Matrix or Grid or 2D Array – Complete Tutorial

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.

#include<iostream>#include<vector>usingnamespacestd;intmain(){// Defining number of rows and columns in matrixintrows=3,cols=3;// Vector of vectors declarationvector<vector<int>>arr(rows,vector<int>(cols));return0;}

#include<stdio.h>intmain(){// Defining number of rows and columns in matrixintrows=3,cols=3;// Array Declarationintarr[rows][cols];return0;}

/*package whatever //do not write package name here */importjava.io.*;classGFG{publicstaticvoidmain(String[]args){// Defining number of rows and columns in matrixintrows=3,cols=3;// Array Declarationint[][]arr=newint[rows][cols];}}

# Defining number of rows and columns in matrixrows=3cols=3# Declaring a matrix of size 3 X 3, and # initializing it with value zerorows,cols=(3,3)arr=[[0]*cols]*rowsprint(arr)

usingSystem;publicclassGFG{staticpublicvoidMain(){// Defining number of rows and columns in matrixintrows=3,cols=3;// Array Declarationint[,]arr=newint[rows,cols];}}

// Defining number of rows and columns in matrixrows=3,cols=3;// Declare a 2D array using array constructorletarr=newArray(3);// Python declarationfor(leti=0;i<arr.length;i++){arr[i]=newArray(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:

#include<iostream>#include<vector>usingnamespacestd;intmain(){// Initializing a 2-D vector with valuesvector<vector<int>>arr={{1,2,3},{4,5,6},{7,8,9}};return0;}

#include<stdio.h>intmain(){// Initializing a 2-D array with valuesintarr[3][3]={{1,2,3},{4,5,6},{7,8,9}};return0;}

/*package whatever //do not write package name here */importjava.io.*;classGFG{publicstaticvoidmain(String[]args){// Initializing a 2-D array with valuesintarr[][]={{1,2,3},{4,5,6},{7,8,9}};}}

# Initializing a 2-D array with valuesarr=[[1,2,3],[4,5,6],[7,8,9]];

usingSystem;publicclassGFG{staticpublicvoidMain(){int[,]arr={{1,2,3},{4,5,6},{7,8,9}};}}

// Initializing a 2-D array with valuesletarr=[[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.

#include<iostream>#include<vector>usingnamespacestd;intmain(){// Initializing a 2-D vector with valuesvector<vector<int>>arr={{1,2,3},{4,5,6},{7,8,9}};// Accessing elements of 2-D vectorcout<<"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";return0;}

#include<stdio.h>intmain(){// Initializing a 2-D array with valuesintarr[3][3]={{1,2,3},{4,5,6},{7,8,9}};// Accessing elements of 2-D arrayprintf("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]);return0;}

/*package whatever //do not write package name here */importjava.io.*;classGFG{publicstaticvoidmain(String[]args){// Initializing a 2-D array with valuesint[][]arr={{1,2,3},{4,5,6},{7,8,9}};// Accessing elements of 2-D arraySystem.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 valuesarr=[[1,2,3],[4,5,6],[7,8,9]]# Accessing elements of 2-D arrayprint("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])

usingSystem;publicclassGFG{staticpublicvoidMain(){// Initializing a 2-D array with valuesint[,]arr={{1,2,3},{4,5,6},{7,8,9}};// Accessing elements of 2-D arrayConsole.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 valuesletarr=[[1,2,3],[4,5,6],[7,8,9]];// Accessing elements of 2-D arrayconsole.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.

#include<bits/stdc++.h>usingnamespacestd;intmain(){// Initializing a 2-D vector with valuesvector<vector<int>>arr={{1,2,3,4},{5,6,7,8},{9,10,11,12}};// Traversing over all the rowsfor(inti=0;i<arr.size();i++){// Traversing over all the columns of each rowfor(intj=0;j<arr[i].size();j++){cout<<arr[i][j]<<" ";}cout<<endl;}return0;}

#include<stdio.h>intmain(){intarr[3][4]={{1,2,3,4},{5,6,7,8},{9,10,11,12}};// Traversing over all the rowsfor(inti=0;i<3;i++){// Traversing over all the columns of each rowfor(intj=0;j<4;j++){printf("%d ",arr[i][j]);}printf("\n");}return0;}

/*package whatever //do not write package name here */importjava.io.*;classGFG{publicstaticvoidmain(String[]args){int[][]arr={{1,2,3,4},{5,6,7,8},{9,10,11,12}};// Traversing over all the rowsfor(inti=0;i<3;i++){// Traversing over all the columns of each rowfor(intj=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 valuesarr=[[1,2,3,4],[5,6,7,8],[9,10,11,12]]# Traversing each rowforrowinarr:# Traversing each element# in the current rowforxinrow:print(x,end=" ")print()

usingSystem;publicclassGFG{staticpublicvoidMain(){int[,]arr=newint[3,4]{{1,2,3,4},{5,6,7,8},{9,10,11,12}};// Traversing over all the rowsfor(inti=0;i<3;i++){// Traversing over all the columns of each rowfor(intj=0;j<4;j++){Console.Write(arr[i,j]);Console.Write(" ");}Console.WriteLine(" ");}}}// This code is contributed by akashish__

// JS code for above approachletarr=[[1,2,3,4],[5,6,7,8],[9,10,11,12]];// Traversing over all the rowsfor(leti=0;i<3;i++){lets="";// Traversing over all the columns of each rowfor(letj=0;j<4;j++){s+=(arr[i][j]+" ");}console.log(s);}// This code is contributed by ishankhandelwals.

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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:

#include<bits/stdc++.h>usingnamespacestd;boolsearchInMatrix(vector<vector<int>>&arr,intx){intm=arr.size(),n=arr[0].size();for(inti=0;i<m;i++){for(intj=0;j<n;j++){if(arr[i][j]==x)returntrue;}}returnfalse;}// Driver program to test aboveintmain(){intx=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;elsecout<<"NO"<<endl;return0;}

// Java code for the above approachimportjava.io.*;classGFG{staticbooleansearchInMatrix(int[][]arr,intx){intm=arr.length,n=arr[0].length;for(inti=0;i<m;i++){for(intj=0;j<n;j++){if(arr[i][j]==x)returntrue;}}returnfalse;}publicstaticvoidmain(String[]args){intx=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 listdefsearch_in_matrix(arr,x):rows,cols=len(arr),len(arr[0])# Traverse each row and columnforiinrange(rows):forjinrange(cols):ifarr[i][j]==x:returnTruereturnFalse# Driver code to test the functionx=8arr=[[0,6,8,9,11],[20,22,28,29,31],[36,38,50,61,63],[64,66,100,122,128]]ifsearch_in_matrix(arr,x):print("YES")else:print("NO")

// C# code for the above approachusingSystem;publicclassGFG{staticboolsearchInMatrix(int[,]arr,intx){intm=arr.GetLength(0),n=arr.GetLength(1);for(inti=0;i<m;i++){for(intj=0;j<n;j++){if(arr[i,j]==x)returntrue;}}returnfalse;}publicstaticvoidMain(string[]args){intx=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 approachfunctionsearchInMatrix(arr,x){letm=arr.length,n=arr[0].length;for(leti=0;i<m;i++){for(letj=0;j<n;j++){if(arr[i][j]==x)returntrue;}}returnfalse;}// Driver program to test aboveletx=8;letarr=[[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");elseconsole.log("NO");

YES

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

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