Introduction
This article talks about Multi-Dimensional Arrays in C/C++. About 1-Dimensional Array see All about Arrays in C/C++ - Part I
Background
Multi-Dimensional Arrays
Multi-dimensional arrays are nothing but Array of Arrays.
Characteristics
All the characteristics that are mentioned for 1-Dimensional array hold good for multi-dimensional arrays too. Apart from that
- Declaration of a multi-dimension array as a argument to a function, must include explicit size declarations in all of the subscript positions except for the first, which is an option.
Memory Mapping
In C/C++, memory mapping for multi-dimensional arrays, is done using Row Major ordering. It means, memory is allocated for successive elements by incrementing the rightmost index until it reaches the end of the current Row.
2-Dimensional Arrays
A 2-Dimensional Array is nothing but Array of 1-Dimensional Array and is represented with two subscripts as below:
data_typeOfArray arrayName [firstDimension] [secondDimension]
whereas firstDimension represents Rows and secondDimension as Columns.
For Example:
int array[2][3];
Can be said as 2 Arrays of 1-Dimensional Array of size 3;
2-Dimensional array can be imagined as a 2-D table made of elements of same data type as in below picture:
Memory Mapping in 2-D Array
For Example if we take int array[2][3];
Here array will be considered as base address and successive address for the elements will be allocated at sizeOfElement*offset in Row Major Ordering. And here if we take the sizeOfElement as 1 then memory mapping for array[2][3] looks as below:
array[0][0] --------> 0
array[0][1] --------> 1
array[0][2] --------> 2
array[1][0] --------> 3
array[1][1] --------> 4
array[1][2] --------> 5
Where 0,1,2 etc at right hand side are offsets
Size of a 2-D Array
Here size of the Array can be calculated as:
firstDimension*secondDimension*sizeOfDataType
For example:
size of the int array[2][3] will be 2*3*4= 24 bytes
Address of an Element
Address of an Element at a given rowIndex and colIndex in an array[rowSize][colSize] can be calculated using the below formula:
Element_Address = Base_Address + (col_size*(rowIndex) + (colIndex)) * Element_Size
For Example:
If we take the above array[2][3] with assumption of baseAddress as 0 and element size as 1, then address of element at indices array[0][1] can be found as:
array[0][1] = 0 + (3*(0)+1)*1
= 0 + (0+1)*1
= 0 + 1
= 1
Initializing a 2-D Array
As like in 1-D Arrays, 2-D Arrays can be initialized as below:
int arry[2][3]={10,20,30,40,50,60}; or
int array[2][3] = {{10,20,30}, {40,50,60}}
And they are assigned with array indices as below:
array[0][0]=10;
array[0][1]=20;
array[0][2]=30;
array[1][0]=40;
array[1][1]=50;
array[1][2]=60;
Like in 1-D array, if some of the indices in an interger 2-D array are not given initilizers, then by default they will be initilized with 0. Also if we assign 2-D Array with {}, it would initialize all it's elements with 0 value.
2-D Array of characters
Like in 1-D Arrays, 2-D Arrays of strings can be initilized in two ways as below:
char array[3][4] = {
'd','o','g'
'c','a','t',
'r','a','t'
}
or
char array[3][4] = {"dog", "cat", "rat"};
As said above for integer arrays, if initilizers are not given for some elements in character arrays, they will be initilized with NULL characters.
Accessing elements in 2-D Arrays
In the above mentioned array i.e. int array[2][3], we can access the 1st Rowth 0th column element as array[1][0] i.e. 40
Dynamic Allocation of 2-D Arrays
Suppose we want an int array[row][col]. where size of row and col are unknown at compile time. Then we can allocate the array dynamically and access it's elements with below steps:
- The name array will be a pointer to a pointer to int.
- Initialliy allocate memory of size x for pointers to int i.e. array of pointers
- Then allocate memory of size y for each of these pointer
- Access each of the element of array as array[i][j], where i>=0 and <x and j>=0 and <y.
- Free the memory by deallocating for each of the pointers and then array of pointers itself.
For Example:
The code
Code: Cpp
#include<iostream.h>
int main()
{
int row, col;
int **array; //array name
int i, j;
cout<<"Enter the matrix size i.e. row and column"<<endl;
cin>>row;
cin>>col;
//allocate memory of size row to pointer to int
array = new int*[row];
//allocate memory of size col to each of the pointer to int
for(i=0; i<row; ++i)
{
array[i] = new int[col];
}
cout<<endl;
cout<<"Please eneter the values array["<<row<<"]["<<col<<"] :\n";
for(i=0; i<row; ++i)
{
for(j=0; j<col; ++j)
{
cin>>array[i][j];
}
}
cout<<endl;
cout<<"Contents of array["<<row<<"]["<<col<<"] are :\n";
for(i=0; i<row; ++i)
{
for(j=0; j<col; ++j)
{
cout<<array[i][j];
}
cout<<endl;
}
cout<<endl;
//now for each pointer, free its array of ints
for (i = 0; i < row; i++)
{
delete [] array[i];
}
//now free the array of pointers
delete [] array;
return(0);
}
Output:
------------
./a.out
Enter the matrix size i.e. row and column
2
3
Please eneter the values array[2][3] :
1
2
3
4
5
6
Contents of array[2][3] are :
123
456
As said above, the size of the first dimension may be omitted, but the second dimension has to be mentioned in the argument.
For Example:
The code
Code: Cpp
#include<iostream.h>
double sum(double array[][3], int size)
{
double temp = 0.0;
for(int i = 0 ; i < size ; i++)
{
for(int j = 0 ; j < 3 ; j++)
{
temp += array[i][j];
}
}
return temp;
}
int main() {
double array[2][3] = {
{ 1.0, 2.0, 3.0},
{ 5.0, 6.0, 7.0}
};
cout << "Sum of all the elements in array[2][3] is: "<< sum(array, sizeof array/sizeof array[0])<< endl;
return 0;
}
Output:
----------
Sum of all the elements in array[2][3] is: 24
Imagine a 2-D array as shown in below example picture and then put the elements at the respective indices in the picture. This helps to read/recognise any element of the array at a given indcies.
3-Dimensional Arrays
Multi Dimensional Arrays are not limited to 2-D alone. They can be of as many indices as needed. But developer must be careful here, as the memory that consume increases with proportional to the dimension.
A 3-Dimensional Array can be said as Array of 2-Dimensional Arrays and is represented with three subscripts as below:
data_typeOfArray arrayName [firstDimension] [secondDimension] [thirdDimension]
whereas firstDiemnsion is also called as depthSize here.
For Example:
int arry[2][3][4]; can be called as
2 Arrays of 2-Dimensional Arrays of size 3X4 !!
Memory Mapping in 3-D Array
If we take int array[2][3][4];
And array will be considered as base address and successive address for the elements will be allocated at sizeOfElement*offset in Row Major Ordering as below:
array[0][0][0] --------> 0
array[0][0][1] --------> 1
array[0][0][2] --------> 2
array[0][0][3] --------> 3
array[0][1][0] --------> 4
.
.
.
array[0][2][0] --------> 8
.
.
.
array[1][0][0] --------> 12
.
.
.
array[1][1][0] --------> 16
.
.
.
array[1][2][0] --------> 20
array[1][2][1] --------> 21
array[1][2][2] --------> 22
array[1][2][3] --------> 23
Where 0,1,2 etc at right hand side are offsets
Size of a 3-D Array
Here size of the Array can be calculated as
firstDimension*secondDimension*thirdDimension*size OfDataType
For example the size of the below array will be:
int array[2][3][4]
2*3*4*4 = 96 bytes
Address of an Element
Address of an Element at a given depthIndex, rowIndex and colIndex in an array[depthSize][rowSize][colSize] can be calculated using the below formula:
Element Address = Base Address + ((depthIndex*colSize+colIndex) * rowSize + rowIndex) * Element_Size
If we take the above array[2][3][4] with assumption of baseAddress as 0 and element size as 1, then address of an element at indices array[1][2][3] can be found as:
array[1][2][3] = 0 + ((1*4+3)*3+2)*1
= 0 + ((4+3)*3+2)1
= 0 + ((7)*3+2)1
= 0 + 23
Easy way of Reading a 3-D Array
Elements in a 3-D array also can easily be read/recognised by imagining the picture of the Array as below:
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