Matrix or Grid or 2D Array - Complete Tutorial
Last Updated :
23 Jul, 2025
Matrix or Grid is a two-dimensional array mostly used in mathematical and scientific calculations. It is also considered as an array of arrays, where array at each index has the same size.
Representation of Matrix Data Structure:
As you can see from the below image, the elements are organized in rows and columns. As shown in the image, the cell a[0][0] is the first element of the first row and first column.
Declaration of Matrix Data Structure :
Declaration of a Matrix or two-dimensional array is very much similar to that of a one-dimensional array, given as follows.
C++
#include <iostream>
#include <vector>
using namespace std;
int main()
{
// Defining number of rows and columns in matrix
int rows = 3, cols = 3;
// Vector of vectors declaration
vector<vector<int>> arr(rows, vector<int>(cols));
return 0;
}
#include <stdio.h>
int main() {
// Defining number of rows and columns in matrix
int rows = 3, cols = 3;
// Array Declaration
int arr[rows][cols];
return 0;
}
/*package whatever //do not write package name here */
import java.io.*;
class GFG {
public static void main(String[] args)
{
// Defining number of rows and columns in matrix
int rows = 3, cols = 3;
// Array Declaration
int[][] arr
= new int[rows][cols];
}
}
# Defining number of rows and columns in matrix
rows = 3
cols = 3
# Declaring a matrix of size 3 X 3, and
# initializing it with value zero
rows, cols = (3, 3)
arr = [[0]*cols]*rows
print(arr)
using System;
public class GFG {
static public void Main()
{
// Defining number of rows and columns in matrix
int rows = 3, cols = 3;
// Array Declaration
int[, ] arr
= new int[rows, cols];
}
}
// Defining number of rows and columns in matrix
rows = 3,
cols = 3;
// Declare a 2D array using array constructor
let arr = new Array(3);
// Python declaration
for (let i = 0; i < arr.length; i++) {
arr[i] = new Array(3); // Each row has 3 columns
}
Initializing Matrix Data Structure:
In initialization, we assign some initial value to all the cells of the matrix. Below is the implementation to initialize a matrix in different languages:
C++
#include <iostream>
#include <vector>
using namespace std;
int main() {
// Initializing a 2-D vector with values
vector<vector<int>> arr = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
return 0;
}
#include <stdio.h>
int main() {
// Initializing a 2-D array with values
int arr[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
return 0;
}
/*package whatever //do not write package name here */
import java.io.*;
class GFG {
public static void main(String[] args)
{
// Initializing a 2-D array with values
int arr[][]
= { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
}
}
# Initializing a 2-D array with values
arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]];
using System;
public class GFG {
static public void Main()
{
int[, ] arr = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
}
}
// Initializing a 2-D array with values
let arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]];
Operations on Matrix Data Structure:
We can perform a variety of operations on the Matrix Data Structure. Some of the most common operations are:
- Access elements of Matrix
- Traversal of a Matrix
- Searching in a Matrix
- Sorting a Matrix
1. Access elements of Matrix Data Structure:
Like one-dimensional arrays, matrices can be accessed randomly by using their indices to access the individual elements. A cell has two indices, one for its row number, and the other for its column number. We can use arr[i][j] to access the element which is at the ith row and jth column of the matrix.
C++
#include <iostream>
#include <vector>
using namespace std;
int main()
{
// Initializing a 2-D vector with values
vector<vector<int>> arr = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
// Accessing elements of 2-D vector
cout << "First element of first row: " << arr[0][0] << "\n";
cout << "Third element of second row: " << arr[1][2] << "\n";
cout << "Second element of third row: " << arr[2][1] << "\n";
return 0;
}
#include <stdio.h>
int main()
{
// Initializing a 2-D array with values
int arr[3][3]
= { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
// Accessing elements of 2-D array
printf("First element of first row: %d\n", arr[0][0]);
printf("Third element of second row: %d\n", arr[1][2]);
printf("Second element of third row: %d\n", arr[2][1]);
return 0;
}
/*package whatever //do not write package name here */
import java.io.*;
class GFG {
public static void main(String[] args)
{
// Initializing a 2-D array with values
int[][] arr
= { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
// Accessing elements of 2-D array
System.out.println("First element of first row: "
+ arr[0][0]);
System.out.println("Third element of second row: "
+ arr[1][2]);
System.out.println("Second element of third row: "
+ arr[2][1]);
}
}
# Initializing a 2-D array with values
arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
# Accessing elements of 2-D array
print("First element of first row:", arr[0][0])
print("Third element of second row:", arr[1][2])
print("Second element of third row:", arr[2][1])
using System;
public class GFG {
static public void Main()
{
// Initializing a 2-D array with values
int[, ] arr
= { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
// Accessing elements of 2-D array
Console.WriteLine("First element of first row: "
+ arr[0, 0]);
Console.WriteLine("Third element of second row: "
+ arr[1, 2]);
Console.WriteLine("Second element of third row: "
+ arr[2, 1]);
}
}
// Initializing a 2-D array with values
let arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]];
// Accessing elements of 2-D array
console.log("First element of first row: " + arr[0][0]);
console.log("Third element of second row: " + arr[1][2]);
console.log("Second element of third row: " + arr[2][1]);
2. Traversal of a Matrix Data Structure:
We can traverse all the elements of a matrix or two-dimensional array by using two for-loops.
C++
#include <bits/stdc++.h>
using namespace std;
int main()
{
// Initializing a 2-D vector with values
vector<vector<int>> arr = { { 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 } };
// Traversing over all the rows
for (int i = 0; i < arr.size(); i++) {
// Traversing over all the columns of each row
for (int j = 0; j < arr[i].size(); j++) {
cout << arr[i][j] << " ";
}
cout << endl;
}
return 0;
}
#include <stdio.h>
int main()
{
int arr[3][4] = { { 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 } };
// Traversing over all the rows
for (int i = 0; i < 3; i++) {
// Traversing over all the columns of each row
for (int j = 0; j < 4; j++) {
printf("%d ", arr[i][j]);
}
printf("\n");
}
return 0;
}
/*package whatever //do not write package name here */
import java.io.*;
class GFG {
public static void main(String[] args)
{
int[][] arr = { { 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 } };
// Traversing over all the rows
for (int i = 0; i < 3; i++) {
// Traversing over all the columns of each row
for (int j = 0; j < 4; j++) {
System.out.print(arr[i][j] + " ");
}
System.out.println();
}
}
}
// This code is contributed by lokesh
# Initializing a 2-D list with values
arr = [
[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12]
]
# Traversing each row
for row in arr:
# Traversing each element
# in the current row
for x in row:
print(x, end=" ")
print()
using System;
public class GFG {
static public void Main()
{
int[, ] arr = new int[3, 4] { { 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 } };
// Traversing over all the rows
for (int i = 0; i < 3; i++) {
// Traversing over all the columns of each row
for (int j = 0; j < 4; j++) {
Console.Write(arr[i, j]);
Console.Write(" ");
}
Console.WriteLine(" ");
}
}
}
// This code is contributed by akashish__
// JS code for above approach
let arr = [[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12]];
// Traversing over all the rows
for (let i = 0; i < 3; i++) {
let s="";
// Traversing over all the columns of each row
for (let j = 0; j < 4; j++) {
s+=(arr[i][j]+" ");
}
console.log(s);
}
// This code is contributed by ishankhandelwals.
Output1 2 3 4
5 6 7 8
9 10 11 12
3. Searching in a Matrix Data Structure:
We can search an element in a matrix by traversing all the elements of the matrix.
Below is the implementation to search an element in a matrix:
C++
#include <bits/stdc++.h>
using namespace std;
bool searchInMatrix(vector<vector<int> >& arr, int x)
{
int m = arr.size(), n = arr[0].size();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (arr[i][j] == x)
return true;
}
}
return false;
}
// Driver program to test above
int main()
{
int x = 8;
vector<vector<int> > arr
= { { 0, 6, 8, 9, 11 },
{ 20, 22, 28, 29, 31 },
{ 36, 38, 50, 61, 63 },
{ 64, 66, 100, 122, 128 } };
if (searchInMatrix(arr, x))
cout << "YES" << endl;
else
cout << "NO" << endl;
return 0;
}
// Java code for the above approach
import java.io.*;
class GFG {
static boolean searchInMatrix(int[][] arr, int x)
{
int m = arr.length, n = arr[0].length;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (arr[i][j] == x)
return true;
}
}
return false;
}
public static void main(String[] args)
{
int x = 8;
int[][] arr = { { 0, 6, 8, 9, 11 },
{ 20, 22, 28, 29, 31 },
{ 36, 38, 50, 61, 63 },
{ 64, 66, 100, 122, 128 } };
if (searchInMatrix(arr, x)) {
System.out.println("YES");
}
else {
System.out.println("NO");
}
}
}
// This code is contributed by lokeshmvs21.
# Function to search for an element in a 2-D list
def search_in_matrix(arr, x):
rows, cols = len(arr), len(arr[0])
# Traverse each row and column
for i in range(rows):
for j in range(cols):
if arr[i][j] == x:
return True
return False
# Driver code to test the function
x = 8
arr = [
[0, 6, 8, 9, 11],
[20, 22, 28, 29, 31],
[36, 38, 50, 61, 63],
[64, 66, 100, 122, 128]
]
if search_in_matrix(arr, x):
print("YES")
else:
print("NO")
// C# code for the above approach
using System;
public class GFG {
static bool searchInMatrix(int[,] arr, int x) {
int m = arr.GetLength(0), n = arr.GetLength(1);
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (arr[i, j] == x)
return true;
}
}
return false;
}
public static void Main(string[] args) {
int x = 8;
int[,] arr = { { 0, 6, 8, 9, 11 },
{ 20, 22, 28, 29, 31 },
{ 36, 38, 50, 61, 63 },
{ 64, 66, 100, 122, 128 }
};
if (searchInMatrix(arr, x)) {
Console.WriteLine("YES");
} else {
Console.WriteLine("NO");
}
}
}
// JavaScript code for the above approach
function searchInMatrix(arr, x)
{
let m = arr.length, n = arr[0].length;
for (let i = 0; i < m; i++) {
for (let j = 0; j < n; j++) {
if (arr[i][j] == x)
return true;
}
}
return false;
}
// Driver program to test above
let x = 8;
let arr = [
[ 0, 6, 8, 9, 11 ],
[ 20, 22, 28, 29, 31 ],
[ 36, 38, 50, 61, 63 ],
[ 64, 66, 100, 122, 128 ]
];
if (searchInMatrix(arr, x))
console.log("YES");
else
console.log("NO");
4. Sorting Matrix Data Structure:
We can sort a matrix in two-ways:
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