data structure and algorithms assignment

7/23/2019 Data Structure and Algorithms Assignment

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DATA STRUCTURE AND ALGORITHMS

ASSIGNMENT

QUESTION-01: DEFINE ARRAY

ANSWER:

In programming, a series of objects all of which are the same size and type.

Each object in an array is called an array element. For example, you could

have an array of integers or an array of characters or an array of anything

that has a dened data type. he important characteristics of an array are!

Each element has the same data type "although they may have di#erent

values$.

he entire array is stored contiguously in memory "that is, there are no gaps

between elements$.

%rrays can have more than one dimension. % one&dimensional array is called

a vector ' a two&dimensional array is called a matrix.

EXPLAIN ALGORITHM FOR INSERTING ELEMENTS IN AN ARRAY?

ARRAY Inser!"n

Inserting an element at end of linear array can be done easily if the array islarge enough to accommodate new item.

If the element is to be inserted in the middle of array then half members

must be moved downward to new location to accommodate new element by

(eeping the order of other elements

ARRAY INSERTION ALGORITHM

%lgorithm for Insertion: "Inserting into Linear Array $ I)*E+ "%, ), -, IE$

/. 0Initialize counter1 *et 2! 3 ).

4. +epeat *teps 5 and 6 while j 73 ('

5. 0ove jth element downward.1 *et % 02 8 /1! 3% 021.

6. 09ecrease counter1 *et 2! 3 2&/



0End of step 4 loop1

:. 0Insert element1 *et % 0-1!3IE.

;. 0+eset )1 *et )!3)8/

<. E=I.

QUESTION-0#: DEFINE DATA STRUCTURE AND EXPLAIN ALGORITHMIC

NOTATION IN DATA STRUCTURE?

In computer science, a data structure is a particular way of organizing data in

a computer so that it can be used e>ciently. 9ata structures can implement

one or more particular abstract data types "%9$, which are the means of

specifying the contract of operations and their complexity. In comparison, adata structure is a concrete implementation of the contract provided by an

%9.

9i#erent (inds of data structures are suited to di#erent (inds of applications,

and some are highly specialized to specic tas(s. For example, relational

databases most commonly use ?&tree indexes for data retrieval, while

compiler implementations usually use hash tables to loo( up identiers.

9ata structures provide a means to manage large amounts of data e>ciently

for uses such as large databases and internet indexing services. @sually,

e>cient data structures are (ey to designing e>cient algorithms. *ome

formal design methods and programming languages emphasize data

structures, rather than algorithms, as the (ey organizing factor in software

design. *toring and retrieving can be carried out on data stored in both main

memory and in secondary memory.

ALGORITHMIC NOTATION

%symptotic notation is a way of expressing the cost of an algorithm. Aoal of

%symptotic notation is to simplify %nalysis by getting rid of unneeded

information

Following are the asymptotic notation!

$!%&O' N"(!"n )O* :

77 B"g"n$$ 3 C f"n$ ! there exist positive constants c and nD such that D

f"n$ cg"n$ for all n 7 nD G.



77 It is asymptotic upper bound.

77he function f"n$ 3 B"g"n$$ i# there exist positive constants c and nD such

that f"n$ H c g"n$ for all n, n nD.

77 he statement f"n$ 3 B"g"n$$ states only that g"n$ is an upper bound onthe value of f"n$ for all n, n no.

O+e%( N"(!"n ),*

77 J "g "n$$ 3 C f"n$ ! there exist positive constants c and nD such that D c

g"n$ f"n$ for all n 7 nD G

77 %symptotic lower bound.

77 he function f"n$ 3 J"g"n$$ iff there exist positive constants c and nD

such that f"n$ c g"n$ for all n, n nD.

77 he statement f"n$ 3 J"g"n$$ states only that g"n$ is only a lower bound

on the value of f"n$ for all n, n no.

T'e( N"(!"n )*

77 K"g"n$$ 3 C f"n$ ! there exist positive constants c/ and c4 and nD such

that D c/ g"n$ f"n$ c4 g"n$ for all n 7 nD G

77 he function f"n$ 3 K"g"n$$ iff there exist positive constants L/, L4 and

nD such that L/ g"n$ H f"n$ H L4 g"n$ for all n, n nD.

L!.e "' N"(!"n )"*

77 o"g"n$$ 3 C f"n$ ! for any positive constant c7D , there exists a constant

nD such that D f"n$ c g"n$ for all n 7 nD G

77 Me use o notation to denote an upper bound that is not asymptotically

tight.

77 he denitions of B&notation and o&notation are similar. he main

di#erence is that in f"n$ 3B"g"n$$, the bound D f"n$ cg"n$ holds for some

constant c7D but in f"n$ 3B"g"n$$, the bound D f"n$ c g"n$ holds for all

constants c 7 D.

L!.e "+e%( N"(!"n )/*



77 w"g"n$$ 3 C f"n$ ! for any positive constant c7D , there exists a constant

nD such that D c g "n$ f"n$ for all n 7 nD G

77 Me use w notation to denote an lower bound that is not asymptotically

tight.

data structure and algorithms assignment

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