2- D Array & Address Calculation using Row Major and Column Major

we can create an array of an array, known as a multidimensional array.

2-D Array:

• Each element is represented as Arr[row][column], where Arr[][] is the 2D array.
• It can also represent matrix

Example 1:

Int arr[4][5];

Where arr is the two dimensional array. It can hold maximum of 20 elements.

Example 2:
Int x[3][4];

Where x is the two dimensional array. It can hold maximum of 12 elements.

We can think of this array as a table with 3 rows and each row has 4 columns as shown below.

Address Calculation in 2-D Array:

While storing the elements of a 2-D array in memory, these are allocated contiguous memory locations. 

Therefore, a 2-D array must be linearized so as to enable their storage. 

There are two alternatives to achieve linearization: Row-Major and Column-Major.

• Column by column called column-major order: fortan, MATLAB  
• Row by row called row major order: C, C++, java, python

The address of a location in Row Major System is calculated using the following formula:

Row_M=Base Address+ Size of elements ( [Number of rows placed before ith row] * [Number Of elements placed in columns]+ [No. Of elements before jth element in ith row ])

Row_M= B+W( [i] * [n] + [j] )

Example:

Loc=[0,0] Addr:[100] Value:10	[0,1] [101] 20	[0,2] [102] 30
[1,0] [103] 41	[1,1] [104] 42	[1,2] [105] 43
[2,0] [106] 54	[2,1] [107] 56	[2,2] [108] 59

Find A[2][1]=?

Means where 43 is stored?

So, for finding memory location of particular element we must know about two things:

1. Base Address :

2. Size of Element:

These was given in example.

Row_M= B+W( [i] * [n] + [j] ) = 100+1(2*3+1)

= 100+7=107


Column Major:

The address of a location in Column Major System is calculated using the following formula:

Col_M=Base Addr.+ Size of elements ( [number of columns placed before jth col] *  [number of elements placed in rows]+ [No. Of elements before ith element in jth col. ])

Col_M= B+W( [j] * [m] + [i] )

Example:

Loc=[0,0] Addr:[100] Value:10	[0,1] [103] 20	[0,2] [106] 30
[1,0] [101] 41	[1,1] [104] 42	[1,2] [107] 43
[2,0] [102] 54	[2,1] [105] 56	[2,2] [108] 59

Find A[2][1]=?

Means where 43 is stored?

Solution:

Col_M= B+W( [j] * [m] + [i] ) = 100+1(1*3+2)

= 100+5=105