Matrix or Grid or 2D Array Complete Tutorial (original) (raw)

Last Updated : 10 Dec, 2024

**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 #include 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;

}

C

#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;

}

Java

/*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];
}

}

Python

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)

C#

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];
}

}

JavaScript

// 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 #include 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;

}

C

#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;

}

Java

/*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 } }; } }

Python

Initializing a 2-D array with values

arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]];

C#

using System;

public class GFG {

static public void Main()
{
    int[, ] arr = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
}

}

JavaScript

// 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 #include using namespace std;

int main() { // Initializing a 2-D vector with values vector<vector> 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;

}

C

#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;

}

Java

/*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]);
}

}

Python

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])

C#

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]);
}

}

JavaScript

// 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> 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;

}

C

#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;

}

Java

/*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

Python

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()

C#

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__

JavaScript

// 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.

`

Output

1 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 >& 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 > 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

// 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.

Python

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#

// 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

// 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:

• Sort the matrix row-wise
• Sort the matrix column-wise

**Related Article:

• Learn Data Structures and Algorithms | DSA Tutorial
• Why Data Structures and Algorithms Are Important to Learn?
• The Ultimate Beginner’s Guide For DSA
• Introduction to Data Structures
• What is Algorithm | Introduction to Algorithms
• Problems on Matrix Data Structure