LECTURE 2: DATA STRUCTURES An array is a data structure consisting of a group of elements that are accessed by indexing. An array is a situation where a set of data items are conveniently arranged into a sequence & referred to by a single identifier. Each data item of an array is known as an element & the elements are referenced by a common name known as the array name An array is a collection of objects of the same data type, allocated contiguously in memory. Individual objects in an array, called elements, are accessed by their position in the array.
Transcript
LECTURE 2: DATA STRUCTURESAn array is a data structure consisting of a group of
elements that are accessed by indexing.An array is a situation where a set of data items are
conveniently arranged into a sequence & referred to by a single identifier.
Each data item of an array is known as an element & the elements are referenced by a common name known as the array name
An array is a collection of objects of the same data type, allocated contiguously in memory. Individual objects in an array, called elements, are accessed by their position in the array.
AN ARRAY The position is given by an index, which is also
called a subscript.An array facilitates the coding of repetitive
tasks by allowing the statements executed on each element to be put into a loop that iterates through each element in the array.
An array, also known as a vector or list (for one-dimensional arrays) or a matrix (for two-dimensional arrays)
ARRAYS
An Array is a variable. It can hold a series of values, essentially, a list of
values.An array provides the logical convenience of being
able to reference all its values by using the single array name.
As a variable, an array is an area in memory, random access memory (RAM) reserved under a name, and referred to by name, into which values can be assigned.
ARRAYS
An array is a structure that holds multiple values of the same type.
An array - known as a vector or list (for one-dimensional arrays) or a matrix (for two-dimensional arrays)
It is one of the simplest data structures.
Examples
E.g. Cartoons = (Popeye, Scooby Doo, Tom & Jerry)
Data Structures = (Stacks, Queues, List)Individual data items are referred to by stating
their position e.g. Cartoons [1] is PopeyeAn array is a structure containing one or more
subdivisions each of which may contain data
TYPES OF ARRAYS
One Dimensional ArrayTwo Dimensional Array
a) One Dimensional Array
Within the array, subscripts are used to indicate the individual elements, written as integers within square brackets.
195.00 491.82 299.95 320.00Thus credit [1] would be the first deposit in the
checking account; credit [2] would be the second deposit and so on.
Credit Array:
[195.00] [491.82] [299.95] [320.00]
Debit Array:
14.79 52.25 44.7516.13
One Dimensional Array
The above diagrams shows a credit and Debit Array in which
They have a single subscript and are called one-dimensional arrays; often thought of as lists.
In mathematics such arrays are often called vectors.
A one dimensional array is therefore an array having only one subscript & the individual elements are of the same type.
EXAMPLE 2
To store the salaries of up to 50 employees in a firm we can use an array called salary in which salary [1], salary [2] … salary [50] are real variables that will store the salaries of the first employee, the second employee…up to the 50th employee.
The array contains real elements and the subscripts run over the integer sub range [1………50].
b) Two Dimensional ArrayA two dimensional array is a generalization of a
linear list, for example an m x n matrix.The rows and column list essentially account
for two dimensional structure of a matrix. An array contains a sequence of elements all of
the same element type. The element type can be any type, even an
array (but not the same array), thus we have an array of arrays
EXAMPLE
c0 c1 c2 c3
r0 0 1 2 3
r1 1 2 3 4
r2 2 3 4 5
r3 3 4 5 6
r4 4 5 6 7
EXAMPLE
Here, we have an array with five rows and four columns.
It has twenty total elements. However we say it has dimension five by
four, not dimension twenty
EXAMPLE
We have a pay array containing 50 rows with 26 real elements on each row. Each row represents an employee and each column a pay period i.e. ( a two – dimensional array ).
The program will need to store a two – part record for each employee, containing both the integer employee number & ID– number salary.
An employee record is therefore heterogeneous & cannot be stored entirely in one array.
Instead we will use a pair of arrays, ID & salary which are said to be parallel arrays, because their subscripts track together: i.e. salary [I] & ID [I] together make up the data record for the 1st employee.
Example
Salary [1] Salary [2] Salary [3]
Example
ID [1] Salary [2] Salary [3]
Question
Class, What are the Components of an
Array???
COMPONENTS OF AN ARRAY
An array consists of elements, data type, subscript & the square brackets.
Arrays hold a series of data elements, usually of the same size & data type.
The series could be of data types such as integers, strings or even floats.
COMPONENTS OF AN ARRAY
Individual elements are accessed by their position in the array.
The position is given by an index, which is also called a subscript.
The index usually uses a consecutive range of integers
CHARACTERISTICS OF ARRAYS
Homogeneous: They store one type of data elements.
Cartesian: Arrays allow their access through an index. This referencing is possible because arrays have subscripts and elements that enable access via index
CHARACTERISTICS OF ARRAYS
Subscripts: In Pascal the subscripts are written as integers within square brackets thus credit [1] would be the first deposit in the checking account, credit [2] would be the second deposit and so on.
We use subscripts to access the individual elements i.e. in a one-dimensional array, it has only one subscript & is imagined as a list or vector.
The elements are stored in sequence in memory beginning with the address of the lowest-subscripted element.
A two dimensional array has two subscripts & is imagined as a table with rows & columns.
Form the basis for several more complex data structures, e.g. hash tables, stacks and queues.
Arrays provide a very special way of sorting or organising data in a computers memory
Arrays serves as parameters in computationArrays help reduce length of algorithm
FUNCTIONS OF ARRAYS
OPERATIONS ON ARRAYS
Creating an array: The create function produces a new, empty array of the appropriate size.
Assigning the array: Once an array has been created a value from a field or variable, is then assigned to an element of the array. The syntax used is:
Array name {element number}:= value. Array elements are numbered by their position in the array, starting at one and going up.
Additionally, every array has zero element number.
OPERATIONS ON ARRAYS
Retrieving : Retrieve operation accepts an array and an index.
This returns the value associated if the index is valid, or error if the index is invalid.
Searching : Searching methods are designed to take advantage of the organization of information & thereby reduce the amount of effort to either locate a particular item or to establish that it is not present in a data set.
OPERATIONS ON ARRAYS
Sorting and Merging: Sorting & merging provide us with a means of organizing information to facilitate the retrieval of specific data.
Field or variable: = array name {element number}
OPERATIONS ON ARRAYS
Displaying arrays: To display the contents of array on a form, you simply give an active object capable of displaying an array
The contents of the array will then automatically be displayed in that object. The objects that can display the contents of an array are: Pop-up Lists/Drop-down Lists, and Combo Boxes.
AN EXAMPLE????
APPLICATION OF ARRAYS
CLASS DISCUSSION
ADVANTAGES OF ARRAYS
Arrays permit efficient random access in constant time making them most appropriate for storing a fixed amount of data which will be accessed in an unpredictable fashion.
This means that the time taken to access a[i] is the same for each index.
Iterating through an array has good locality of reference, and so is much faster than iterating through a linked list of the same size, which tends to jump around in memory.
ADVANTAGES OF ARRAYS
Compact data structures; storing 100 integers in an array takes only 100 times the space required to store an integer, takes no additional storage space.
Arrays simplify algorithms by compressing repetitive iterations, as they perform computations on collections of data with common attribute.
DISADVANTAGES OF ARRAYS
It has a single fixed sizeTherefore, there are some indexes which refer
to invalid elements, e.g., the index 17 in an array of size 5.
This brings range error, since it is difficult to allow a subscript to reach a value outside its declared range, as this will make a compiler to generate an error.
DISADVANTAGES OF ARRAYS
Multidimensional arrays cannot be accessed by simple indexing & these incur additional overheads in programming its access.
For a large number of programming languages, except for Java, the array sizes must be known at compile time, since once space is allocated it cannot be extended, as there is no guarantee that the next block of memory will be free at some time later in the execution making arrays static data structures.
REFERENCESEncyclopedia of Computer Science (3rd Ed) (1993) Edited
by Ralston, A and Reilly E. D. London: Chapman and HallFrench, C. S. (1996) Computer Science. 5th ed. London:
Book PowerMegson, G.M. (1992) An Introduction to Systolic Algorithm
Design. Oxford: ClarendonSalmon, W. I. (1991) Structures and Abstractions: An
introduction to Computer Science with Pascal. Boston. Irwin Inc.
Society Schools Committee (1998) A glossary of Computing terms (9th ed.) England: Longman
Williams, P.M. (2004) Data Structures. Sussex: University of Sussex Computer Science and Artificial Intelligence.
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