Array and two-dimensional array, Data Structure & Algorithms

Q. Describe the term array.  How do we represent two-dimensional arrays in memory?  Explain how we calculate the address of an element in a two dimensional array.                                                

Ans:

An array is a systematic arrangement of objects generally in rows and columns

Each memory location is defined by an array element. An array element is similar to one variable except it is identified by an index value as a substitute of a name. An index value is a number used to recognize an array element.

Declaration of a two dimensional array- A two dimensional array is declared similarly as we declare a one-dimensional array except that we specify the number of elements in both dimensions. Such as,

int grades[3][4];

The first bracket ([3]) tells the compiler that we are declaring 3 number of pointers, each of them pointing to an array. Here we are not talking about a pointer variable or pointer array. Instead of that, we are saying that each element of the first dimension of a two dimensional array reference a corresponding second dimension. In the above example, all the arrays pointed to by the first index are of the same size. The second index may be of variable size. For example, the earlier statement declares a two- dimensional  array  where  there  are  3  elements  in  the  first  dimension  and  4 elements in the second dimension array.

Two-dimensional array can be represented in memory by following two ways:

1.  Row major representation: To attain b this linear representation, the first row of the array is stored in the first memory locations reserved for the array, then the second row and this process continues.

2.  Column major representation: In this elements of the column are stored next to one another.

In row major representation, the address is always calculated in a two dimensional array as per the formula written below. The address of a[i][j]=base(a)+(i*m+ j)*size in which base(a) is the address of a[0][0], m is second dimension of array a and size represent size of the data type.

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