewing?) CS 24 curriculum A table ADT (a.k.a. Dictionary, Map) Table public interface: // Put information in the table, and a unique key to identify

### CITS2200 Data Structures and Algorithms. Topic 15. Hash Tables

CITS2200 Data Structures and Algorithms Topic 15 Hash Tables Introduction to hashing basic ideas Hash functions properties, 2-universal functions, hashing non-integers Collision resolution bucketing and

### Chapter 20 Hash Tables

Chapter 20 Hash Tables Dictionary All elements have a unique key. Operations: o Insert element with a specified key. o Search for element by key. o Delete element by key. Random vs. sequential access.

### CSC263 Week 5. Larry Zhang.

CSC263 Week 5 Larry Zhang http://goo.gl/forms/s9yie3597b Announcements PS3 marks out, class average 81.3% Assignment 1 due next week. Response to feedbacks -- tutorials We spent too much time on working

### CS 241 Analysis of Algorithms

CS 241 Analysis of Algorithms Professor Eric Aaron Lecture T Th 9:00am Lecture Meeting Location: OLB 205 Business HW5 extended, due November 19 HW6 to be out Nov. 14, due November 26 Make-up lecture: Wed,

### CSE 332: Data Structures & Parallelism Lecture 12: Comparison Sorting. Ruth Anderson Winter 2019

CSE 332: Data Structures & Parallelism Lecture 12: Comparison Sorting Ruth Anderson Winter 2019 Today Sorting Comparison sorting 2/08/2019 2 Introduction to sorting Stacks, queues, priority queues, and

### Today: Finish up hashing Sorted Dictionary ADT: Binary search, divide-and-conquer Recursive function and recurrence relation

Announcements HW1 PAST DUE HW2 online: 7 questions, 60 points Nat l Inst visit Thu, ok? Last time: Continued PA1 Walk Through Dictionary ADT: Unsorted Hashing Today: Finish up hashing Sorted Dictionary

### Data Structures and Algorithms. Chapter 7. Hashing

1 Data Structures and Algorithms Chapter 7 Werner Nutt 2 Acknowledgments The course follows the book Introduction to Algorithms, by Cormen, Leiserson, Rivest and Stein, MIT Press [CLRST]. Many examples

### AAL 217: DATA STRUCTURES

Chapter # 4: Hashing AAL 217: DATA STRUCTURES The implementation of hash tables is frequently called hashing. Hashing is a technique used for performing insertions, deletions, and finds in constant average

### Hashing. Hashing Procedures

Hashing Hashing Procedures Let us denote the set of all possible key values (i.e., the universe of keys) used in a dictionary application by U. Suppose an application requires a dictionary in which elements

### Lecture 12 Notes Hash Tables

Lecture 12 Notes Hash Tables 15-122: Principles of Imperative Computation (Spring 2016) Frank Pfenning, Rob Simmons 1 Introduction In this lecture we re-introduce the dictionaries that were implemented

### CSE 373 Spring 2010: Midterm #2 (closed book, closed notes, NO calculators allowed)

Name: Email address: CSE 373 Spring 2010: Midterm #2 (closed book, closed notes, NO calculators allowed) Instructions: Read the directions for each question carefully before answering. We may give partial

### Data Structures And Algorithms

Data Structures And Algorithms Hashing Eng. Anis Nazer First Semester 2017-2018 Searching Search: find if a key exists in a given set Searching algorithms: linear (sequential) search binary search Search

### CSE 332 Spring 2013: Midterm Exam (closed book, closed notes, no calculators)

Name: Email address: Quiz Section: CSE 332 Spring 2013: Midterm Exam (closed book, closed notes, no calculators) Instructions: Read the directions for each question carefully before answering. We will

### CSE 214 Computer Science II Searching

CSE 214 Computer Science II Searching Fall 2017 Stony Brook University Instructor: Shebuti Rayana shebuti.rayana@stonybrook.edu http://www3.cs.stonybrook.edu/~cse214/sec02/ Introduction Searching in a

### CSE 332 Spring 2014: Midterm Exam (closed book, closed notes, no calculators)

Name: Email address: Quiz Section: CSE 332 Spring 2014: Midterm Exam (closed book, closed notes, no calculators) Instructions: Read the directions for each question carefully before answering. We will

### Today s Outline. CS 561, Lecture 8. Direct Addressing Problem. Hash Tables. Hash Tables Trees. Jared Saia University of New Mexico

Today s Outline CS 561, Lecture 8 Jared Saia University of New Mexico Hash Tables Trees 1 Direct Addressing Problem Hash Tables If universe U is large, storing the array T may be impractical Also much

### Hashing Techniques. Material based on slides by George Bebis

Hashing Techniques Material based on slides by George Bebis https://www.cse.unr.edu/~bebis/cs477/lect/hashing.ppt The Search Problem Find items with keys matching a given search key Given an array A, containing

### CSE 332: Data Structures & Parallelism Lecture 7: Dictionaries; Binary Search Trees. Ruth Anderson Winter 2019

CSE 332: Data Structures & Parallelism Lecture 7: Dictionaries; Binary Search Trees Ruth Anderson Winter 2019 Today Dictionaries Trees 1/23/2019 2 Where we are Studying the absolutely essential ADTs of

### COSC160: Data Structures Hashing Structures. Jeremy Bolton, PhD Assistant Teaching Professor

COSC160: Data Structures Hashing Structures Jeremy Bolton, PhD Assistant Teaching Professor Outline I. Hashing Structures I. Motivation and Review II. Hash Functions III. HashTables I. Implementations

### CHAPTER 9 HASH TABLES, MAPS, AND SKIP LISTS

0 1 2 025-612-0001 981-101-0002 3 4 451-229-0004 CHAPTER 9 HASH TABLES, MAPS, AND SKIP LISTS ACKNOWLEDGEMENT: THESE SLIDES ARE ADAPTED FROM SLIDES PROVIDED WITH DATA STRUCTURES AND ALGORITHMS IN C++, GOODRICH,

### Hash Tables. Computer Science S-111 Harvard University David G. Sullivan, Ph.D. Data Dictionary Revisited

Unit 9, Part 4 Hash Tables Computer Science S-111 Harvard University David G. Sullivan, Ph.D. Data Dictionary Revisited We've considered several data structures that allow us to store and search for data

### ! A Hash Table is used to implement a set, ! The table uses a function that maps an. ! The function is called a hash function.

Hash Tables Chapter 20 CS 3358 Summer II 2013 Jill Seaman Sections 201, 202, 203, 204 (not 2042), 205 1 What are hash tables?! A Hash Table is used to implement a set, providing basic operations in constant

### Lecture 4. Hashing Methods

Lecture 4 Hashing Methods 1 Lecture Content 1. Basics 2. Collision Resolution Methods 2.1 Linear Probing Method 2.2 Quadratic Probing Method 2.3 Double Hashing Method 2.4 Coalesced Chaining Method 2.5

### Hashing. Manolis Koubarakis. Data Structures and Programming Techniques

Hashing Manolis Koubarakis 1 The Symbol Table ADT A symbol table T is an abstract storage that contains table entries that are either empty or are pairs of the form (K, I) where K is a key and I is some

### Dictionaries and Hash Tables

Dictionaries and Hash Tables 0 1 2 3 025-612-0001 981-101-0002 4 451-229-0004 Dictionaries and Hash Tables 1 Dictionary ADT The dictionary ADT models a searchable collection of keyelement items The main

### CSE373 Fall 2013, Final Examination December 10, 2013 Please do not turn the page until the bell rings.

CSE373 Fall 2013, Final Examination December 10, 2013 Please do not turn the page until the bell rings. Rules: The exam is closed-book, closed-note, closed calculator, closed electronics. Please stop promptly

### Lecture 10: Introduction to Hash Tables

Lecture 10: Introduction to Hash Tables CSE 373: Data Structures and Algorithms CSE 373 19 WI - KASEY CHAMPION 1 Warm Up CSE 373 SP 18 - KASEY CHAMPION 2 Administrivia HW 2 part 1 grades went out HW 2

### Hash Tables and Hash Functions

Hash Tables and Hash Functions We have seen that with a balanced binary tree we can guarantee worst-case time for insert, search and delete operations. Our challenge now is to try to improve on that...

### Hashing. October 19, CMPE 250 Hashing October 19, / 25

Hashing October 19, 2016 CMPE 250 Hashing October 19, 2016 1 / 25 Dictionary ADT Data structure with just three basic operations: finditem (i): find item with key (identifier) i insert (i): insert i into

### Comp 335 File Structures. Hashing

Comp 335 File Structures Hashing What is Hashing? A process used with record files that will try to achieve O(1) (i.e. constant) access to a record s location in the file. An algorithm, called a hash function

### Data Structures and Algorithms. Roberto Sebastiani

Data Structures and Algorithms Roberto Sebastiani roberto.sebastiani@disi.unitn.it http://www.disi.unitn.it/~rseba - Week 07 - B.S. In Applied Computer Science Free University of Bozen/Bolzano academic

### CMSC 132: Object-Oriented Programming II. Hash Tables

CMSC 132: Object-Oriented Programming II Hash Tables CMSC 132 Summer 2017 1 Key Value Map Red Black Tree: O(Log n) BST: O(n) 2-3-4 Tree: O(log n) Can we do better? CMSC 132 Summer 2017 2 Hash Tables a

### CS 206 Introduction to Computer Science II

CS 206 Introduction to Computer Science II 04 / 16 / 2018 Instructor: Michael Eckmann Today s Topics Questions? Comments? Graphs Shortest weight path (Dijkstra's algorithm) Besides the final shortest weights

### Hash tables. hashing -- idea collision resolution. hash function Java hashcode() for HashMap and HashSet big-o time bounds applications

hashing -- idea collision resolution Hash tables closed addressing (chaining) open addressing techniques hash function Java hashcode() for HashMap and HashSet big-o time bounds applications Hash tables

### Algorithms and Data Structures

Lesson 4: Sets, Dictionaries and Hash Tables Luciano Bononi http://www.cs.unibo.it/~bononi/ (slide credits: these slides are a revised version of slides created by Dr. Gabriele D Angelo)

### Part I Anton Gerdelan

Hash Part I Anton Gerdelan Review labs - pointers and pointers to pointers memory allocation easier if you remember char* and char** are just basic ptr variables that hold an address

### CSE373: Data Structures & Algorithms Lecture 28: Final review and class wrap-up. Nicki Dell Spring 2014

CSE373: Data Structures & Algorithms Lecture 28: Final review and class wrap-up Nicki Dell Spring 2014 Final Exam As also indicated on the web page: Next Tuesday, 2:30-4:20 in this room Cumulative but

### CS 2150 (fall 2010) Midterm 2

Name: Userid: CS 2150 (fall 2010) Midterm 2 You MUST write your name and e-mail ID on EACH page and bubble in your userid at the bottom of EACH page, including this page. If you are still writing when

### Chapter 9: Maps, Dictionaries, Hashing

Chapter 9: 0 1 025-612-0001 2 981-101-0002 3 4 451-229-0004 Maps, Dictionaries, Hashing Nancy Amato Parasol Lab, Dept. CSE, Texas A&M University Acknowledgement: These slides are adapted from slides provided

### Fundamental Algorithms

Fundamental Algorithms Chapter 7: Hash Tables Michael Bader Winter 2011/12 Chapter 7: Hash Tables, Winter 2011/12 1 Generalised Search Problem Definition (Search Problem) Input: a sequence or set A of

### CSE373: Data Structures & Algorithms Lecture 4: Dictionaries; Binary Search Trees. Kevin Quinn Fall 2015

CSE373: Data Structures & Algorithms Lecture 4: Dictionaries; Binary Search Trees Kevin Quinn Fall 2015 Where we are Studying the absolutely essential ADTs of computer science and classic data structures

### Tirgul 7. Hash Tables. In a hash table, we allocate an array of size m, which is much smaller than U (the set of keys).

Tirgul 7 Find an efficient implementation of a dynamic collection of elements with unique keys Supported Operations: Insert, Search and Delete. The keys belong to a universal group of keys, U = {1... M}.