Slide 1
Data Structure and AlgorithmsContentsAbstract Data
TypesComplexity AnalysisHashingIntroduction to Graphs and
TreesShortest Paths: Dijkstras AlgorithmMinimum Spanning Trees:
Prims and Kruskals Algorithm2ContentsAbstract Data TypesStackQueue
and Priority QueueLinked ListsComplexity
AnalysisHashingIntroduction to Graphs and TreesShortest Paths:
Dijkstras AlgorithmMinimum Spanning Trees: Prims and Kruskals
Algorithm3StackA stack is a linear data structure which allows
access to only one data item: the last item inserted [1, 2].The
last tray put on the stack is the first tray removed from the
stack.Stack is called an LIFO structure: Last in First
out.4Operators of Stack in STLClear( ) Clear the stack.empty()
Check to see if the stack is empty.push(el) put the element el on
the topmost of the stack.pop() Remove the topmost element from the
stack.top() Return the topmost element in the stack without
removing.5Operation Executed on a Stack6Push (10)Push (5)Pop()Push
(15)Pop ()1051010Push (7)1510715101510ContentsAbstract Data
TypesStackQueue and Priority QueueLinked ListsComplexity
AnalysisHashingIntroduction to Graphs and TreesShortest Paths:
Dijkstras AlgorithmMinimum Spanning Trees: Prims and Kruskals
Algorithm7QueueA queue is simple a waiting line that grows by
adding elements to the end and shrinks by taking elements from the
front.Queue is an FIFO structure: First in First out.8Queue
Operations in STLback() return the last element.empty() return true
if the queue includes no element and false otherwise.front() return
the first element.pop() remove the first element.push(el) insert el
at the end of queue.size() return the number of elements.
9Operation Executed on a Queue1010Push (10)Push (5)Pop()Push
(15)Pop ()Push (7)10555155157157Priority QueuePriority queue is
exactly like a regular queueor stackdata structure, but
additionally, each element is associated with a priority.Priority
queue: elements are pulled highest-priority or lowest-priority
first.11Operations of Priority
Queue431093026328911250143109302501632891FrontRearFrontRear109302501632891FrontRear43ContentsAbstract
Data TypesStackQueue and Priority QueueLinked ListsComplexity
AnalysisHashingIntroduction to Graphs and TreesShortest Paths:
Dijkstras AlgorithmMinimum Spanning Trees: Prims and Kruskals
Algorithm13Linked ListsA linked list is a collection of nodes
storing data and links to other nodes.Nodes can be located anywhere
in memory, and linked from one node to another by storing the
address.14Links in a list15firstDataNextDataNextDataNextNullLinked
ListLinkLinkLinkDataNextLinkInserting a New
Link16firstDataNextDataNextDataNextNullLinked
ListLinkLinkLinkDataNextLinka. Before InsertionLinked
ListfirstDataNextDataNextDataNextNullLinkLinkLinkDataNextLinkDataNextb.
After InsertionDeleting a
Link17firstDataNextDataNextDataNextNullLinked
ListLinkLinkLinkDataNextLinka. Before deletingLinked
ListfirstDataNextDataNextNullLinkLinkLinkDataNextLinkb. After
deletingContentsAbstract Data TypesComplexity
AnalysisHashingIntroduction to Graphs and TreesShortest Paths:
Dijkstras AlgorithmMinimum Spanning Trees: Prims and Kruskals
Algorithm18Computational ComplexityA measure of resources in terms
of Time and SpaceIf A is an algorithm that solves a decision
problem f then run time of A is the number of steps taken on the
input of length n.Time Complexity T(n) of a decision problem f is
the run time of the best algorithm A for f.Space Complexity S(n) of
a decision problem f is the amount of memory used by the best
algorithm A for f.19Big-O NotationThe Big-O indicates the time or
the memory needed.The Big-O notation is used to give an
approximation to run-time-efficiency of an algorithm.
20The Big-O of an Algorithm AIf an algorithm A requires time
proportional to f(n), then the algorithm A is said to be of order
f(n), and it is denoted as O(f(n)).If an algorithm A requires time
proportional to n2, then order of the algorithm is said to be
O(n2).If an algorithm A requires time proportional to n, then order
of the algorithm is said to be O(n).
Similarly, for algorithms having performance complexity
O(log2(n)), O(n3),21Example1-D array, determine the Big-O of an
algorithm;
Determine the Big-O:Ignoring constants such as 2 and 3, the
algorithm is of the order n.The Big-O of algorithm is O(n)22Line
noInstructionsNo of execution stepsline 1sum = 0;1line 2for ( i =
0; i < n; ++i )n+1line 3 sum += a[ I ];nline 4cout
