Array (Types of Arrays)

Arrays

Pankaj Kumar Gupta

Head, BCA Department

Durga Prasad Baljeet Singh (PG) College, Anoopshahr

District Bulandshahr (Uttar Pradesh)

 

Abstract:

This Paper describes full discussion about arrays. All topics about array like: Definition of an array, Declaration of array, Types of arrays (SDA, DDA, MDA), Memory allocation, Subscripting, Initialization, Inputting, Outputting etc.  

 

Keywords:

Array, Homogenous, Contiguous, Linear, Primary, Lower Bound, Upper Bound, SDA, DDA, MDA, Declaration, Allocation, Initialization, Subscripting, Indexing.

 

Meaning of array:

According to Cambridge Dictionary is:

“A large group of things or people, especially one that is attractive or causes administration or has been position or has been positioned in a particular way.”

 

According to Oxford Dictionary is:

“A group or collection of things or people, often one that is large or impressive.”

 

Here in Computer Application we define Array as: it is a Linear Data Structure. It is also termed as a collection of homogenous data elements. All the elements of an array share common name and stored on contiguous locations. It is also categorized into derived data types.

Example:

1.      A collection of roll numbers of 50 students (int).

2.      A collection of marks of 50 students in 6 subjects for a class (float).

3.      A collection of names of 50 students (char).

 

Categories of Arrays:

Arrays are categorized into 3 categories that are defined as follows:

1.      Single Dimensional Arrays.

2.      Two Dimensional Arrays.

3.      Multidimensional Arrays.

 

1.      Single Dimensional Array (SDA) :

It is also known as One Dimensional Array (1D). All the elements of this type of Array are stored in one dimension only. 

For example: A collection of Roll Numbers of 50 students.

Declaration of SDA:

Variables of primary data types are declared to use the same. And Arrays are categorized into secondary data types, variables of array must also be declared like primary data types. So followings are the syntaxes of array data type.

Syntax:
data_type array_name[size];

For example:

To declare Roll Numbers of 5 Students (in integer form):

int rn[5];

To declare Marks of 4 Subjects (in float form):

float m[4];

To declare Name of 10 characters (in character form):

char n[10];

Memory Allocation (SDA):

All the elements of Array (SDA) are stored at contiguous locations in memory.

Indexing or Subscripting (SDA):

Since all the elements of array share common name, to recognize the elements of an array has become the problem. To overcome this problem all the elements uses the indexing or subscripting. Indexing of SDA always starts from 0 and goes up to     n-1. Where n is the size of array.

Initialization (SDA):

Boxes created in the memory (i.e. memory allocation) must be filled with some values. Same values may be filled with initialization or may be input form user. here initialization is shown in following diagram:

Inputting (SDA):

If values of SDA are required to input from user, we may input same from user by following method:

Algorithm INPUTARRAY(A,N,LB,UB)

/* Here INPUTARRAY is an algorithm which is used to input all the elements of Array A with the Capacity of N elements. LB is Lower bound & UB is the Upper bound of Array. */

Step-1 Start

Step-2 set K=LB.

Step-3 Repeat steps 4 and 5 while K<=UB

Step-4 Input value of A[K].

Step-5 set K=K+1.

Step-6 Exit.

Outputting:

If values of SDA stored in the memory are required to show to user, we may output same to user by following method:

Algorithm OUTPUTARR(A,N,LB,UB)

/* Here OUTPUTARR is an algorithm which is used to output all the elements of Array A with the Capacity of N elements. LB is Lower bound & UB is the Upper bound of Array. */

Step-1 Start

Step-2 set K=LB.

Step-3 Repeat steps 4 and 5 while K<=UB

Step-4 print the value of A[K].

Step-5 set K=K+1.

Step-6 Exit.

 

2.      Two Dimensional Array (2DA/DDA):

It is also known as Double Dimensional Array (DDA). All the elements of this type of Array are stored in two dimensions (i.e. rows & columns) only.

For example: A collection of marks of 5 students in 3-3 subjects (float) etc.

Declaration of DDA:

Syntax:
datatype arrayname[row][col];

For example:

To declare Marks of 5 Students in 3-3 subjects (in floating point form):

float m[5][3];

Memory Allocation (DDA):

All the elements of Array (DDA) are stored at contiguous locations in memory.

float m[5][3];

Indexing or Subscripting (DDA):

Since all the elements of array share common name, to recognize the elements of an array has become the problem. To overcome this problem all the elements uses the indexing or subscripting. Indexing always starts from [0][0] and goes up to     [r-1][c-1]. Where r is the no. of rows and c is the no. of columns.

Initialization (DDA):

Boxes created in the memory (i.e. memory allocation) must be filled with some values. Same values may be filled with initialization or may be input form user. Here initialization is shown in following diagram:

Inputting (DDA):

If values of DDA are required to input from user, we may input same from user by following method:

Algorithm INPUT2DARRAY(A,R,C,LR,UR,LC,UC)

/* Here INPUT2DARRAY is an algorithm which is used to input all the elements of Array A with the Capacity of R X C elements. LR is Lower bound of Row & UR is the Upper bound Row. LC is Lower bound of Column & UC is the Upper bound Column. R is the No. of Rows & C is the No. of Columns. */

Step-1 Start

Step-2 set K=LR.

Step-3 Repeat steps 4 to 8 while K<=UR

Step-4 set J=LC.

Step-5 Repeat steps 6 and 7 while J<=UC

Step-6 Input value of A[K][J].

Step-7 set J=J+1.

Step-8 set K=K+1.

Step-9 Exit.

Outputting (DDA):

If values of DDA stored in the memory are required to show to user, we may output same to user by following method:

Algorithm OUTPUT2DARRAY(A,R,C,LR,UR,LC, UC)

/* Here OUTPUT2DARRAY is an algorithm which is used to input all the elements of Array A with the Capacity of R X C elements. LR is Lower bound of Row & UR is the Upper bound Row. LC is Lower bound of Column & UC is the Upper bound Column. R is the No. of Rows & C is the No. of Columns. */

Step-1 Start

Step-2 set K=LR.

Step-3 Repeat steps 4 to 8 while K<=UR

Step-4 set J=LC.

Step-5 Repeat steps 6 and 7 while J<=UC

Step-6 Output the value of A[K][J].

Step-7 set J=J+1.

Step-8 set K=K+1.

Step-9 Exit.

 

3.      Multidimensional Array (MDA): 

It may be 3-D, 4-D … and n-D Array. All the elements of this type of Array are stored in 3-Dimensions,  4-Dimensions, ……….. n-Dimensions. Here we will consider 3-D Array for an example. Consider A collection of marks of 5 students in 3-3 subjects for 2 Classes (float) etc.

Declaration of 3D Array:

Syntax:

datatype arrayname[room][row][col]; 

For example:

To declare Marks of 5 Students in 3-3 subjects for 2 Classes (in floating point form):
float m[2][5][3];

Memory Allocation (3DA):

All the elements of Array (3DA) are stored at contiguous locations in memory.

 

Indexing or Subscripting (3DA):

Since all the elements of array share common name, to recognize the elements of an array has become the problem. To overcome this problem all the elements uses the indexing or subscripting. Indexing always starts from [0][0][0] and goes up to [x-1][y-1][z-1]. Where x is the no. of rooms, y is the no. of rows and z is the no. of columns.
Initialization (3DA):

Boxes created in the memory (i.e. memory allocation) must be filled with some values. Same values may be filled with initialization or may be input form user. Here initialization is shown in following diagram:

Inputting (3DA):

If values of 3DA are required to input from user, we may input same from user by following method:

Algorithm INPUT3DARRAY(A,B,R,C,LB,UB,LR, UR,LC,UC)

/* Here INPUT3DARRAY is an algorithm which is used to input all the elements of Array A with the Capacity of B X R X C elements. LB is Lower bound of Room & UB  is the Upper bound Room. LR is Lower bound of Row & UR is the Upper bound Row. LC is Lower bound of Column & UC is the Upper bound Column. B is the No. of Rooms, R is the No. of Rows & C is the No. of Columns. */

Step-1 Start

Step-2 set I=LB.

Step-3 Repeat steps 4 to 11 while I<=UB

Step-4 set J=LR.

Step-5 Repeat steps 6 to 10 while J<=UR

Step-6 set K=LC.

Step-7 Repeat steps 8 and 9 while K<=UC

Step-8 Input value of A[I][J][K].

Step-9 set K=K+1.

Step-10 set J=J+1.

Step-11 set K=K+1.

Step-12 Exit.

Outputting (3DA):

If values of 3DA stored in the memory are required to show to user, we may output same to user by following method:

Algorithm OUTPUT3DARRAY(A,B,R,C,LB,UB, LR,UR,LC,UC)

/* Here OUTPUT3DARRAY is an algorithm which is used to output all the elements of Array A with the Capacity of B X R X C elements. LB is Lower bound of Room & UB  is the Upper bound Room. LR is Lower bound of Row & UR is the Upper bound Row. LC is Lower bound of Column & UC is the Upper bound Column. B is the No. of Rooms, R is the No. of Rows & C is the No. of Columns. */

Step-1 Start

Step-2 set I=LB.

Step-3 Repeat steps 4 to 11 while I<=UB

Step-4 set J=LR.

Step-5 Repeat steps 6 to 10 while J<=UR

Step-6 set K=LC.

Step-7 Repeat steps 8 and 9 while K<=UC

Step-8 Output the value of A[I][J][K].

Step-9 set K=K+1.

Step-10 set J=J+1.

Step-11 set K=K+1.

Step-12 Exit.

 

Conclusion:

An array can also be termed as a collection of homogeneous values. Anybody can treat an array as a single object by referring to it through a variable. Variable name is succeeded by square brackets (that is                  [ ] symbols) But you can also treat the components of the array as if they are themselves variables.

References:

https://dictionary.cambridge.org

https://www.oxfordlearnersdictionaries.com