Data Structures and Algorithms

implementation

-provides the internal representation of a data structure -also provides the definition of the algorithms used in the operations of the data structure

interface

-represents the set of operations that a data structure supports -only provides the list of supported operations, type of parameters they can accept and return type of these operations

characteristics of data structures

1) correctness 2) time complexity 3) space complexity

need for data structure

1) data search 2) processor speed 3) multiple requests

foundations of data structures

1) interface AND 2) implementation

kinds of algorithm analysis

1) priori analysis 2) posterior analysis

categories of algorithms

1) search 2) sort 3) insert 4) update 5) delete

Characteristics of an Algorithm

1) unambiguous 2) input 3) output 4) finiteness 5) feasibility 6) independent

execution time cases

1) worst case 2) average case 3) best case

umabigious

Algorithm should be clear and ________. Each of its steps (or phases), and their input/outputs should be clear and must lead to only one meaning.

finitieness

Algorithms must terminate after a ______ number of steps

input

An algorithm should have 0 or more well defined _____

output

An algorithm should have 1 or more well defined ______, and should match the desired _________

independent

An algorithm should have step-by-step directions which should be _________ of any programming code

data search

Consider an inventory of 1 million(106) items of a store. If application is to search an item. It has to search item in 1 million(106) items every time slowing down the search. As data grows, search will become slower

entity set

Entities of similar attributes form an ___

posterior analysis

This is empirical analysis of an algorithm. The selected algorithm is implemented using programming language. This is then executed on target computer machine. In this analysis, actual statistics like running time and space required, are collected.

average case

This is the scenario depicting the average execution time of an operation of a data structure. If a operation takes ƒ(n) time in execution then m operations will take mƒ(n) time.

best case

This is the scenario depicting the least possible execution time of an operation of a data structure. If a operation takes ƒ(n) time in execution then actual operation may take time as random number which would be maximum as ƒ(n).

worst case

This is the scenario where a particular data structure operation takes maximum time it can take. If a operation's worst case time is ƒ(n) then this operation will not take time more than ƒ(n) time where ƒ(n) represents function of n.

record

a collection of field values of a given entity

file

a collection of records of the entities in a given entity set

interface

a group of related methods with empty bodies

expression

a literal, a variable, or a sequence of operations on literals and/or variables that produces a value

identifier

a sequence of letters, digits, __, and $, the first of which is not a digit

primitive data type

a set of values and a set of operations on those values

field

a single elementary unit of information representing an attribute of an entity

processor speed

although being very high, falls limited if data grows to billion records

integers (int)

arithmetic operations

real numbers (double)

arithmetic operations

multiple requests

as thousands of users can search data simultaneously on a web server,even very fast server fails while searching the data

assignments

associate a data-type value (defined by an expression) with a variable

initializing declarations

combine a declaration with an assignment to initialize a variable at the same time it is declared

algorithm complexity

considers TIME and SPACE

declarations

create variables of a specified type and name them with identifiers

correctness

data structure implementation should implement its interface correctly

statements

define the computation by creating and manipulating variables, assigning data-type values to them, and controlling the flow of execution of such operations

priori analysis

his is theoretical analysis of an algorithm. Efficiency of algorithm is measured by assuming that all other factors e.g. processor speed, are constant and have no effect on implementation.

attribute and entity

is that which contains certain attributes or properties which may be assigned values

group items

item that are divided into sub items

elementary items

items that cannot be divided

space factor

measured by counting the maximum memory space required by the algorithm

time factor

measured by counting the number of key operations such as comparisons in sorting algorithm

space complexity

memory usage of a data structure operation should be as little as possible

operator

names a data-type operation

variable

names a data-type value

loops

provide for a more profound change in the flow of execution—execute the statements in a block as long as a given condition is true

conditionals

provide for a simple change in the flow of execution—execute the statements in one of two blocks

data item

refers to single unit of values

time complexity

running time or execution time of operations of data structure must be as small as possible

literal

source-code representation of a value

characters (char)

the alphanumeric characters and symbols that you type

booleans

the set of values { true, false } with logical operations

delete algorithm

to delete item in a datastructure

insert algorithm

to insert item in a datastructure

search algorithm

to search an item in a datastructure

sort algorithm

to sort items in certain order

data

values or set of values

continue statement

which immediately begins the next iteration of the loop

break statement

which immediately exits the loop

feasibility

Should be _________ with the available resources