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Data Structure and
Algorithm: CIT231
Lecture 2:
Arrays
Bajuna Salehe
[email protected]
Arrays
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Data structures can be classified into two
categories:
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Linear Data Structure
Non Linear Data Structure
Linear data structure – its elements form a
sequence.
Non linear data structure – its elements do
not form a sequence.
Arrays

Two ways of representing linear data
structure in memory.


Through linear relationship between the elements
of by means of sequential memory locations.
Such linear structures are called Arrays
- An array of 5 integers
Through linear relationship between the elements
represented by means of pointers or links.
Arrays
In linked list each node contains the data
and address of the next node.

- A linked list containing 4 integers
Arrays are useful when the number of
elements to be stored are is fixed.
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Easy to traverse, search and sort
Linked lists are used when the number of
data items in the collection are likely to vary.
They are hard to maintain.
So What are Arrays?
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An array is a finite collection of similar
elements stored in adjacent memory
locations.
By ‘finite’ we mean that there are specific
number of elements in an array.
By ‘similar’ we mean that all the elements in
array are of the same type.

E.g An array may contain all integers or all
characters.
What are arrays

An array containing ‘n’ number of elements is
referenced using an index that varies from 0
to n-1.
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For example, the elements of an array arr[n]
containing n elements are denoted by arr[0],
arr[1], arr[2],…,arr[n-1].
0 is the lower bound and n-1 is the upper bound
of the array.
The lowest index of an array is called its
lower bound
The highest index is called its upper bound
The number of elements in the array is called
its range.
So What are Arrays?


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Intuitively an array is a set of an index and a
value. For each index there is a value
associated with it.
Arrays are fundamental data structures in
that they have direct correspondence with
memory systems on virtually all computers.
To retrieve the contents of a word from a
memory in a machine language, we provide
an address
So What are Arrays?


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Thus we could think of the entire computer
memory as an array, with the memory
addresses corresponding to array indices.
In C++ it is the responsibility of programmer
to use indices that are non negative and
smaller than the array size.
Neglecting of that responsibility is the one of
the common programming mistakes.
Arrays Categories

There are two types of arrays.
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One dimensional arrays
Multidimensional arrays
Multidimensional array can be a 2-D array, 3D array, 4-D array etc.
To know that an array is 1-D or 2-D is
determined by array syntax used to declare
that array.
Array Declaration

The following examples show how to declare
one-dimensional as well as multidimensional
arrays.
- arr1[5] – A 1-D array holding 5 elements.
- arr1[2][5] – A 2-D array with 2 rows and 5
columns holding 10 elements.
- arr1[2][5][3] – A 3-D array with 2-D arrays
each of which is having 5 rows and 3
columns thus holding totally 30 elemnts.
Example of the Application of
Dimension Arrays

If we want to store and process the premier
league results we can use 2 D arrays:
Array Declaration
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Array declaration necessitate that any array
cannot be used before you have declared it.
Note the elements field in the brackets []
must be a constant value since arrays are
blocks of non dynamic memory whose size
must be determined before execution
For variable length use dynamic memory
Initialising arrays
The elements of global and static arrays are
automatic initialised with their default values.
 We have the possibility to assign initial
values to each one of its elements by
enclosing the values in braces { }
int billy [5] = { 16, 2, 77, 40, 12071 }
 This declaration would have created an array
like this:

Initialising arrays
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The amount of values between braces { }
must not be larger than the number of
elements that we declare for the array
between square brackets [ ].
For example, in the example of array billy we
have declared that it has 5 elements and in
the list of initial values within braces { } we
have specified 5 values, one for each
element.
Initialising arrays
When an initialization of values is provided
for an array, C++ allows the possibility of
leaving the square brackets empty [ ].
 In this case, the compiler will assume a size
for the array that matches the number of
values included between braces { }:
Int billy [] = { 16, 2, 77, 40, 1207};
 After this declaration, array billy would be 5
ints long, since we have provided 5
initialization values.

Accessing the value of an
Array
The elements of an array can be accessed
individually as if it is a normal variable. The
format is as:
Name[index]
 Following the previous examples in which
billy had 5 elements and each of those
elements was of type int, the name which we
can use to refer to each element is the
following:

Accessing the value of an
Array
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For example, to store the value 75 in the third
element of billy, we could write the following
statement:
billy[2] = 75;

For example, to store the value 75 in the third
element of billy, we could write the following
statement:
billy[2] = 75;
Accessing the value of an
Array

To pass the value of the third element
of billy to a variable called a, we could
write:
a=billy[2];

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In C++ it is syntactically correct to exceed the
valid range of indices for an array.
This can create problems, since accessing
out-of-range elements do not cause
compilation errors but can cause runtime
errors.
Array Operations

There are several operations that can be
performed on arrays.
Operation
Description
Insertion
Adding a new element to an array
Deletion
Removing an element from an array
Traversal
Processing each element in the array
Search
Finding the location of an element with a
given value
Sorting
Organising the element in some order
Merging
Combining two arrays into single array
Reversing
Reversing the elements of an array
Array Insertion

There are generally two scenarios for
inserting a value into an array.

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Inserting a value into a specified location of an
array.
Inserting a value into a sorted array
Array Insertion

If a value needs to be inserted into a
specified location, the programmer can
simply follow the following steps.
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Insert the value into the position
Move all other following elements to the next
position
Increment the size of the array.
Array Insertion

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If a value needs to be inserted into a sorted
array, the programmer must first find the
location in the array where the value should
be placed in order to keep the original order
in intact.
Once the target location is found, the steps
outlined in the previous slide can then be
executed.
Array Deletion
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Array deletion aimed at removing a certain
element at particular position in that array.
This operation can be carried out through a
deletion function which deletes the element at
the given position
While doing so it shifts the numbers placed
after the position from where the number is to
be deleted, one place to the left of their
existing positions.
The place that is vacant after deletion of an
element is filled with 0.
Reversing Array
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In the reversing operation the entire array is
reversed by swapping the elements.
Merging of Two Arrays
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Merging of two arrays involve two steps.
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Sorting the arrays are to be merged.
Adding the sorted elements of both the arrays to a
new array in a sorted order.