10. Introduction to Datastructure

Introduction to Algorithms
By
Nilesh Dalvi
Lecturer, Patkar-Varde College.Lecturer, Patkar-Varde College.
http://www.slideshare.net/nileshdalvi01
Java and DataJava and Data
StructuresStructures

Algorithm
The algorithm is defined as the a collection of
unambiguous instructions occurring in some specific
sequence and such an algorithm should produce
output for given set of input in finite amount of time.
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

Algorithm
• write an algorithm to count the sum of n numbers
Algorithm sum (1, n)
{
//Problem Desc: Algorithm for finding sum of n numbers
//Input: 1 to n numbers
//Output: Sum of n numbers
result := 0;
for i:= 1 to n do i:= i + 1
result := result + i;
}

Algorithm
• write an algorithm to check whether the given no is
even or odd.
Algorithm EvenOddTest(val)
{
//Problem Desc: Algorithm for checking whether the given no is even or odd.
//Input: 1 to n number
//Output: Even or odd number
if(val % 2 == 0)
write("No is even");
esle
write ("No is odd");
}

Algorithm
• write an algorithm for sorting the given elements
Algorithm Sort (a, n)
{
//Problem Desc: Algorithm for sorting the elements.
//Input: An array
//Output: Sorted array
for i:=1 to n do
{
for j:= i +1 to n-1 do
{
if(a[i]) > a[j]) then
{
temp := a[i];
a[i] := a[j];
a[j] := temp;
}
}
write("List is sorted!");
}
}

Algorithm
• write an algorithm for calculating factorial of n
numbers
Algorithm factCalc (n)
{
//Problem Desc: For calculating factorial of given no
//Input: Number
//Output: Factorial of given number
if n := 1 then
return 1;
else
return n * factCalc(n - 1);
}

Algorithm
• write an algorithm for multiply two matrices
Algorithm mulMatrix (A, B, n)
{
//Problem Desc: Multilpy two matrices
//Input: Matrix A and Matrix B
//Output: Matrix C
for i := 1 to n do
for j := 1 to n do
C[i][j] := 0;
for k := 1 to n do
C[i][j] := C[i][j] + A[i][k] * B[k][j];
}

Fundamentals of analysis of algorithms
• The efficiency of an algorithm can be decided by
measuring the performance of an algorithm.
• We can measure the performance of an algorithm by
computing two factors
– Amount of time required by an algorithm to execute (time
complexity)
– Amount of storage required by an algorithm (space
complexity)

Space Complexity
• Space complexity can be defined as amount of memory
required by an algorithm to run.
• To compute space complexity we use two factors : constant
space and variable space
• Constant space includes instructions, variables and constants
• Variable space includes dynamic allocations, function recursion.
• Space requirement, s(p) = C + sp
• sp is the space dependent upon instance characteristics.

Time Complexity
• The time complexity of an algorithm is the amount of computer
time required by an algorithm to run complete the task.
• The time complexity, T(p), taken by a program p is the sum of
the compile time and the run time.
• Total Time, T(p) = compile time + run (execution) time

Asymptotic Notations:
• To choose the best algorithm, we need to check efficiency of
each algorithm.
• Efficiency can be measured by computing space and time
complexity.
• So, Asymptotic notation is a shorthand way to represent the
time complexity.
• Using asymptotic notations we can give time complexity as
“fastest possible”, “slowest possible” or “average time”.

Big Oh Notation:
• Denoted by ‘O’
• Method if representing upper time of representing the upper
bound of algorithms running time.
• Using big Oh notation we can give longest amount of time taken
by the algorithm to complete.

Omega Notation:
• Denoted by ‘Ω’
• It is used to represent the lower bound of algorithm running
time.
• Using omega (Ω) notation we can denote shortest amount of
time taken by algorithm.

Theta Notation:
• Denoted by ‘Θ’
• By this method the running time is between upper bound and
lower bound.

Data Structure
• Data may be organized in many different ways.
• A data structure is a arrangement of data in a
computer memory or on a disk.
• The logical or mathematical model of a particular
organization of data is called data structure.

Data Structure

Data Structure Operation
Data appearing in data structures are processed by
means of operations.
Operations are:
•Traversing: Accessing each record exactly once so that
certain items in the record may be processed.
•Searching: Finding the location of the record with a
given key value, or finding the locations of all records
which satisfy one or more conditions.

Data Structure Operation
• Inserting: Adding the new record to the structure.
• Deleting: Removing a record from the structure.
Special operations:
• Sorting: Arranging the records in some logical order
• Merging: Combining the records in two-different
sorted files into a single-sorted file.

Linear
1. Array:
2. Stack
3. Queue
4. Linked List

Array
• An array is a collection of homogeneous type of data
elements.
• An array is consisting of a collection of elements .
• Operation Performed On Array:
1. Traversing
2. Search
3. Insertion
4. Deletion
5. Sorting
6. Merging
1
2
3
4
5
Representation of array

Stack
• A Stack is a list of elements in which an element may
be inserted or deleted at one end which is known as
TOP of the stack.
• Operation Performed On Array:
1. Push: add an element in stack
2. Pop: remove an element in stack
3. Peek :Current processed element
a
b
c TOP

Queue
• A queue is a linear list of element in which insertion
can be done at one end which is known as REAR and
deletion can be done which is known as FRONT.
• Operation:
1. Insertion : add a new element in queue
2. Deletion: Removing an element in queue

Queue

Linked List
• A Linked list is a linear collection of data elements .
• It has two part one is info and other is link part.
• info part gives information and link part is address of
next node
• Operation:
1. Traversing
2. Searching
3. Insertion
4. Deletion

Non-Linear
1. Graph
2. Tree
3. Table
4. Set

Graph
• A graph is a collection of sets V and E where V is a
finite non-empty set of vertices and E is finite non-
empty set of edges.
• Vertices – node in graph
• Edges – Two adjacent nodes are joined by edges.
• Graph G = {V, E}
• Operation:
1. Insertion
2. Deletion
3. Searching

Tree
• Tree is a finite set of one or more nodes such that
– There is a specially designed node called root.
– The remaining nodes are partitioned into n>=0 disjoint sets T1, T2, T3,
…., Tn are called the sub-trees of the Root.
• Operation:
1. Insertion
2. Deletion
3. Searching

Tables
• This is kind of data structure plays an important role in
information retrieval.
• Types of tables:
– Rectangular
– Jagged
– Inverted
– Hash
• Operation:
1. Insertion
2. Deletion
3. Searching
Key Value
0 “Abc”
1 “Pqr”

Sets
• Heap is a complete binary tree

10. Introduction to Datastructure

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