Arrays

Defination:

Array is a collection of homogeneous data elements with following properties

1. All the data elements are stored contiguous memory location
2. Data elements are accessed with index number.

There are 3 types of Array

• 1-D Array (Linear Array)
• 2-D Array (Matrix)
• N-D Array (Multidimensional Array)

Linear Array

  In this type of array there will be single index all the element of array will be stored in contiguous memory location. NAME of array is actually a pointer which points the 1st element of Array.

Declaration

In C:    data_type arrName[array_size]

       in c starting index of array is always 0

General Way:     declare arrName[LB, UB] as DataType

                           *LB - Lower Bound

                           *UB - Upper Bound

Access Element

            In C:     arrName[ELEMENT_INDEX]

            where ELEMENT_INDEX must be from 0 to array_size -1

Total Size of Array

           Size of array can be found by following formulas

            Array_Size = UB - LB + 1

           

Memory allocation of Linear Array

Suppose we have n elements in an array which are allocated memory from starting location 100, and each element of the array is having size of 2 bytes. so that 1st element of the array will be stored at index memory location 100 and next element will be stored at memory location 102, this will be continued for nth element.

 Calculation of memory location for mth element of array

To fetch the element of index m from the array we use following formula

Add_Of_Element_m = Base_Address+size * (m - LB)
  where   Base_Address: Address of starting element
              size: Size of element
              m: Index of the element whose address is to be found.
              LB: Lower Bound of array

  Example
Suppose we have an array having 10 elements, Lower Bound of array is 0, Starting address of Array is 1200, element size is 4 bytes, than what will be the address of element of index 5.

  Soln:
              we are given: 
               Base_Address = 1200, size=4, LB=0, m = 5
               Add_of_Element_m = 1200+4*(5-0)
               Add_of_Element_m = 1220            --> Ans.

2-D Array

These are also known as Matrix. These are collection of homogeneous data elements in rows and columns format. The name of 2 D array is actually a pointer which points the element at 1st Row and 1st Index.

Declaration

General Way: declare arr[LBR,UBR][LBC,UBC] as DataType

In C: data_type arr_Name[NO_OF_ROWS][NO_COLS];

                                  *LBR: Lower Bound for Rows;   UBR: Upper Bound for Rows

                                  *LBC: Lower Bound for Columns;  UBC: Upper Bound for Columns

                                  *NO_OF_ROWS: No of Rows

                                  *NO_OF_COLS: No of Columns

Accessing Element

In C:      arr_Name[Row_Index][Col_Index]

             where  Row_Index is index of row 0<= Row_Index< NO_OF_ROWS

                        Col_Index is index of columns 0<=Col_Index< NO_OF_COLS

Total size of Matrix

             Total Size of Matrix is given by below formula:
             NO_OF_ROWS = UBR - LBR +1
             NO_OF_COLS = UBC-LBC+1

             SIZE_OF_MATRIX = NO_OF_ROWS * NO_OF_COLS

Memory Allocation For Matrix
There are two ways in which matrix can be allocated memory these are:
1. Row Major
2. Column Major

• Row Major: In this scenario matrix is stored in memory Row by Row. For Eg: Suppose there is a matrix of called Mat[3][4]. Starting location(Base address) of matrix is 2000, in this case LBR=0,UBR=2; LBC=0,LBR=3. For Row Major memory allocation (Row 1)Mat[0][0],Mat[0][1],Mat[0][2],Mat[0][3],(Row 2) Mat[1][0],Mat[1][1]... will be the sequence.
• Memory Location for i,j element of Matrix in Row Major Allocation

                    i: row index of element

                    j: column index of element

                    size: size of datatype 

                    m: no. of rows

                    n: no. of cols

                    LBC: Lower bound of columns

                    LBR: Lower bound of Row

                    BA: Base Address

                    LOC_OF_IJ_ELEMENT = BA + size * [(i-LBR)*n + (j-LBC)]

• Column Major: In this scenario matrix is stored in memory column by column. For Eg: Suppose there is a matrix of called Mat[3][4]. Starting location(Base address) of matrix is 2000, in this case LBR=0,UBR=2; LBC=0,LBR=3. For Column Major memory allocation (Column1)Mat[0][0],Mat[1][0],Mat[2][0],(Column2) Mat[0][1],Mat[1][1]... will be the sequence.
• Memory Location for i,j indexed element of Matrix in Column allocation

                    i: row index of element

                    j: column index of element

                    size: size of datatype 

                    m: no. of rows

                    n: no. of cols

                    LBC: Lower bound of columns

                    LBR: Lower bound of Row

                    BA: Base Address

                    LOC_OF_IJ_ELEMENT = BA + size * [(i-LBR) + (j-LBC)*m]