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Three dimensional (3D) array in C

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A 3D array is a multi-dimensional array (array of arrays). A 3D array is a collection of 2D arrays . It is specified by using three subscripts:Block size, row size and column size. More dimensions in an array means more data can be stored in that array.

Visualizing 3D array:

If we want to visualize a 2D array , we can visualize it in this way: int arr[3][3] , it means a 2D array of type integer having 3 rows and 3 columns.It is just a simple matrix

But, what happen if we add one more dimension here, i.e, int arr[3][3][3] , now it becomes a 3D array.

• int shows that the 3D array is an array of type integer .
• arr is the name of array .
• first dimension represents the block size (total number of 2D arrays).
• second dimension represents the rows of 2D arrays .
• third dimension represents the columns of 2D arrays . i.e; int arr[3][3][3], so the statement says that we want three such 2D arrays which consists of 3 rows and 3 columns.

Declaring a 3D array:

To declare 3D array:

• Specify data type, array name, block size, row size and column size.
• Each subscript can be written within its own separate pair of brackets.
• Syntax: data_type array_name[block_size][row_size][column_size]; example:

Ways to declare 3D array:

1). int arr[2][3][3]; In this type of declaration, we have an array of type integer, block size is 2, row size is 3 and column size is 3.Here we have not stored any values/elements in the array.So the array will hold the garbage values.

2). int arr[2][3][3]={}; In this type of declaration, we have an array of type integer, block size is 2, row size is 3 and column size is 3 and we have put curly braces after assignment operator.So the array will hold 0 in each cells of array.

3). int arr[3][2][2]={0,1,2,3,4,5,6,7,8,9,3,2} In this type of declaration, we have an array of type integer, block size is 3, row size is 2, column size is 2 and we have mentioned the values inside the curly braces during the declaration of array. So all the values will be stored one by one in the array cells.

4). int arr[3][3][3]= { {{10,20,30},{40,50,60},{70,80,90}}, {{11,22,33},{44,55,66},{77,88,99}}, {{12,23,34},{45,56,67},{78,89,90}} }; In this type of declaration, we have an array of type integer, block size is 3, row size is 3, column size is 3 and the values of each blocks are assigned during its declaration.

Inserting values in 3D array:

In 3D array, if a user want to enter the values then three for loops are used.

• First for loop represents the blocks of a 3D array.
• Second for loop represents the number of rows.
• Third for loop represents the number of columns. Example:

Following is the implementation in C :

In the above program;

• We have declared three variables i,j,k for three for loops .
• we have declared an array of type integer int arr[2][3][3]; (blocks:2 rows:3 columns:3)
• First section of nested for loops ask the user to insert the values.
• second section of nested for loops will print the inserted values in the matrix form.

Updating the 3D array:

We can update the elements of 3D array either by specifying the element to be replaced or by specifying the position where replacment has to be done. For updating the array we require,

• Elements of an array
• Element or position, where it has to be inserted
• The value to be inserted Example
• We have declared three variables i,j,k for three for loops and num variable which will hold the value/element to be updated.
• Position/value will be updated.
• Third section of nested for loop will print the updated 3D array.

Converting 3D array into 2D array

We can convert a 3D array into a 2D array. As we know that a 3D array is a colection of 2D arrays, we just have to follow certain steps to convrt a 3D array into 2D array;

• First declare a 3D array and enter the elements in it.
• After that, declare the 2D arrays(number of 2D arrays should be equal to the total number of blocks of 3D array).
• Copy the elements of 3D array into 2D array. Example:

Converting 2D array into 3D array

We can also convert a 2D array into a 3D array by following given steps;

• Declare a 2D array and enter the elements in it and can print it.
• Now declare a 3D array and copy the elements of 2D array into 3D array and print them. Example

Dynamically allocating memory using malloc in 3D array

As we know that static array variables are fixed in size and can't be changed(enlarged or shrinked).To remove this drawback we use dynamic memory allocation.dynamic array is nothing but it is allocated during runtime with malloc or calloc. *syntax: int *array=int(int *)malloc(sizeof(int) element-count); Example

With this article at OpenGenus , you will have complete idea of handling 3D arrays in C. Enjoy.

Learn more:

• 2D arrays in C by Subhash Bhandari at OpenGenus
• List of C topics at OpenGenus

Introduction to Multi-Dimensional Arrays

In the realm of programming, multi-dimensional arrays are essential data structures that provide a way to organize and work with data in multiple dimensions. They allow you to store and manipulate information in a structured manner, particularly in scenarios where data is naturally organized in rows and columns or grids.

What are Multi-Dimensional Arrays?

A multi-dimensional array is an array of arrays. It's a structured collection of elements, where each element is identified by multiple indices, often corresponding to different dimensions. Common examples of multi-dimensional arrays include 2D arrays (matrices), 3D arrays, and beyond. These arrays are used to represent data in a tabular form, such as spreadsheets or images.

Example: 2D Array in Python

Here's an example of a 2D array in Python representing a simple 3x3 grid:

In this case, the grid is a 2D array with three rows and three columns.

Accessing Multi-Dimensional Array Elements

Accessing elements in a multi-dimensional array involves specifying indices for each dimension. For a 2D array, you need to provide both the row and column indices.

Example: Accessing 2D Array Elements in Java Consider a 2D array matrix in Java:

Practical Use Cases

Multi-dimensional arrays find extensive applications in fields like mathematics, image processing, and game development. They are especially useful for representing data that has multiple attributes or dimensions, such as representing a color image where each pixel has red, green, and blue components.

Example: Image Processing In image processing, a 2D array can be used to represent a grayscale image where each element stores the pixel intensity. A 3D array is suitable for color images, with each element representing a pixel's color.

Nesting and Complexity

As you work with multi-dimensional arrays, you may encounter arrays of higher dimensions (3D, 4D, and so on). It's crucial to understand the concept of nesting, where arrays are placed within arrays. This nesting introduces added complexity but allows for representing complex data structures effectively.

Multi-dimensional arrays are a powerful tool in the world of programming, offering a structured way to store and manipulate data in multiple dimensions. In this introduction, we've covered the basics of multi-dimensional arrays, their representation, access, and practical applications.

As you delve deeper into programming, you'll encounter more complex use cases for multi-dimensional arrays, such as solving mathematical problems, simulating 3D worlds, and handling vast datasets. Mastering multi-dimensional arrays is a key step in becoming a proficient programmer.

Feel free to experiment with multi-dimensional arrays in your coding projects and explore the diverse possibilities they offer.

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Multi-Dimensional Arrays (3D Arrays) in C Programming Language

• Author: RAJKISHOR SAHU

Multi-dimensional array in C

3D Array in C

C allows for arrays of two or more dimensions. A two-dimensional (2D) array is an array of arrays. A three-dimensional (3D) array is an array of arrays of arrays.

In C programming, an array can have two, three, or even ten or more dimensions. The maximum dimensions a C program can have depends on which compiler is being used.

More dimensions in an array means more data to be held, but also means greater difficulty in managing and understanding arrays.

How to Declare a Multidimensional Array in C

A multidimensional array is declared using the following syntax:

type array_name[d1][d2][d3][d4]………[dn];

Where each d is a dimension, and dn is the size of the final dimension.

• int table[5][5][20];
• float arr[5][6][5][6][5];

In Example 1:

• int designates the array type integer.
• table is the name of our 3D array.
• Our array can hold 500 integer-type elements. This number is reached by multiplying the value of each dimension. In this case: 5x5x20=500 .

In Example 2:

• Array arr is a five-dimensional array.
• It can hold 4500 floating-point elements ( 5x6x5x6x5=4500 ).

Can you see the power of declaring an array over variables? When it comes to holding multiple values in C programming, we would need to declare several variables. However, a single array can hold thousands of values.

Note: For the sake of simplicity, this tutorial discusses 3D arrays only. Once you grab the logic of how the 3D array works, then you can handle 4D arrays and larger.

Explanation of a 3D Array

Let's take a closer look at a 3D array. A 3D array is essentially an array of arrays of arrays: it's an array or collection of 2D arrays, and a 2D array is an array of 1D arrays.

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It may sound a bit confusing but don't worry. As you practice working with multidimensional arrays, you start to grasp the logic.

The diagram below may help you understand:

3D array conceptual view

3D array memory map

Initializing a 3D Array in C

Like any other variable or array, a 3D array can be initialized at the time of compilation. By default, in C, an uninitialized 3D array contains “garbage” values that are not valid for the intended use.

Let’s see a complete example of how to initialize a 3D array:

Declaration and Initialization 3D Array

In the code above, we have declared a multidimensional integer array named “arr,” which can hold 3x3x3 (or 27) elements.

We have also initialized the multidimensional array with some integer values.

As I said earlier, a 3D array is an array of 2D arrays. I have divided elements accordingly for easy understanding. Looking at the C code sample above,

• In lines 9-13, 14-18, and 19-23, each block is a 2D array.
• Collectively, lines 2-24 make a 3D array.

To call values from the array, imagine the 3D array above as a collection of tables. Each nested bracket cluster is a table with rows and columns. To access or store any element in a 3D array, you need to know its table number, row number, and column number.

For example, you need to access value 25 from the above 3D array. So, first, check the table: in this case, 25 is in Table 1 (remember: tables, rows, and columns are counted starting at 0, so the second table is Table 1). Once you find the table number, check which row of that table has the value, and then check the column number. So applying the above logic, 25 located in table 1, row 1, and column 1, hence the address is arr[1][1][1] . Print this address, and you will get the output: 25.

The Conceptual Syntax of a 3D Array in C

The conceptual syntax for the 3D array is this:

data_type array_name[table][row][column];

If you want to store values in any 3D array, point first to the table number, then the row number, and lastly to the column number.

Some hypothetical examples:

arr[0][1][2] = 32; arr[1][0][1] = 49;

Storing Values in a Continuous Location Using a Loop

The pointer syntax above assigns values to a particular location of an array, but if you want to store values in multiple locations automatically, then you should use a loop.

Here is an example using the for loop command:

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© 2009 RAJKISHOR SAHU

Slavek on December 16, 2019:

Hi, thanks for the article, but it unfortunately don't help anyone to handle 3D-arrays with functions.

I mean, that any function call can copy or change variable data in its storage, but when you call func wth "char" type parameter, you always type it like — void func_name(char * var_name) — so, if you have to change the value, you type it in like that, and when have not to — you only add "const" before "char * var"...

Could u please explain how to behave properly when I have to operate 3D-arrays in my functions? How I have to write function prototype to change the value of 3D-array?

void func_name(char *array[][][]) — is that correct?

void func_name( char *(***array) ) — or maybe like that?

if I have to operate with elements in EACH dimension, do I have to prototype functions like this? :

void func_name( char *(*array), char *(**array), char *(***array) ) {. . .}

Anyway, thank you for your site!

Neha Sharma on October 05, 2019:

Features are not available

p0st1e64 on July 15, 2019:

Thank you, a clear explanation and the 3D array conceptional view made it very clear to me

Muhammad Muddassar from Pakistan on June 22, 2019:

Thanks! For the complete information

Good on June 08, 2019:

manish on February 19, 2019:

its was helpful for me

Nitin Gupta on January 22, 2019:

How 3-dimensional array store in column major order?

la vita e bella on December 27, 2018:

very helpful for an inexperienced programmer

Jeevan on November 22, 2018:

RAJKISHOR SAHU (author) from Bangalore, Karnataka, INDIA on September 19, 2018:

Thank You guys, let me know if you have any doubts.

chinni on September 19, 2018:

super, very understandable

Dhruv Gaharwar on August 30, 2018:

Sorry but I can not understand this logic

RAJKISHOR SAHU (author) from Bangalore, Karnataka, INDIA on August 07, 2018:

thanks mavesh

Mahvesh on August 07, 2018:

Its really understandable:-)

Meenakshi on April 25, 2018:

I need to store the value to the 3 dimensions from 2 dimensions either in c or java...can any tell me plz

Roma Lohar on March 05, 2018:

Thanks alot.. this is really helpful

Mayur on February 03, 2018:

Shivam Sharma on January 17, 2018:

can u tell me the logic to make star pattern in c

Asad on December 13, 2017:

yes it help me

Habib ahmad on December 11, 2017:

thank you so much..

Bappa saikh on November 13, 2017:

Thank you brother

Mike on October 16, 2017:

An example where the values of the array size values are different will help distinguish how the size will be affected

kushi on October 12, 2017:

looking for more appropriate example

Maheswari on September 20, 2017:

This tutorial is very useful.but please explain how to implement in 3d arithmetic operation in this array please explain............

Khushi on September 18, 2017:

Nice but difficult

Ankitha on August 20, 2017:

please tell me how to represent character 3dimensional matrix

Riya on June 09, 2017:

Thank you.This is very useful for us.

priya on February 18, 2017:

thank u but very difficult

Udit Tiwari on December 05, 2016:

Could you please tell me

A(1:8,-5:5,-10:5) is an 3D array then what will be the size of A?

taurus on November 11, 2016:

Bang on, thank you

K.Akila Jetkin on October 10, 2016:

wycliff on August 31, 2016:

so helpful. satisfied

Tarun on August 23, 2016:

explain the multi dimensional array using 3d array multiplication

priti on May 20, 2016:

how to find the address of an item placed at particular location ?

Karan on April 15, 2016:

Can you please explain how below array will be represented {Similar to pictorial representation shown above (Fig. 3D array memory map)}

I believe that in the 0th 2-D array there should be 3 rows (row0 , row1,row2)with 2 elements

But with some examples I've found it to be 2 rows with 3 elements in oth 2-D array and similar in 1st 2-d array

Below is the example

int a[2][3][2] = {{{2,4},{7,8},{3,4}},{{2,3},{2,3},{3,4}}};

printf("%d\n",sizeof(int));

printf("%u %u %u %d\n",a,*a,**a,***a);

printf("%u %u %u %d\n",a+1,*a+1,**a+1,***a+1);

Parveen Anand on March 19, 2016:

Great explain the 3D programmin g. Thanks alot.

balaganesh on February 23, 2016:

i can't understand that 3D array. can u explain this

jp on February 12, 2016:

arr[0][1][2] = 32;

arr[1][0][1] = 49;

how about in character or string?

how to initialize in 3d array?

ganesh on September 14, 2014:

in three dimentional array arr[3][3][3] means 3table 3rows and 3columns like that in four dimentional array arr[3][3][3][3] means?????

SANDEEP VERMA on February 24, 2014:

THANK YOU........YOUR PROGRAMME IS GOOD

ritesh khanna on October 17, 2013:

natasha jane on October 17, 2013:

hey........the codes and the explanation really helped me..bt I really cant understand the difference between the 3D array being demonstrated here

and a 2D array with multiple endls ???pls help me to figure out the difference

ritesh patel on September 26, 2013:

welll good, but i would like to know that how to perform subtraction of two array of 3d. for example a[0]-a1[1]. could u help me

ivy biswas on August 13, 2013:

i need to know the syntax for 3 D Array

Chris Goodwin on March 27, 2013:

has expanded my view

alfred on December 01, 2012:

write a program that reads in an array type int. you may assume that there are fewer than 50 entries in that array. your program determines how many entries are used. the output is to be a two column is a list of the district array elements; the second column is the count of the number of occurences of each element the list should be sorted on entries int first column largest to smallest

sukh on March 15, 2012:

sir am live in punjab,and i have solve my problam.thanks sir.

tharani on February 27, 2012:

its vry useful to us vry nice................

Jamal on February 18, 2012:

what is the purpose of multiple dimensional arrays if i can do the same with a one intentional array

like what ares the advantages and stuff like that

thivya on February 02, 2012:

its very useful for me to refer my doubt

Janet on January 29, 2012:

The example would be more useful if all of the dimensions were different [2][3][4] rather than [3][3][3].

Ali on January 12, 2012:

i need to write a code that emulates an LED display, and for the numbers ive set a 3D array. the problem i have is getting it to read from an input. ive tried storing the input in a char array and reading it using scanf() but it doesn't work. can you please tell me what i need to do

RAJKISHOR SAHU (author) from Bangalore, Karnataka, INDIA on January 05, 2012:

@Santu: that is right...

santu das on January 05, 2012:

in 3-D array 1st one is page 2nd is row and 3rd is coloum.is it right??

Razi Ahmad on December 20, 2011:

Thanks it's really nice........

R.Nandhini on December 08, 2011:

Thank u for the clear explanation.

c language easy for concepts on December 06, 2011:

thanks you sir c language understand help and concpet for easy understand.plz sir requst for c langague method

for easy understand.plz sir send my e-mail

id [email protected].

i am mca student and the not undertstand the c and c is very important of IT student plz sir help send replay my email id.

thanks sir.

drosanda on December 05, 2011:

Are multidimensional arrays can be returned in a function? if can,i need an example, thx be4.

ian on December 02, 2011:

nice,thank you for explain.

Rintu_achiever on October 18, 2011:

thanx.I have solved my problem

RAJKISHOR SAHU (author) from Bangalore, Karnataka, INDIA on October 13, 2011:

@Vijay : I think you can try array of structure, please check this link.

https://hubpages.com/technology/Arrays-of-Structur...

Vijay on October 12, 2011:

how to store array of different data types?

santhosh on October 12, 2011:

how to imlpementthat array

Ashish Kasampara on August 07, 2011:

Nice example of the 3D arry but more example and easy to understand that type of example

Suraj Verma on January 30, 2011:

Thanks for the concept of 3D array

chokies on October 31, 2010:

thx for your clear explanation,

Parvez on October 21, 2010:

Thank you. Nicely explained.

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Before we learn about the multidimensional array, make sure you know about Java array .

A multidimensional array is an array of arrays. Each element of a multidimensional array is an array itself. For example,

Here, we have created a multidimensional array named a . It is a 2-dimensional array, that can hold a maximum of 12 elements,

Remember, Java uses zero-based indexing, that is, indexing of arrays in Java starts with 0 and not 1.

Let's take another example of the multidimensional array. This time we will be creating a 3-dimensional array. For example,

Here, data is a 3d array that can hold a maximum of 24 (3*4*2) elements of type String .

How to initialize a 2d array in Java?

Here is how we can initialize a 2-dimensional array in Java.

As we can see, each element of the multidimensional array is an array itself. And also, unlike C/C++, each row of the multidimensional array in Java can be of different lengths.

Example: 2-dimensional Array

In the above example, we are creating a multidimensional array named a . Since each component of a multidimensional array is also an array ( a[0] , a[1] and a[2] are also arrays).

Here, we are using the length attribute to calculate the length of each row.

Example: Print all elements of 2d array Using Loop

We can also use the for...each loop to access elements of the multidimensional array. For example,

In the above example, we are have created a 2d array named a . We then used for loop and for...each loop to access each element of the array.

How to initialize a 3d array in Java?

Let's see how we can use a 3d array in Java. We can initialize a 3d array similar to the 2d array. For example,

Basically, a 3d array is an array of 2d arrays. The rows of a 3d array can also vary in length just like in a 2d array.

Example: 3-dimensional Array

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Table of Contents

• Java Multidimensional Array
• 2-dimensional array in Java
• Example: 2d Array
• 3-dimensional array in Java
• Example: 3d Array

Sorry about that.

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3D Arrays in C

Updated March 16, 2023

Introduction to 3D Arrays in C

An Array is a group of elements with the same (homogeneous) data type. It is also called a Derived data type. As already noticed, a 3D array increases the space exponentially, and, an extra position added to locate the element in the array. In this topic, we are going to learn about 3D Arrays in C.

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For example, consider a 4 level building with many slots for bike parking. So, here for getting the perfect slot directions of the bike that is parked, we need to tell the level number with row and column number. When you just tell the array, row 7 and column 4, which level does it search for? This 3D array is just for storing more amounts of data and representing the positions.

How can we define and implement them? Going further, let’s understand those concepts.

In C, Dimensional arrays can be declared as follows:

So, in the same way, we can declare the 3-D array as:

The meaning of the above representation can be understood as:

• The memory allocated to variable c is of data type int.
• The total capacity that this array can hold is 2*3*4, which is equal to 24 elements.
• The data is being represented in the form of 2 arrays with 3 rows and 4 columns each.

The data inside the array can be accessed through the above representation. In 3D arrays representation , the first square bracket represents the level of the array that has to be considered, second would be the number of rows, and the third one is for the number of columns.

The index representation of the array for the first element always starts with zero and ends with size-1. So, for example, if the number of rows is 3, then the index representation for accessing the data in rows will be 0, 1 and 2. The same logic applies for the array level and column indexes too. For the above representation, to get the data of 1 st level of the array with 2 nd row 3 rd column, we can access by c[0][1][2].

Initializing 3D Arrays in C

We can initialize a 3D array similar to the 2-D array.

As mentioned above, the total number of elements that can be fit into the array would be arraysize1*arraysize2*arraysize3. Here it is 2*4*3, which gives 24.

Inserting elements

Similar to the 2D array, for inserting elements in a 3-D array, we need to insert the data in levels, rows, and columns. So, for this, we use the concept of loops. In the above process for initializing the data in the array, we had predefined the values.

Here, elements can be dynamically inserted by the user, as per the requirements. Below is an example code for inserting the elements.

As observed in the code:

• First, we are declaring the array variable and the dimensions of the array with the number of levels of the array, rows, and columns.
• We are then declaring three variables for iterating over the elements in the array.
• Then, for loops are used. The first loop is for the levels iteration, the second is for the rows and the third loop is for the columns.
• Scanf function is used to read the data as we input, and then place the value inserted at those positions of i, j and k.

In the above example, we inserted the data in a matrix having 2 levels, 4 rows, and 3 columns. The output of the following can be obtained as below:

As we have not used the printf function to display the output, the program written had only read the user inputted values. After writing the print function (using for loops), the output would be displayed as:

Update Elements

The updating of elements in the array can be done by either specifying a particular element to be replaced or by identifying a position where the replacement has to be done. For updating, we generally require the following details.

• Elements of an array
• Position/element, where it has to be inserted
• The value to be inserted.

For updating the data in an array through element details, first, we need to search for that element in the array, understand its position, and then replace the old element with the new element.

Here, we have given below two examples of updating the element of a 3D array.

Firstly, let us go through an example where the position of the element to be updated is already known.

In the above program, the element on the 1 st level, 1 st row, and 1 st column is selected and the value of the data in that position has been updated.

Output for above is as follows:

In the second example, we are going to show how the position of the element can be dynamically taken as a user inputted value and update the value of the element at that particular position.

The output is as follows. Here, we used the scanf function to read the value given by the user as per their choice for the position of an element based on array level, row, and column numbers.

As an exercise, can you try writing a program in updating the whole column of the matrix with user-inputted values?

Now, as we know, in the 3D array, we declare the size of the array at the beginning itself. We are aware of the size of the array but what if the user gives a random row and column number outside our array size?

What if, we input more elements than required inside the array?

Notice that as we had not written any if/else condition or try/catch blocks, the output of the matrix does not change. However, we can write the code using the above-mentioned conditions to display errors for such cases.

As the last example, are you not curious about, what happens if we skip some elements in between? What does my program do?

As observed in the above output:

• We missed up 4 values in the input, just by giving space and pressed enter
• But we had got that scope to enter the 4 remaining elements.
• Then we specified the last level, last row, and last column element to be changed to 78. And the output is as expected isn’t it?

Deleting Elements

After the concepts of insertion and updating of the data inside the 3D array, let’s now see how we can delete an entire row from the array.

We have written a program in a simple format so that the concept of different operations can be understood easily.

Took the values of an array dynamically.The steps followed are:

• Asked user to input the number (index) of the row that has to be deleted.
• Using for loop iteration of array levels, rows, and columns. We are comparing if the row number and the user input number are matching or not.
• If they are matching and if the row number is less than the size of the array, we are printing the next row. Else, we are printing the row as it is.
• Here, as we didn’t have any condition on the level of the array, the row number specified is deleted from both the array levels.

The output is as follows:

What if, we give the row number outside the array boundary?

It will not find the row to delete and exit the program by printing the whole array.

As already known, we can even declare the values for the number of rows and columns dynamically and write the program accordingly.

Doesn’t this look simple and easy to learn?

As an exercise, can you try in deleting a particular element for the 3d array now?

In this section, we have learned the basic operations on 3-dimensional arrays.

The 3D array contains many sets of 2-D arrays. As we have seen the chessboard as an example of a 2D array, if we had placed many chess boards together, the 3D array can help us first choose the chessboard you want to play with and then go for the rows and columns of that chessboard.

Try solving the basic operations of the 3d arrays and have fun learning C.

Recommended Articles

This is a guide to 3D Arrays in C. Here we discuss the initializing of a 3D array similar to the 2D array and elements of Array. You may also look at the following article to learn more –

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9.5: Multidimensional Arrays

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In C++, we can define multidimensional arrays, an array of arrays. Data in multidimensional arrays are stored in tabular form (in row major order).

I general, the form of declaring multidimensional arrays:

Size of multidimensional arrays

Total number of elements that can be stored in a multidimensional array can be calculated by multiplying the size of all the dimensions. For example: The above array named two_d[10][20]  can store total (10*20) = 200 elements. Similarly the array  three_d[10][20][30]  can store total (10*20*30) = 6000 elements.

Two-Dimensional Array

A two dimensional array is the simplest form of a multidimensional array. We can see a two dimensional array as an array of one dimensional array for easier understanding.

• The basic form of declaring a two-dimensional array of size row, col. Syntax: data_type array_name[row][col]; data_type : Type of data to be stored. Valid C/C++ data type.
• We can declare a two dimensional integer array say ‘newArray’ of size 10,20 as: int newArray[10][20];
• Elements in two-dimensional arrays are commonly referred with a syntax of newArray[row][col].
• A two dimensional array can be seen as a table with rows and columns where the row number ranges from 0 to (row-1) and column number ranges from 0 to (col-1). A two dimensional array ‘newArray’ with 3 rows and 3 columns is shown below:

Initializing Two Dimensional Arrays

There are two ways in which a Two-Dimensional array can be initialized.

First Method :

The above array has 3 rows and 4 columns. The elements in the braces from left to right are stored in the table also from left to right. The elements will be fill the array, the first 4 elements from the left in first row, the next 4 elements in second row and so on.

This is a valid approach, but it can be difficult to read and to debug in the case of a large array.

Better Method :

This type of initialization make use of nested braces. Each set of inner braces represents one row. In the above example there are total three rows so there are three sets of inner braces.

Accessing Elements of Two-Dimensional Arrays

Elements in two dimensional arrays are accessed using the both of the indexes.

The above example represents the element present in third row and second column.

Remember : Arrays always count from 0 therefore, row index 2 is actually the third row, and column index 1 is actually the second column.

To output all the elements of two dimensional array we can use nested for loops. One loop to traverse the rows and another to traverse columns.

Three-Dimensional Array

Initializing Three-Dimensional Array

Initialization in three dimensional array is same as that of two dimensional arrays. The difference is as the number of dimension increases so the number of nested braces will also increase.

As with the tewo dimensional arrays, it is allowable to simply initialize a series of values that equals the length of the array.

Accessing elements in Three-Dimensional Arrays

Accessing elements in three dimensional arrays is also similar to accessing two dimensional array elements. The difference is we have to use three loops instead of two loops for one additional dimension in three dimensional rrays.

In similar ways, we can create arrays with any number of dimension. However the complexity also increases as the number of dimension increases.

Adapted from: "Multidimensional Arrays in C / C++"  by  Harsh Agarwal ,  Geeks for Geeks  is licensed under  CC BY-SA 4.0

Multidimensional Arrays in Python: A Complete Guide

An array with multiple dimensions can represent relational tables and matrices and is made up of many one-dimensional arrays, multi-dimensional arrays are frequently used to store data for mathematical computations, image processing, and maintaining records.

In this article, the creation and implementation of multidimensional arrays (2D, 3D as well as 4D arrays) have been covered along with examples in Python Programming language. To understand and implement multi-dimensional arrays in Python, the NumPy package is used. It is a Python library that gives users access to a multidimensional array object, a variety of derived objects (such as masked arrays and matrices), and a selection of functions for quick operations on arrays and multi-dimensional matrices.

The standard way of Python language creates lists which are very similar to arrays but remember, there is a very slight difference between a List and an array in Python programming language. You can learn more about the differences between lists vs arrays in python. In this article let’s look purely at arrays. The following example will show the difference between the datatype of creating a 2D array created by the standard way and by using the Numpy package.

Make sure to install and import the Numpy package in your current IDE before beginning with the array implementation to avoid any kind of errors. To do so run the following lines of code.

Two-dimensional (2D) array

An array of arrays is a simple definition that applies to the two-dimensional array. The rows and columns of the matrices that make up the 2D array’s organizational structure can be viewed as its primary component. The 2D array can be visualized as a table (a square or rectangle) with rows and columns of elements. The image below depicts the structure of the two-dimensional array.

Implementing 2D array in Python

Let’s start with implementing a 2 dimensional array using the numpy array method.

• arr: array’s name
• np.array: function of the Numpy package

Three-dimensional (3D) array in Python

A 3-D (three-dimensional) array is mainly composed of an array of 2-D arrays. The rows, columns, and page elements can be viewed as primary components of a 3D array. We can visualize it as multiple tables comprising of rows and columns attached (like a cube). The image below depicts the structure of the three-dimensional array.

Four-dimensional (4D) array

A simple way to define a 4D array is that it’s an array of 3D arrays. It is a bit complicated to visualize a 4D array but we can say that it’s a set of 3D arrays (like a row of cubes). The image below depicts the structure of the four-dimensional array.

arr = numpy.array([3D_array1],[3D_array2]…)

• numpy.array: function of the numpy package

Arrays are great data structures used to store homogenous data. the default array is more like a list data structure in python. Numpy is one of the applicable open-sourced free-to-use packages that help in creating and working on arrays faster and in a much more efficient manner. The Numpy package also many other built-in functions to manipulate and reshape multidimensional arrays. A few other built-in functions of the Numpy package to create multi-dimensional arrays are as follows:

• numpy.zeros
• numpy.identity

To view more such detailed and easy-to-understand articles on Python programming language  click here!

7.2. Visualizing Arrays

Arrays are relatively simple data structures that programmers create much like any other variable: the definition establishes the variable's data type and name. But arrays are also aggregates or containers. When programmers define an array, they must specify its size. The previous section illustrated a one-dimensional array, which is the most simple. But it is possible to create arrays with more than one dimension.

• array_type array_name [n 1 ][n 2 ] ... [n m ] ;
• one-dimensional : looks like a list or vector
• two-dimensional : looks like a table
• three-dimensional : looks like a box
• four or more dimensions : higher dimensional arrays are allowed but are hard to visualize
• Each array definition includes the array's name, type (the type of each element), and a dimension list. Each dimension is the size of the corresponding dimension enclosed in square brackets. Although some programming languages allow a comma-separated list of sizes, C++ requires one pair of brackets for each dimension size. The generalized array definition illustrated here has m dimensions, and a total capacity of n 1  × n 2  × ... × n m
• Common array dimensions and their associated shapes.

int test[10];

float test_scores[10][4];

double class_score[5][5][5];

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Representation of Array

The representation of an array can be defined by its declaration. A declaration means allocating memory for an array of a given size.

Arrays can be declared in various ways in different languages. For better illustration, below are some language-specific array declarations.

Array declaration

However, the above declaration is static or compile-time memory allocation, which means that the array element’s memory is allocated when a program is compiled.

Here only a fixed size (i,e. the size that is mentioned in square brackets [] ) of memory will be allocated for storage, but don’t you think it will not be the same situation as we know the size of the array every time, there might be a case where we don’t know the size of the array. If we declare a larger size and store a lesser number of elements will result in a waste of memory or either be a case where we declare a lesser size then we won’t get enough memory to store the rest of the elements. In such cases, static memory allocation is not preferred.

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element address in 3 dimensional array

I am looking for the formulas to find the memory location of an element in a 3-D Array for row major and for column major. After using my logic I end up with the following formulas. say array is A[L][M][N] .

row-major: Loc(A[i][j][k])=base+w(M*N(i-x)+N*(j-y)+(k-z)) column-major: Loc(A[i][j][k])=base+w(M*n(i-x)+M*(k-z)+(j-y))

where x, y, z are lower bounds of 1st(L) 2nd(M) and 3rd(N) index. I tried this formula and got the correct result but when I applied this formula on a Question in the book then the answer did not match. Please can anyone help me out with this.

• data-structures

• 1 Please refer to : eli.thegreenplace.net/2015/… to get the correct and clear understanding of multi dimensional arrays, row and column major representations –  Vinay Yadav Sep 26, 2020 at 9:17

3 Answers 3

Formula for 3d array, row major order:, column major order:.

• B = Base Address (start address)
• W = Weight (storage size of one element stored in the array)
• R = Row (total number of rows)
• C = Column (total number of columns)
• D = Width (total number of cells depth-wise)
• R o = Lower Bound of Row
• C o = Lower Bound of Column
• D o = Lower Bound of Width

• 2 Here are some guidelines for How do I write a good answer? . This provided answer may be correct, but it could benefit from an explanation. Code only answers are not considered "good" answers. From review . –  Trenton McKinney Sep 22, 2019 at 8:00

Right one is:

• I think formula for column major would be base + w((i-x) + L*(j-y) + L*M*(k-z)) . Or am I wrong. –  Vimal Patel Dec 12, 2019 at 3:52

Thanks! @Vinay Yadav for your comment. As suggested by Vinay please visit the link to understand this in great detail: https://eli.thegreenplace.net/2015/memory-layout-of-multi-dimensional-arrays .

Keep this in mind and you never get it wrong: Row Major: Lexicographical Order Column Major: Co-lexicographical Order

If you don't know what Co-lexicographical and Lexicographical are: Check out this Wikipedia page for more. Let me highlight important part for you, do give it a read:

The words in a lexicon (the set of words used in some language) have a conventional ordering, used in dictionaries and encyclopedias, that depends on the underlying ordering of the alphabet of symbols used to build the words. The lexicographical order is one way of formalizing word order given the order of the underlying symbols. The formal notion starts with a finite set A, often called the alphabet, which is totally ordered. That is, for any two symbols a and b in A that are not the same symbol, either a < b or b < a. The words of A are the finite sequences of symbols from A, including words of length 1 containing a single symbol, words of length 2 with 2 symbols, and so on, even including the empty sequence varepsilon with no symbols at all. The lexicographical order on the set of all these finite words orders the words as follows: Given two different words of the same length, say a = a1a2...ak and b = b1b2...bk, the order of the two words depends on the alphabetic order of the symbols in the first place i where the two words differ (counting from the beginning of the words): a < b if and only if ai < bi in the underlying order of the alphabet A. If two words have different lengths, the usual lexicographical order pads the shorter one with "blanks" (a special symbol that is treated as smaller than every element of A) at the end until the words are the same length, and then the words are compared as in the previous case.

After this you can learn about Co-Lexicographical Order from the same Wikipedia page mentioned above. Above quoted part is taken directly from the Motivation and Definition titled part of the Wikipedia page mentioned above. Visit it once and you will have a better understanding of both.

You just need to find the Lexicographical and Co-Lexicographical position of (i, j, k) among all possible (foo1, foo2, foo3) in the array A of yours:

Based on the this knowledge, you will get that: 1). Number of elements A[foo1][foo2][foo3] (foo1, foo2, foo3) present before element A[i][j][k] (i, j, k) in Row Major Order or Lexicographical Order are: [ (i - x)*M*N + (j - y)*N + (k - z) ]

2). Number of elements A[foo1][foo2][foo3] (foo1, foo2, foo3) present before element A[i][j][k] (i, j, k) in Column Major Order or Co-lexicographical Order are: [ (i - x) + (j - y)*L + (k - z)*L*M ]

Now, you can do the rest of your calculation where you bring in your base and W thing to get the final answer you need.

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