Unit 1 · Foundation of DSA
Array (2D)
Learn two-dimensional arrays in DSA with matrix representation, row-column indexing, traversal, operations, and C examples.
Introduction
A two-dimensional array stores data in rows and columns, just like a table or matrix.
2D arrays are useful for matrices, grids, images, game boards, and many graph representation techniques.
Each element is accessed using two indexes: row index and column index.
Column
0 1 2
Row 0: 1 2 3
Row 1: 4 5 6
Row 2: 7 8 9
Where 2D Arrays Are Used
Matrices
Mathematical matrix operations use 2D arrays.
Tables
Rows and columns can store structured records.
Grids
Games, maps, and boards often use grid storage.
Images
Pixels can be represented using row and column positions.
Table of Contents
What is a 2D Array?
A 2D array is an array of arrays. It stores elements in tabular form.
In C, a 2D array declaration such as int matrix[3][3] creates 3 rows and 3 columns.
Access syntax: matrix[row][column]
Declaration and Initialization
A 2D array needs row size and column size. Values are usually written row by row.
int matrix[2][3];declares a matrix with 2 rows and 3 columns.int matrix[2][3] = {{1, 2, 3}, {4, 5, 6}};initializes values.matrix[1][2]accesses the element in second row and third column.
Traversing a 2D Array
2D arrays are usually traversed using nested loops. The outer loop handles rows, and the inner loop handles columns.
- Row-major traversal visits one complete row at a time.
- Column-major traversal visits one complete column at a time.
- C stores 2D arrays in row-major order.
Applications of 2D Arrays
2D arrays appear whenever data has two-dimensional structure.
- Matrix addition and multiplication.
- Sparse matrix representation.
- Chess board or tic-tac-toe board.
- Graph adjacency matrix.
- Image pixel processing.
2D Array Operation Complexity
| Operation | Time Complexity | Explanation |
|---|---|---|
| Access matrix[i][j] | O(1) | Direct row-column address calculation |
| Traverse all elements | O(rows * columns) | Every cell is visited |
| Search unsorted matrix | O(rows * columns) | May scan all cells |
| Print diagonal of square matrix | O(n) | Only n diagonal elements |
C Program Example
This program prints a 3 by 3 matrix using nested loops.
#include <stdio.h>
int main() {
int matrix[3][3] = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
printf("%d ", matrix[i][j]);
}
printf("\n");
}
return 0;
}
Output:
1 2 3
4 5 6
7 8 9
Key Points
- A 2D array stores elements in rows and columns.
- Each element is accessed using row and column indexes.
- Nested loops are used for traversal.
- 2D arrays are useful for matrices, grids, images, and adjacency matrices.
Interview Tip
When solving matrix problems, clearly identify row count, column count, and boundary conditions before coding.
Common Beginner Mistakes
- Mixing row index and column index.
- Using wrong loop limits.
- Forgetting that C indexes start from 0.
- Assuming every matrix is square.
Quick Revision
- Syntax: array[row][column].
- Traversal usually needs nested loops.
- Total elements = rows * columns.
- C stores 2D arrays row by row.
Summary
A two-dimensional array is a matrix-like structure that stores data in rows and columns. It is essential for matrix operations, grid-based problems, and many real-world data representations.
