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[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: #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 2-Dimensional array as an Argument to a function 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: #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 Easy way of reading a 2-D Array 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*sizeOfDataType 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:

well written. Such an article with examples, figures and code examples always help people to understand the concept better. Thanks for writing and sharing.