Review of basic data structures

 Review of Basic Data Structures
 The List ADT
 Stack ADT
 Queue ADT
 Array and Linked Implementations using
Template Classes in C++.
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 To learn the implementation of list, stack,
and queueADTs in C++ using templates.
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 A data object is a set of instances or values.
 Examples:
 An instance may be primitive or may be
composed of other instances. (Eg: 123, total)
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 A data structure is a data object together with
the relationships that exist among the
instances and among the individual elements
that compose an instance.
 These relationships are provided by specifying the
operations of interest.
 Most frequently used data objects and their
operations are already implemented in C++ as
primitive data types.
▪ Boolean (bool)
▪ Integer (int)
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 Each instance of linear list (or ordered list) is an
ordered collection of elements.
 e0, e1, e2, e3, e4, …, en-1
 Index of ei is i.
 n is the list length or size.
 When n = 0, the list is empty.
 When n > 0, e0 is the zeroth element, en-1 is the last.
 e0 comes before e1, e1 comes before e2, and so on.
 Examples:
 List of students in a class in alphabetic order.
 List of percentages of students in decreasing order.
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 Operations on a Linear List
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 ADT provides a specification of
 Instances, and
 Operations that are to be performed.
 It is independent of any programming
language.
 All representations of ADT must satisfy the
specification.
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 An array is used to store the list of elements.
 If we use one dimensional array, the elements of
the array are accessed as:
 A[0] accesses zeroth element.
 A[1] accesses first element.
 A[n] accesses nth element.
 Elements are mapped to positions in the array.
 location (i) = i is the most natural mapping.
 other ways of mapping are also possible.
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 Different ways of mapping [5, 2, 4, 8, 1]
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 Each element of an instance of a data object
is represented in a cell or a node.
 Each node keeps the location of next node,
called a link or a pointer.
 As each node links to only one other node,
the structure is called as a singly linked list or
a chain.
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 Removing the third element from the list
involves:
 Locating the second node.
 Linking the second node to the fourth node.
 Similar steps are followed for removing any
element.
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 To insert an element as ith element,
 Find the location on i-1th element.
 Insert the new node after that element.
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 Defines a data type called chainNode for
storing nodes.
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 Implements a
linear list as
singly linked
list of nodes.
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Array and Linked List Representation
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 A stack is a linear list in which insertions and
removals take place at the same end, called
top.The other end is called bottom.
 Insertions are also called as pushes.
 Removals are also called as pops.
 A stack is a LIFO (Last In First Out) list.
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 Adding element E to the following stack.
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 Stack of books in a library.
 Stack of CDs.
 Stack of papers in a printer.
 Identify more examples of stacks from real
world?
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 For implementing function calls.
 For implementing recursive functions.
 For converting infix expression to postfix.
 For evaluating postfix expressions.
 For construction of compilers.
 For depth first search of a graph.
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 Can be implemented in two ways:
 derivedArrayStack
▪ Derived from arrayList and stack classes.
▪ Uses the methods of arrayList for performing push and
pop operations.
▪ Efficiency of this class is low due to the usage of
methods of arrayList for push and pop.
 arrayStack
▪ Derived from stack class.
▪ Improves the run-time performance.
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 Better in
performance than
derivedArrayStack
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 Left end of the chain or the right end of the
chain can be used as a stack top.
 Using right end as top takes more time.
 So, left end of the stack is used as top.
 Push and pop operations are done at the left
end.
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 Can be implemented in two ways:
 derivedLinkedStack
▪ Derived from chain and stack classes.
▪ Can be obtained by changing derivedArrayStack.
 linkedStack
▪ Derived from stack.
▪ Improves the run-time performance.
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Array and Linked Representations
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 A queue is a linear list in which insertions take
place from rear end and deletions take place
from front end.
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 Railway reservation counters.
 Soda vending machines.
 Normally at all service centers.
 What other example queues can you think of?
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 For job processing in operating systems.
 For printing documents in printers.
 For breadth-first search of a graph.
 For file handling in distributed file systems.
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 ith element may be stored in ith location.
 location(i) = i
 queueFront and queueBack are used to
denote front and rear of the queue.
 queueFront = 0.
 Queue size = queueBack+1.
 queueBack = -1, for empty queue.
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 Insertion
 Increments queueBack by 1.
 Places new element in queue[queueBack].
 Takes O(1) time.
 Deletion
 Shifts all the elements one position to the left.
 Takes O(n) time, where n is number of elements.
 Very time consuming.
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 We can improve the deletion operation by the
following method:
 Use the equation
▪ location(i) = location(front element) + i.
 Does not require shifting of elements by one
position to the left.
 Increment queueFront by 1 for every deletion.
 Queue is empty, if queueBack < queueFront.
 Takes O(1) time.
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 When the second equation is used, every
deletion increments queueFront by 1.
 This may result in a situation shown below,
where no new elements can be inserted even
when space is available.
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 One method is
 To shift all the elements to the left end, which
leaves space at the right end allowing insertions.
 Deletion time is O(1).
 Insertion time is O(arrayLength) in worst case.
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 Another method is
 To insert the elements from the queueFront when
no space is available at the queueBack.
 Both insertion and deletion take O(1) time.
 In this case, the array is viewed as a circle.
 The queue is called as a circular queue.
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 Position 0 is preceded by arrayLength-1.
 When queueBack = arrayLength-1, then the
new element is inserted into position 0.
 Uses the following equation:
 location(i) = (location(front element) + i) %
arrayLength
 Queue is empty iff
 queueFront = queueBack = 0 (initially)
 queueFront = queueBack (otherwise)
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 Even when Queue is full, the condition
queueFront = queueBack becomes true.
 To avoid this confusion , a queue is never
made full, and the size is doubled whenever
such a situation arises.
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 Same as arrayStack, except push operation.
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 May be implemented in the following two
ways:
 But, which is better?
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 Initial values
 queueFront = queueBack = NULL.
 Boundary value
 queueFront = NULL iff queue is empty.
 All operations require O(1) time.
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 Linear Lists
 Array lists
 Linked lists
 Stacks
 Array implementation
 Linked implementation
 Queues
 Array implementation
 Linked implementation
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Review of Basic Data Structures
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Review of basic data structures

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Review of basic data structures