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Lecture Materials

If you wish, you can read through a seven-page course description . A 21-page topic summary is also available: Algorithms and data structures—topic summary .

This is a collection of PowerPoint (pptx) slides ("pptx") presenting a course in algorithms and data structures. Associated with many of the topics are a collection of notes ("pdf"). Some presentations may be associated with videos ("V") and homework questions ("Q"), possibly with answers ("A"). Some topics also links to corresponding Wikipedia page ("W"), entries in the NIST Dictionary of Algorithms and Data Structures (DADS) ("D"), and references to cplusplus.com ("C").

You will note that the section numbering in the notes is paralleled in the top left corner of the slides; thus, anyone watching the slides can follow along in the notes.

Spanish notes translated by Christian von Lücken.

Table of contents

• Introduction and review
• Algorithm analysis
• List, stacks and queues
• Trees and hierarchical orders
• Ordered trees
• Search trees
• Priority queues
• Sorting algorithms
• Hash functions and hash tables
• Equivalence relations and disjoint sets
• Graph algorithms
• Algorithm design
• Theory of computation
• Other topics
• Concluding remarks

1. Introduction and review

2. Algorithm analysis

3. Lists, stacks, and queues

4. Trees and hierarchical orders

Before we proceed with looking at data structures for storing linearly ordered data, we must take a diversion to look at trees. At first glance, it appears as if trees are most appropriate for storing hierarchically ordered data; however, we will later see how trees can also be used to allow efficient storage of linearly ordered data, as well.

5. Ordered trees

A general tree is appropriate for storing hierarchical orders, where the relationship is between the parent and the children. There are many cases, however, where the tree data structure is more useful if there is a fixed number of identifiable children. This topic looks at binary trees as well as perfect and complete binary trees, N-ary trees, the concept of balance, binomial trees, and left-child right-sibling binary trees (a technique for storing general trees as binary trees).

6. Search trees

This topic looks at storing linearly ordered data in search trees. The focus is to ensure that operations on individual elements stored in the tree run in Θ(ln( - )) time.

7. Priority queues

A priority queue stores linearly ordered data based on the priority; however, by restricting the operations, those operations can be optimized.

8. Sorting algorithms

9. Hash functions and hash tables

Note that previously I used to teach linear probing and double hashing; however, it has been brought to my attention that quadratic hashing is better—especially when we consider the effects of caching and the additional cost of cache misses.

10. Equivalence relations and disjoint sets

11. Graph algorithms

12. Algorithm design

13. Theory of computation

14. Other topics

15. Concluding remarks

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Introduction Of Stack.

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Linear Data Structures

Mar 31, 2019

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Linear Data Structures. Chapters 6, 7. Outline. Our goal in this lecture is to Review the basic linear data structures Demonstrate how each can be defined as an Abstract Data Type (ADT) Demonstrate how each of these ADTs can be specified as a Java interface.

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Linear Data Structures Chapters 6, 7

Outline • Our goal in this lecture is to • Review the basic linear data structures • Demonstrate how each can be defined as an Abstract Data Type (ADT) • Demonstrate how each of these ADTs can be specified as a Java interface. • Outline the algorithms for creating, accessing and modifying each data structure • Analyze the running time of these operations • Identify particular applications for which each data structure would be suited.

Learning Outcomes • Based on this lecture, you should: • Know the basic linear data structures • Be able to express each as an Abstract Data Type (ADT) • Be able to specify each of these ADTs as a Java interface. • Be able to outline the algorithms for creating, accessing and modifying each data structure • Be able to analyze the running time of these operations • Be able to identify particular applications for which each data structure would be suited.

Linear Data Structures Arrays (Ch. 3.1) Array Lists (Ch. 6.1) Stacks (Ch. 5.1) Queues (Ch. 5.2 – 5.2) Linked Lists (Ch. 3.2 – 3.3)

Arrays • Array: a sequence of indexed components with the following properties: • array size is fixed at the time of array’s construction • int[] numbers = new int[10]; • array elements are placed contiguously in memory • address of any element can be calculated directly as its offset from the beginning of the array • consequently, array components can be efficiently inspected or updated in O(1) time, using their indices • randomNumber = numbers[5]; • numbers[2] = 100;

Arrays in Java • For an array of length n, the index bounds are 0 to n-1. • Java arrays are homogeneous • all array components must be of the same (object or primitive) type. • but, an array of an object type can contain objects of any respective subtype • An array is itself an object. • it is allocated dynamically by means of new • it is automatically deallocated when no longer referred to • When an array is first created, all values are automatically initialized with • 0, for an array of int[] or double[] type • false, for a boolean[] array • null, for an array of objects • Example [ common error –unallocated arrays] int[] numbers; numbers[2] = 100;

Arrays in Java • The length of any array object can be accessed through its instance variable ‘length’. • the cells of an array A are numbered: 0, 1, .., A.length-1 • ArrayIndexOutOfBoundsException • thrown at an attempt to index into array A using a number larger than A.length-1. • helps Java avoid ‘buffer overflow attacks’ • Example [ declaring, defining and determining the size of an array] int[] A={12, 24, 37, 53, 67}; for (inti=0; i < A.length; i++) { …}

Buffer Overflows Windows Buffer Overflow Protection Programs: Not Much <"Paul Robinson" <[email protected]>> • Tue, 10 Aug 2004 15:26:44 GMT An 9 Aug 2004 • …there is a bug in AOL Instant Messenger allowing an attacker to send a message that can cause a buffer overflow and possibly execute code on the attacked machine. Apparently this will only occur if the attacker sends a url - like the one in this message - as a hyperlink and the victim clicks on it, which makes the probability of attack much lower than a "standard buffer overflow attack" upon a program. Mon, 09 Aug 2004 17:24:19 GMT …a buffer overflow exploit is one in which someone sends too much data to a program (such as a web server application), sending far more data than the program would expect, in order to force arbitrary data into a storage area (a "buffer") so the amount of data forced into the buffer goes beyond the expected limits, causing the data to overflow the buffer and makes it possible for that data to be executed as arbitrary program code. Since the attacker forces code of his choosing into the execution stream, he now 0wns your box, because as the saying goes, if I can run code on your machine - especially if it's a Windows machine where there is not much protection - I can pretty much do anything I please there.

Arrays in Java A B A B A B A B • Since an array is an object, the name of the array is actually a reference (pointer) to the place in memory where the array is stored. • reference to an object holds the address of the actual object • Example [ copying array references] int[] A={12, 24, 37, 53, 67}; int[] B=A; B[3]=5; • Example [ cloning an array] int[] A={12, 24, 37, 53, 67}; int[] B=A.clone(); B[3]=5;

Example Examples [ 2D array in Java = array of arrays] int[][] nums = new int[5][4]; OR int[][] nums; nums = new int[5][]; for (inti=0; i<5; i++) { nums[i] = new int[4]; }

Example Example [ 2D array of objects in Java = an array of arrays of references] Square[][] board = new Square[2][3];

Arrays in Java The Java.util.Arrays Class • Useful Built-In Methods in Java.util.Arrays • equals(A,B) • returns true if A and B have an equal number of elements and every corresponding pair of elements in the two arrays are equal • fill(A,x) • store element x into every cell of array A • sort(A) • sort the array A in the natural ordering of its elements • binarySearch([int] A, int key) • search the specified array of sorted ints for the specified value using the binary search algorithm (A must be sorted)

Example int[] A={12, 24, 37, 53, 67}; int[] B=A.clone(); if (A==B) System.out.println(“ Superman ”); if (A.equals(B)) System.out.println(“ Snow White ”); Answer: Snow White What is printed?

Limitations of Arrays Source start idx Dest start idx • Static data structure • size must be fixed at the time the program creates the array • once set, array size cannot be changed • if number of entered items > declared array size ⇒ out of memory • fix 1: use array size > number of expected items ⇒ waste of memory • fix 2: increase array size to fit the number of items ⇒ extra time • Insertion / deletion in an array is time consuming • all the elements following the inserted element must be shifted appropriately • Example [ time complexity of “growing” an array] if (numberOfItems > numbers.length) { int[] newNumbers = new int[2*numbers.length]; System.arraycopy(numbers, 0, newNumbers, 0, numbers.length); numbers = newNumbers; }

The Array List ADT (§6.1) TheArray List ADT extends the notion of array by storing a sequence of arbitrary objects An element can be accessed, modified, inserted or removed by specifying its rank (number of elements preceding it) An exception is thrown if an incorrect rank is specified (e.g., a negative rank)

The Array List ADT /** Simplified version of java.util.List */ public interface List<E> { /** Returns the number of elements in this list */ public intsize(); /** Returns whether the list is empty. */ public booleanisEmpty(); /** Inserts an element e to be at index I, shifting all elements after this. */ public void add(int I, E e) throws IndexOutOfBoundsException; /** Returns the element at index I, without removing it. */ public E get(inti) throws IndexOutOfBoundsException; /** Removes and returns the element at index I, shifting the elements after this. */ public E remove(inti) throws IndexOutOfBoundsException; /** Replaces the element at index I with e, returning the previous element at i. */ public E set(int I, E e) throws IndexOutOfBoundsException; }

Use an array V of size N A variable n keeps track of the size of the array list (number of elements stored) Operationget(r) is implemented in O(1) time by returning V[r] A Simple Array-based Implementation V 0 1 2 n r

Insertion • In operationadd(o, r), we need to make room for the new element by shifting forward the n-r elements V[r], …, V[n-1] • In the worst case (r=0), this takes O(n) time V 0 1 2 n r V 0 1 2 n r V o 0 1 2 n r

V 0 1 2 n r V 0 1 2 n r V o 0 1 2 n r Deletion • In operation remove(r), we need to fill the hole left by the removed element by shifting backward the n-r-1 elements V[r+1], …, V[n-1] • In the worst case (r=0), this takes O(n) time

Performance • In the array based implementation • The space used by the data structure is O(n) • size, isEmpty,get and set run in O(1) time • add and remove run in O(n) time • In anadd operation, when the array is full, instead of throwing an exception, we could replace the array with a larger one. • In fact java.util.ArrayListimplements this ADT using extendable arrays that do just this.

Implementing Array Lists using Extendable Arrays Algorithmadd(o) ifn = N then Anew array of size N* N = N* fori0toN-1 do A[i]S[i] SA n n+1 S[n] o • In an add operation, when the array is full, instead of throwing an exception, we can replace the array with a larger one • How large should the new array be? • incremental strategy: increase the size by a constant c • doubling strategy: double the size • Let n = current number of elements in array N = capacity of array

Comparison of the Strategies • We compare the incremental strategy and the doubling strategy by analyzing the total time T(n) needed to perform a series of nadd operations • We simplify the analysis by assuming add(o) operations that append the object to the end of the list. • We assume that we start with an empty array list (n = 0) represented by an array of capacity 0 (N = 0). • The amortized time of an add(o) operation is the average time taken over the series of operations, i.e., T(n)/n

Incremental Strategy

Incremental Strategy Analysis • We replace the array times • The total time T(n) of a series of nadd(o) operations is proportional to n + c+ 2c + 3c + 4c + … + kc= n + c(1 + 2 + 3 + … + k) = n + ck(k+ 1)/2 • (Recall that JAVA initializes all elements of an allocated array.) • Since c is a constant, T(n) is O(n +k2),i.e., O(n2) • The amortized time of an add(o) operation is O(n)

Doubling Strategy

geometric series 2 4 1 1 8 Doubling Strategy Analysis • We replace the array times • The total time T(n) of a series of nadd(o) operations is proportional to n+ 1 + 2 + 4 + 8 + …+ 2k= n+ 2k + 1-1 ≤ 5n • Thus T(n) is O(n) • The amortized time of an add operation is O(1)!

Applications of Array Lists • Maintaining a sorted list when insertions and removals are relatively rare.

The Stack ADT stores arbitrary objects Insertions and deletions follow the last-in first-out scheme Think of a spring-loaded plate or Pez dispenser Main stack operations: push(object): inserts an element object pop(): removes and returns the last inserted element Auxiliary stack operations: object top(): returns the last inserted element without removing it integer size(): returns the number of elements stored booleanisEmpty(): indicates whether no elements are stored The Stack ADT Note: java.util.Stack provides push and pop, but differs in other respects.

Stack Interface in Java • Example java interface public interfaceStack{ public int size(); public boolean isEmpty(); public Object top()throwsEmptyStackException; public voidpush(Object o); public Object pop()throwsEmptyStackException;}

Applications of Stacks • Page-visited history in a Web browser • Undo sequence in a text editor • Chain of method calls in the Java Virtual Machine • Parsing math

Method Stack in the JVM main() { int i = 5; foo(i); } foo(int j) { int k; k = j+1; bar(k); } bar(int m) { … } bar PC = 1m = 6 • The Java Virtual Machine (JVM) keeps track of the chain of active methods with a stack • When a method is called, the JVM pushes on the stack a frame containing • Local variables and return value • Program counter, keeping track of the statement being executed • When a method ends, its frame is popped from the stack and control is passed to the method on top of the stack • Allows for recursion foo PC = 3 j = 5 k = 6 main PC = 2 i = 5

The Stack ADT can be implemented with an array We add elements from left to right A variable keeps track of the index of the top element Array-based Stack Algorithmsize() returnt +1 Algorithmpop() ifisEmpty()then throw EmptyStackException else tt-1 returnS[t+1] … S 0 1 2 t

… S 0 1 2 t Array-based Stack (cont.) • If using an array of fixed size,the stack may become full • A push operation will then throw a FullStackException • Limitation of the array-based implementation • Not intrinsic to the Stack ADT • For example, in java.util.Stack, the array is extendable. Algorithmpush(o) ift=S.length-1then throw FullStackException else tt +1 S[t]o

Performance and Limitations • Performance • Let n be the number of elements in the stack • The space used is O(n) • Each operation runs in time O(1)

Example array-based stack in Java public classArrayStackimplements Stack{ // holds the stack elements private Object S[ ]; // index to top elementprivateint top = -1; // constructorpublicArrayStack(int capacity){S = new Object[capacity]);} public Object pop()throwsEmptyStackException{ifisEmpty()throw newEmptyStackException(“Empty stack: cannot pop”);Object temp = S[top];// facilitates garbage collection S[top] = null; top = top – 1;returntemp;}

Example Application: Parenthesis Matching • Each “(”, “{”, or “[” must be paired with a matching “)”, “}”, or “[” • correct: ( )(( )){([( )])} • correct: ((( )(( )){([( )])} • incorrect: )(( )){([( )])} • incorrect: ({[ ])} • incorrect: (

Parentheses Matching Algorithm Algorithm ParenMatch(X,n): Input: An array X of ntokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let S be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then S.push(X[i]) else if X[i] is a closing grouping symbol then if S.isEmpty() then return false {nothing to match with} if S.pop() does not match the type of X[i] then return false {wrong type} if S.isEmpty() then return true {every symbol matched} else return false {some symbols were never matched}

The Queue ADT • The Queue ADT stores arbitrary objects • Insertions and deletions follow the first-in first-out (FIFO) scheme • Insertions are at the rear of the queue and removals are at the front of the queue • Main queue operations: • enqueue(object): inserts an element at the end of the queue • object dequeue(): removes and returns the element at the front of the queue • Auxiliary queue operations: • object front(): returns the element at the front without removing it • integer size(): returns the number of elements stored • booleanisEmpty(): indicates whether no elements are stored • Exceptions • Attempting the execution of dequeue or front on an empty queue throws an EmptyQueueException • Attempting to enqueue an element on a queue that is full can be signaled with a FullQueueException.

Queue Example Operation OutputQ enqueue(5) –(5) enqueue(3)–(5, 3) dequeue()5(3) enqueue(7)–(3, 7) dequeue()3(7) front() 7(7) dequeue()7() dequeue()“error” () isEmpty() true() enqueue(9)–(9) enqueue(7)–(9, 7) size() 2(9, 7) enqueue(3)–(9, 7, 3) enqueue(5)–(9, 7, 3, 5) dequeue()9(7, 3, 5)

Q 0 1 2 f r Q 0 1 2 r f Array-Based Queue • Use an array of size N in a circular fashion • Two variables keep track of the front and rear f index of the front element r index immediately past the rear element • Array location r is kept empty normal configuration wrapped-around configuration

Q 0 1 2 f r Q 0 1 2 r f Queue Operations Algorithmsize() return(r + N–f) mod N AlgorithmisEmpty() return(f=r) We use the modulo operator (remainder of division)

Q 0 1 2 f r Q 0 1 2 r f Queue Operations (cont.) Algorithmenqueue(o) ifsize()=N - 1then throw FullQueueException else Q[r]o r(r+ 1) mod N Operation enqueue may throw an exception if the array is full

Q 0 1 2 f r Q 0 1 2 r f Queue Operations (cont.) Algorithmdequeue() ifisEmpty()then throw EmptyQueueException else oQ[f] f(f+ 1) mod N returno Operation dequeue throws an exception if the queue is empty

Queue Interface in Java public interfaceQueue{ public int size(); public boolean isEmpty(); public Object front()throwsEmptyQueueException; public voidenqueue(Object o); public Object dequeue()throwsEmptyQueueException;} NB: The java.util.Queue interface uses quite different signatures, and does not insist that the queue be FIFO. Java interface corresponding to our Queue ADT Requires the definition of class EmptyQueueException

Linked Lists By virtue of their random access nature, arrays support non-structural read/write operations (e.g., get(i), set(i)) in O(1) time. Unfortunately, structural operations (e.g., add(i,e)remove(i)) take O(n) time. For some algorithms and inputs, structural operations may dominate the running time. For such cases, linked lists may be more appropriate.

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Data Structuring Powerpoint Presentation Slides

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A data structure is a method of organising and storing information. Sometimes data structures are used to organise significant data (for example, a collection of names and phone numbers), while other times data structures are used for bookkeeping while an algorithm is running. The world of data is always changing, and it can be difficult to keep up with the latest trends. That’s where SlideTeam comes in. We provide templates for data analytics PowerPoint presentations that will help you get up to speed quickly and easily. Our templates are easy to use and customizable, so you can create a presentation that meets your specific needs.So there’s no excuse not to get started today.

• Data Architecture
• Data Designing
• Data Structuring
• Data Construction

Org Structure Fundraising Pitch For Data Management Company

This slide represents organizational chart of company. It comprises of key members such as CEO, Head of field operations, data strategy, marketing director, CDO, global head of business development, etc. Present the topic in a bit more detail with this Org Structure Fundraising Pitch For Data Management Company. Use it as a tool for discussion and navigation on Serviceable Available Market, Serviceable Obtainable Market. This template is free to edit as deemed fit for your organization. Therefore download it now.

This slide represents organizational chart of company. It comprises of key members such as CEO, Head of field operations, data strategy, marketing director, CDO, global head of business development, etc.

• Serviceable Available Market
• Serviceable Obtainable Market

Data structures vs abstract data types ppt powerpoint presentation model example introduction cpb

Presenting our Data Structures Vs Abstract Data Types Ppt Powerpoint Presentation Model Example Introduction Cpb PowerPoint template design. This PowerPoint slide showcases eight stages. It is useful to share insightful information on Data Structures Vs Abstract Data Types This PPT slide can be easily accessed in standard screen and widescreen aspect ratios. It is also available in various formats like PDF, PNG, and JPG. Not only this, the PowerPoint slideshow is completely editable and you can effortlessly modify the font size, font type, and shapes according to your wish. Our PPT layout is compatible with Google Slides as well, so download and edit it as per your knowledge.

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• Data Structures Vs Abstract Data Types

Agenda For Data Structure In DBMS

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Linked Data Structure Reverse Operation Performed On Simple Linked List Ppt Slides Infographic Template

This slide demonstrates the thorough five step reverse operation performed on the linked list, and the components include the head, nodes with data items, null and temporary node. In this operation, the last node is directed by the head element and reverses the entire linked list. Deliver an outstanding presentation on the topic using this Linked Data Structure Reverse Operation Performed On Simple Linked List Ppt Slides Infographic Template. Dispense information and present a thorough explanation of Preceding Element, Temporary Element, New Successor using the slides given. This template can be altered and personalized to fit your needs. It is also available for immediate download. So grab it now.

This slide demonstrates the thorough five step reverse operation performed on the linked list, and the components include the head, nodes with data items, null and temporary node.In this operation, the last node is directed by the head element and reverses the entire linked list.

• Preceding Element
• Temporary Element
• New Successor

Linked Data Structure Powerpoint Presentation Slides

Enthrall your audience with this Linked Data Structure Powerpoint Presentation Slides. Increase your presentation threshold by deploying this well-crafted template. It acts as a great communication tool due to its well-researched content. It also contains stylized icons, graphics, visuals etc, which make it an immediate attention-grabber. Comprising fifty one slides, this complete deck is all you need to get noticed. All the slides and their content can be altered to suit your unique business setting. Not only that, other components and graphics can also be modified to add personal touches to this prefabricated set.

This PowerPoint presentation briefly explains the linked data, its principles, benefits, and critical terms. In this Linked Data Structure PowerPoint Presentation, we have covered the introduction to linked data by covering its overview, the role of linked data on the web, and the importance of linked data. Moreover, this deck shows linked data principles, their benefits, data quality in linked data by covering dataset quality in the linked web data, and the importance of publishing five star data. In addition, this PPT talks about the things that linked data cant do and critical terms in linked data, such as linked open data, its principles and advantages, and resource description framework RDF. Furthermore, this Linked Data template includes the overview of schema in linked data, triples in linked data, an overview of the semantic web, the relationship between the semantic web and linked data, turtles in linked data, and the role of uniform resource identifier URI. Lastly, the module comprises a data structure timeline, a roadmap, and a dashboard. Download our 100 parcent editable and customizable template, which is also compatible with Google Slides.

• Linked Open Data
• Overview Of Linked Data
• Role Of Linked Data In Web
• Principles And Benefits Of Linked Data
• Key Terms Of Linked Data
• data structure

It Ot Convergence Strategy The Organizational Structure Around Data Use

This slide covers actions and roles for data use in business. In the sense of IT or OT integration multiple organizational data uses positions and functions as well. Present the topic in a bit more detail with this It Ot Convergence Strategy The Organizational Structure Around Data Use. Use it as a tool for discussion and navigation on Organizational, Structure, Structuring. This template is free to edit as deemed fit for your organization. Therefore download it now.

This slide covers actions and roles for data use in business. In the sense of IT or OT integration multiple organizational data uses positions and functions as well.

• organizational
• Structuring

Goal presentation visual of data operations team structure infographic template

This is a single slide titled Goal Presentation Visual Of Data Operations Team Structure Infographic Template. It is crafted using high quality vector based visuals that are 100 percent editable and available for immediate download in standard and widescreen aspect ratios.

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• Goal Presentation Visual Infographic

Team structure for cloud data migration project

Presenting this set of slides with name Team Structure For Cloud Data Migration Project. This is a four stage process. The stages in this process are Architecture Team, Migration Team, Operations Team. This is a completely editable PowerPoint presentation and is available for immediate download. Download now and impress your audience.

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• Architecture Team
• Migration Team
• Operations Team

Half yearly data governance roadmap structure

Presenting Half Yearly Data Governance Roadmap Structure PowerPoint slide. This PPT theme is available in both 4,3 and 16,9 aspect ratios. This PowerPoint template is customizable so you can modify the font size, font type, color, and shapes as per your requirements. This PPT presentation is Google Slides compatible hence it is easily accessible. You can download and save this PowerPoint layout in different formats like PDF, PNG, and JPG.

Visualize your work plan and communicate your ideas impactfully with our pre designed Half Yearly Data Governance Roadmap Structure. Showcase the detailed overview of the project, the key deliverables, and the milestones to be achieved with the help of our fully customizable PowerPoint layout. You can easily emphasize on the project goals and discuss all the activities involved in an easy to comprehend manner by utilizing our professionally designed PPT theme. This roadmap PowerPoint layout is a perfect strategic planning tool that can help in keeping the project on track. With our attractive PowerPoint theme, you can articulate the workflow, track the work progress, and have a clear vision of the goal to be achieved. Download this versatile Half Yearly Data Governance Roadmap Structure and save your hours of work.