multidimensional array

MULTIDIMENSIONAL ARRAY IN DATA STRUCTURE Understanding 2D and 3D Arrays, Memory Representation, and Applications Presented by: Rachit Joshi

INTRODUCTION TO MULTIDIMENSIONAL ARRAYS A multidimensional array is essentially an array of arrays.

It stores data across multiple dimensions.

Data can be organized in rows, columns, and additional dimensions.

Common forms include 2D, 3D, and n-dimensional arrays.

Useful for matrices, grids, tables, and structured datasets

2D AND 3D ARRAYS 2D Array Stores elements in rows and columns.

Example: 1 2 3 4 5 6 7 8 9 3D Array An extension of a 2D array.

Consists of multiple 2D arrays or blocks.

Useful for representing layered or volumetric data.

MEMORY REPRESENTATION Memory is essentially linear, so multidimensional arrays need to be mapped into a linear sequence.

A 2D array can be stored using: – Row-Major Order — elements of each row are stored together.

– Column-Major Order — elements of each column are stored

together.

The choice of memory layout can affect how efficiently data is accessed.

ACCESSING ELEMENTS IN A MULTIDIMENSIONAL ARRAY Each element is accessed using multiple indices.

In a 2D array, two indices represent the row and column.

In a 3D array, three indices represent the layer, row, and column.

Array indexing generally starts from 0 in languages such as C, C++, Java, and Python.

Example: A = [ 10 20 30 40 50 60 70 80 90 ] A[0][0] → 10 A[1][2] → 60 A[2][1] → 80

APPLICATIONS • Matrix representation • Grid-based problems • Dynamic programming • Graph adjacency matrices • Matrix multiplication • Game boards and structured datasets

CONCLUSION Multidimensional arrays provide an organized way to represent data across multiple dimensions.

Understanding their structure and memory representation is important for efficient data handling and programming