ELEMENTARY DATA STRUCTURES

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ELEMENTARY DATA STRUCTURES

• Stacks, Queues, and
• Linked Lists

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Elementary Data Structures

• Used as programming tools (stacks queues)-
  software (i.e. compilers)- used in the
  operations of a certain task
• Implemented in CPU instructions- hardware

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Stacks

• Definition
• container of objects
• uses LIFO principle for object operations
• operations are push and pop
• Sample uses
• Internet browsers
• Undo / Redo feature

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Other Applications

• Parsing- check for matching parenthesis or
  brackets- aid for algorithms applied to complex
  data structures (traverse nodes of a tree and
  searching vertices of a graph)

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Basic Stack Operations

• push(o)
• pop()

• Inserts object o onto top of stack
• Input object Output none
• Removes the top object of stack and returns it to
  calling method Input none
  Output object

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Related Stack Operations

• isEmpty()
• isFull()

• Returns a boolean indicating if stack is empty.
• Input none Output boolean
• Returns a boolean indicating if stack is full
• Input none Output boolean

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Other Stack Operations

• size()
• top()

• Returns the number of objects in stack.
• Input none Output integer
• Returns the top object of the stack. Input none
• Output object

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An Array-Based Stack

• Create an array A of size N
• Store elements of stack S in array A
• Let t (integer) - index of the top element of
  stack S
• S
• 0 1 2 3 t ... N-1

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Array Implementation

• Algorithm size()return t 1
• Algorithm isempty()return (tlt0)
• Algorithm push(o)if size()N then throw a
  STACKEMPTYEXCEPTIONtt1Sto

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Array Implementation

• Algorithm pop()if isempty() then throw a
  STACKEMPTYEXCEPTIONeStStnulltt-1return
  e
• Algorithm top()if isempty() then throw a
  STACKEMPTYEXCEPTIONreturn St

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Class Problem

• Using the stack functions, make an algorithm that
  will determine that given a string x a) has
  matching operands (i.e. (),,) b) report an
  error if an operand is missing
• Example x (12xxs3e), correctx
  (sdfsdfs, error

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Class Problem - Summary

• 1. Make an empty stack
• 2. Read characters until end of file
• 3. If the character is an open anything, push it
  in the stack
• 4. If its a close anything,then if stack is
  empty, report an error, otherwise, pop the stack
• 5. If popped symbol is not the corresponding
  opening symbol, then report an error
• 6. At end of file, if stack is not empty report
  an error

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Stacks- other applications

• Recursion- i.e. computing for N factorial
• Operand parsing- evaluating an expression- i.e.
  ((45)(62)/5))- postfix notation ABC
  ABC
• function calls- variables and routine position
  are saved

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Stacks - Query

• How can the undo/redo function be implemented
  using stacks ?

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QUEUES

• A queue is a container of objects that are
  inserted and removed according to the FIFO
  principle.
• Operations Enqueue - insert an item at the
  rear of queue
• Dequeue - remove an item from the front of the
  queue
• Sample uses movie line
  printing queue

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The Queue Abstract Data Type

• enqueue(o)
• dequeue()

• Insert object o at the rear of the queue
  Input object Output none
• Remove the object from the front of the queue and
  return it. Input none Output object

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The Queue Abstract Data Type

• size() Returns the number of objects in the
  queue. Input none Output object
• isEmpty() Return a boolean indicating if the
  queue is empty. Input
  none Outputboolean
• front() Return the front object of the queue.
• Input none Output object

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Array Implementation

• Create a queue using an array in a circular
  fashion
• Queue consists of an N-element array Q and two
  integer variables f index of the front
  element r index of the element after the
  rear one
• Configurations normal wrapped
  around

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Queue Implementation
f
r
Array Q
f is an index to a cell Q storing the first
element, r is an index to the next available cell
in Q
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Queues- Example

• Print Jobs- All requests from workstations are
  enqueued to the print queue on a first come first
  served basis- The current (first) printjob is
  dequeued and sent to the printer for processing

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Queue - Applications

• I/O Request Handling File server - Workstation
  (print, data access,etc.)
• Telephone Call Handling
• History functions in applications

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Limitations - Using Arrays

• Maximum size needs to be predetermined
• Potential wastage of allocated memory
• Need to handle overflow

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Linked List ADT

• Head
• next
  next next
  null

Each node stores a reference to an element and a
reference, called next to another node
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Singly Linked List Queue Implementation

• Nodes connected in a chain by links head
  tail
• head of the list - front of the queue tail of
  the list - rear of the queue

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Removing at the Head

• head tail
• advance head reference head tail

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Inserting at the Tail

• create a new node
• head tail
• chain it and move the tail reference
• head tail

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Other Advantages

• Insertions and deletions are easier compared to
  an array implementation when dealing with lists

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Linked Lists - Query

• If a stack will be implemented using a linked
  list, is it better to assign the head or the tail
  as the top of the stack ? Why ?

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Double-Ended Queues

• Data structure that allows insertion and deletion
  at the front and the rear end of the queue
  (pronounced as deck)

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Doubly linked lists

• A node in a doubly linked list is like a node in
  a singly linked list except that, in addition to
  the next link, it also has a prev link to the
  previous node in the list.
• Advantage over singly linked lists deletions at
  the tail of the list can be done in constant time

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Doubly-Linked Lists
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Linked Lists - Query

• What is the running time to search for an entry
  in a linked list ? Deleting from the tail ?
  Inserting from the head ?