In this post, a program to search, insert, and delete operations in an unsorted array is discussed.
Search Operation:
In an unsorted array, the search operation can be performed by linear traversal from the first element to the last element.
Coding implementation of the search operation:
// C++ program to implement linear // search in unsorted array #include <bits/stdc++.h> using namespace std;
// Function to implement search operation int findElement( int arr[], int n, int key)
{ int i;
for (i = 0; i < n; i++)
if (arr[i] == key)
return i;
// If the key is not found
return -1;
} // Driver's Code int main()
{ int arr[] = { 12, 34, 10, 6, 40 };
int n = sizeof (arr) / sizeof (arr[0]);
// Using a last element as search element
int key = 40;
// Function call
int position = findElement(arr, n, key);
if (position == -1)
cout << "Element not found" ;
else
cout << "Element Found at Position: "
<< position + 1;
return 0;
} // This code is contributed // by Akanksha Rai |
// C program to implement linear // search in unsorted array #include <stdio.h> // Function to implement search operation int findElement( int arr[], int n, int key)
{ int i;
for (i = 0; i < n; i++)
if (arr[i] == key)
return i;
// If the key is not found
return -1;
} // Driver's Code int main()
{ int arr[] = { 12, 34, 10, 6, 40 };
int n = sizeof (arr) / sizeof (arr[0]);
// Using a last element as search element
int key = 40;
// Function call
int position = findElement(arr, n, key);
if (position == -1)
printf ( "Element not found" );
else
printf ( "Element Found at Position: %d" ,
position + 1);
return 0;
} |
// Java program to implement linear // search in unsorted arrays class Main {
// Function to implement
// search operation
static int findElement( int arr[], int n, int key)
{
for ( int i = 0 ; i < n; i++)
if (arr[i] == key)
return i;
// If the key is not found
return - 1 ;
}
// Driver's Code
public static void main(String args[])
{
int arr[] = { 12 , 34 , 10 , 6 , 40 };
int n = arr.length;
// Using a last element as search element
int key = 40 ;
// Function call
int position = findElement(arr, n, key);
if (position == - 1 )
System.out.println( "Element not found" );
else
System.out.println( "Element Found at Position: "
+ (position + 1 ));
}
} |
# Python program for searching in # unsorted array def findElement(arr, n, key):
for i in range (n):
if (arr[i] = = key):
return i
# If the key is not found
return - 1
# Driver's code if __name__ = = '__main__' :
arr = [ 12 , 34 , 10 , 6 , 40 ]
key = 40
n = len (arr)
# search operation
index = findElement(arr, n, key)
if index ! = - 1 :
print ( "Element Found at position: " + str (index + 1 ))
else :
print ( "Element not found" )
# Thanks to Aditi Sharma for contributing
# this code
|
// C# program to implement linear // search in unsorted arrays using System;
class main {
// Function to implement
// search operation
static int findElement( int [] arr, int n, int key)
{
for ( int i = 0; i < n; i++)
if (arr[i] == key)
return i;
// If the key is not found
return -1;
}
// Driver Code
public static void Main()
{
int [] arr = { 12, 34, 10, 6, 40 };
int n = arr.Length;
// Using a last element as
// search element
int key = 40;
int position = findElement(arr, n, key);
if (position == -1)
Console.WriteLine( "Element not found" );
else
Console.WriteLine( "Element Found at Position: "
+ (position + 1));
}
} // This code is contributed by vt_m. |
// Javascript program to implement linear // search in unsorted array // Function to implement search operation function findElement( arr, n, key)
{ let i;
for (i = 0; i < n; i++)
if (arr[i] == key)
return i;
return -1;
} // Driver program
let arr = [12, 34, 10, 6, 40];
let n = arr.length;
// Using a last element as search element
let key = 40;
let position = findElement(arr, n, key);
if (position == - 1)
document.write( "Element not found" );
else
document.write( "Element Found at Position: "
+ (position + 1));
|
<?php // PHP program to implement linear // search in unsorted array // Function to implement // search operation function findElement( $arr , $n , $key )
{ $i ;
for ( $i = 0; $i < $n ; $i ++)
if ( $arr [ $i ] == $key )
return $i ;
// If the key is not found
return -1;
} // Driver Code $arr = array (12, 34, 10, 6, 40);
$n = sizeof( $arr );
// Using a last element // as search element $key = 40;
$position = findElement( $arr , $n , $key );
if ( $position == - 1)
echo ( "Element not found" );
else echo ( "Element Found at Position: " . ( $position + 1));
// This code is contributed by Ajit. ?> |
Element Found at Position: 5
Time Complexity: O(N)
Auxiliary Space: O(1)
Insert Operation:
1. Insert at the end:
In an unsorted array, the insert operation is faster as compared to a sorted array because we don’t have to care about the position at which the element is to be placed.
Coding implementation of inserting an element at the end:
#include <iostream> using namespace std;
// Inserts a key in arr[] of given capacity. // n is the current size of arr[]. This // function returns n + 1 if insertion // is successful, else n. int insertSorted( int arr[], int n, int key, int capacity)
{ // Cannot insert more elements if n is
// already more than or equal to capacity
if (n >= capacity)
return n;
arr[n] = key;
return (n + 1);
} int main()
{ int arr[20] = { 12, 16, 20, 40, 50, 70 };
int capacity = sizeof (arr) / sizeof (arr[0]);
int n = 6;
int i, key = 26;
cout << "Before Insertion: " ;
for (i = 0; i < n; i++)
cout << arr[i] << " " ;
// Inserting key
n = insertSorted(arr, n, key, capacity);
cout << "\nAfter Insertion: " ;
for (i = 0; i < n; i++)
cout << arr[i] << " " ;
return 0;
} |
// C program to implement insert // operation in an unsorted array. #include <stdio.h> // Inserts a key in arr[] of given capacity. // n is current size of arr[]. This // function returns n + 1 if insertion // is successful, else n. int insertSorted( int arr[], int n, int key, int capacity)
{ // Cannot insert more elements if n is
// already more than or equal to capacity
if (n >= capacity)
return n;
arr[n] = key;
return (n + 1);
} // Driver Code int main()
{ int arr[20] = { 12, 16, 20, 40, 50, 70 };
int capacity = sizeof (arr) / sizeof (arr[0]);
int n = 6;
int i, key = 26;
printf ( "\n Before Insertion: " );
for (i = 0; i < n; i++)
printf ( "%d " , arr[i]);
// Inserting key
n = insertSorted(arr, n, key, capacity);
printf ( "\n After Insertion: " );
for (i = 0; i < n; i++)
printf ( "%d " , arr[i]);
return 0;
} |
// Java program to implement insert // operation in an unsorted array. class Main {
// Function to insert a given key in
// the array. This function returns n+1
// if insertion is successful, else n.
static int insertSorted( int arr[], int n, int key,
int capacity)
{
// Cannot insert more elements if n
// is already more than or equal to
// capacity
if (n >= capacity)
return n;
arr[n] = key;
return (n + 1 );
}
// Driver Code
public static void main(String[] args)
{
int [] arr = new int [ 20 ];
arr[ 0 ] = 12 ;
arr[ 1 ] = 16 ;
arr[ 2 ] = 20 ;
arr[ 3 ] = 40 ;
arr[ 4 ] = 50 ;
arr[ 5 ] = 70 ;
int capacity = 20 ;
int n = 6 ;
int i, key = 26 ;
System.out.print( "Before Insertion: " );
for (i = 0 ; i < n; i++)
System.out.print(arr[i] + " " );
// Inserting key
n = insertSorted(arr, n, key, capacity);
System.out.print( "\n After Insertion: " );
for (i = 0 ; i < n; i++)
System.out.print(arr[i] + " " );
}
} |
# Python program for inserting # an element in an unsorted array # method to insert element def insert(arr, element):
arr.append(element)
# Driver's code if __name__ = = '__main__' :
# declaring array and key to insert
arr = [ 12 , 16 , 20 , 40 , 50 , 70 ]
key = 26
# array before inserting an element
print ( "Before Inserting: " )
print (arr)
# array after Inserting element
insert(arr, key)
print ( "After Inserting: " )
print (arr)
# Thanks to Aditi Sharma for contributing
# this code
|
// C# program to implement insert // operation in an unsorted array. using System;
class main {
// Function to insert a given
// key in the array. This
// function returns n + 1
// if insertion is successful,
// else n.
static int insertSorted( int [] arr, int n, int key,
int capacity)
{
// Cannot insert more elements
// if n is already more than
// or equal to capacity
if (n >= capacity)
return n;
arr[n] = key;
return (n + 1);
}
// Driver Code
public static void Main()
{
int [] arr = new int [20];
arr[0] = 12;
arr[1] = 16;
arr[2] = 20;
arr[3] = 40;
arr[4] = 50;
arr[5] = 70;
int capacity = 20;
int n = 6;
int i, key = 26;
Console.Write( "Before Insertion: " );
for (i = 0; i < n; i++)
Console.Write(arr[i] + " " );
Console.WriteLine();
// Inserting key
n = insertSorted(arr, n, key, capacity);
Console.Write( "After Insertion: " );
for (i = 0; i < n; i++)
Console.Write(arr[i] + " " );
}
} // This code is contributed by vt_m. |
// Javascript program to implement insert // operation in an unsorted array. // Function to insert a given // key in the array. This // function returns n + 1 // if insertion is successful, // else n. function insertSorted(arr, n, key, capacity)
{ // Cannot insert more elements
// if n is already more than
// or equal to capacity
if (n >= capacity)
return n;
arr[n] = key;
return (n + 1);
} let arr = new Array(20);
arr[0] = 12; arr[1] = 16; arr[2] = 20; arr[3] = 40; arr[4] = 50; arr[5] = 70; let capacity = 20; let n = 6; let i, key = 26; document.write( "Before Insertion: " );
for (i = 0; i < n; i++)
document.write(arr[i]+ " " );
document.write( "</br>" );
// Inserting key n = insertSorted(arr, n, key, capacity); document.write( "After Insertion: " );
for (i = 0; i < n; i++)
document.write(arr[i]+ " " );
|
<?php // PHP program to implement insert // operation in an unsorted array. // Inserts a key in arr[] of given // capacity. n is current size of arr[]. // This function returns n + 1 if // insertion is successful, else n. function insertSorted(& $arr , $n , $key ,
$capacity )
{ // Cannot insert more elements if n is
// already more than or equal to capacity
if ( $n >= $capacity )
return $n ;
array_push ( $arr , $key );
return ( $n + 1);
} // Driver Code $arr = array (12, 16, 20, 40, 50, 70);
$capacity = 20;
$n = 6;
$key = 26;
echo "Before Insertion: " ;
for ( $i = 0; $i < $n ; $i ++)
echo $arr [ $i ] . " " ;
// Inserting key $n = insertSorted( $arr , $n ,
$key , $capacity );
echo "\nAfter Insertion: " ;
for ( $i = 0; $i < $n ; $i ++)
echo $arr [ $i ] . " " ;
// This code is contributed by // Rajput-Ji ?> |
Before Insertion: 12 16 20 40 50 70 After Insertion: 12 16 20 40 50 70 26
Time Complexity: O(1)
Auxiliary Space: O(1)
2. Insert at any position
Insert operation in an array at any position can be performed by shifting elements to the right, which are on the right side of the required position
Coding implementation of inserting an element at any position:
// C++ Program to Insert an element // at a specific position in an Array #include <bits/stdc++.h> using namespace std;
// Function to insert element // at a specific position void insertElement( int arr[], int n, int x, int pos)
{ // shift elements to the right
// which are on the right side of pos
for ( int i = n - 1; i >= pos; i--)
arr[i + 1] = arr[i];
arr[pos] = x;
} // Driver's code int main()
{ int arr[15] = { 2, 4, 1, 8, 5 };
int n = 5;
cout<< "Before insertion : " ;
for ( int i = 0; i < n; i++)
cout<<arr[i]<< " " ;
cout<<endl;
int x = 10, pos = 2;
// Function call
insertElement(arr, n, x, pos);
n++;
cout<< "After insertion : " ;
for ( int i = 0; i < n; i++)
cout<<arr[i]<< " " ;
return 0;
} |
// C Program to Insert an element // at a specific position in an Array #include <stdio.h> // Function to insert element // at a specific position void insertElement( int arr[], int n, int x, int pos)
{ // shift elements to the right
// which are on the right side of pos
for ( int i = n - 1; i >= pos; i--)
arr[i + 1] = arr[i];
arr[pos] = x;
} // Driver's code int main()
{ int arr[15] = { 2, 4, 1, 8, 5 };
int n = 5;
printf ( "Before insertion : " );
for ( int i = 0; i < n; i++)
printf ( "%d " , arr[i]);
printf ( "\n" );
int x = 10, pos = 2;
// Function call
insertElement(arr, n, x, pos);
n++;
printf ( "After insertion : " );
for ( int i = 0; i < n; i++)
printf ( "%d " , arr[i]);
return 0;
} |
/*package whatever //do not write package name here */ import java.io.*;
// Java Program to Insert an element // at a specific position in an Array class GFG {
static void insertElement( int arr[], int n, int x,
int pos)
{
// shift elements to the right
// which are on the right side of pos
for ( int i = n - 1 ; i >= pos; i--)
arr[i + 1 ] = arr[i];
arr[pos] = x;
}
public static void main(String[] args)
{
int arr[] = new int [ 15 ];
arr[ 0 ] = 2 ;
arr[ 1 ] = 4 ;
arr[ 2 ] = 1 ;
arr[ 3 ] = 8 ;
arr[ 4 ] = 5 ;
int n = 5 ;
int x = 10 , pos = 2 ;
System.out.print( "Before Insertion: " );
for ( int i = 0 ; i < n; i++)
System.out.print(arr[i] + " " );
// Inserting key at specific position
insertElement(arr, n, x, pos);
n += 1 ;
System.out.print( "\n\nAfter Insertion: " );
for ( int i = 0 ; i < n; i++)
System.out.print(arr[i] + " " );
}
} // This code is contributed by syedsarfarazahammed |
# python Program to Insert an element # at a specific position in an Array def insertElement(arr, n, x, pos) :
# shift elements to the right
# which are on the right side of pos
for i in range (n - 1 ,pos - 1 , - 1 ) :
arr[i + 1 ] = arr[i]
arr[pos] = x
# Driver's code if __name__ = = '__main__' :
# Declaring array and key to delete
# here -1 is for empty space
arr = [ 2 , 4 , 1 , 8 , 5 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 , - 1 ]
n = 5
print ( "Before insertion : " )
for i in range ( 0 ,n) :
print (arr[i],end = ' ' )
print ( "\n" )
x = 10 ;
pos = 2 ;
# Function call
insertElement(arr, n, x, pos);
n + = 1
print ( "After insertion : " )
for i in range ( 0 ,n) :
print (arr[i],end = ' ' )
#This Code is contributed by aditya942003patil
|
// C# program to implement insert // operation in an unsorted array. using System;
class main {
static void insertElement( int [] arr, int n, int x,
int pos)
{
// shift elements to the right
// which are on the right side of pos
for ( int i = n - 1; i >= pos; i--)
arr[i + 1] = arr[i];
arr[pos] = x;
}
public static void Main()
{
int [] arr = new int [20];
arr[0] = 2;
arr[1] = 4;
arr[2] = 1;
arr[3] = 8;
arr[4] = 5;
int x = 10;
int n = 5;
int pos = 2;
Console.Write( "Before Insertion: " );
for ( int i = 0; i < n; i++)
Console.Write(arr[i] + " " );
Console.WriteLine();
// Inserting key at specific position
insertElement(arr, n, x, pos);
n += 1;
Console.Write( "\n\nAfter Insertion: " );
for ( int i = 0; i < n; i++)
Console.Write(arr[i] + " " );
}
} // This code is contributed by sourabhdalal0001 |
// javascript Program to Insert an element // at a specific position in an Array function insertElement(arr, n, x, pos)
{
// shift elements to the right
// which are on the right side of pos
var i = n - 1;
for (i; i >= pos; i--)
{
arr[i + 1] = arr[i];
}
arr[pos] = x;
}
var arr = Array(15).fill(0);
arr[0] = 2;
arr[1] = 4;
arr[2] = 1;
arr[3] = 8;
arr[4] = 5;
var n = 5;
var x = 10;
var pos = 2;
console.log( "Before Insertion: " );
var i = 0;
for (i; i < n; i++)
{
console.log(arr[i] + " " );
}
// Inserting key at specific position
insertElement(arr, n, x, pos);
n += 1;
console.log( "\n\nAfter Insertion: " );
i = 0;
for (i; i < n; i++)
{
console.log(arr[i] + " " );
}
// This code is contributed by sourabhdalal0001.
|
<?php // Function to insert element at a specific position function insertElement(& $arr , $n , $x , $pos ) {
// shift elements to the right which are on the right side of pos
for ( $i = $n - 1; $i >= $pos ; $i --) {
$arr [ $i + 1] = $arr [ $i ];
}
// insert the new element at the specified position
$arr [ $pos ] = $x ;
} // Driver's code $arr = array (2, 4, 1, 8, 5);
$n = 5;
echo "Before insertion : " ;
for ( $i = 0; $i < $n ; $i ++) {
echo $arr [ $i ] . " " ;
} echo "\n" ;
$x = 10;
$pos = 2;
// Function call insertElement( $arr , $n , $x , $pos );
$n ++;
echo "After insertion : " ;
for ( $i = 0; $i < $n ; $i ++) {
echo $arr [ $i ] . " " ;
} ?> |
Before insertion : 2 4 1 8 5 After insertion : 2 4 10 1 8 5
Time complexity: O(N)
Auxiliary Space: O(1)
Delete Operation:
In the delete operation, the element to be deleted is searched using the linear search, and then the delete operation is performed followed by shifting the elements.
// C++ program to implement delete operation in a // unsorted array #include <iostream> using namespace std;
// To search a key to be deleted int findElement( int arr[], int n, int key);
// Function to delete an element int deleteElement( int arr[], int n, int key)
{ // Find position of element to be deleted
int pos = findElement(arr, n, key);
if (pos == -1) {
cout << "Element not found" ;
return n;
}
// Deleting element
int i;
for (i = pos; i < n - 1; i++)
arr[i] = arr[i + 1];
return n - 1;
} // Function to implement search operation int findElement( int arr[], int n, int key)
{ int i;
for (i = 0; i < n; i++)
if (arr[i] == key)
return i;
return -1;
} // Driver's code int main()
{ int i;
int arr[] = { 10, 50, 30, 40, 20 };
int n = sizeof (arr) / sizeof (arr[0]);
int key = 30;
cout << "Array before deletion\n" ;
for (i = 0; i < n; i++)
cout << arr[i] << " " ;
// Function call
n = deleteElement(arr, n, key);
cout << "\n\nArray after deletion\n" ;
for (i = 0; i < n; i++)
cout << arr[i] << " " ;
return 0;
} // This code is contributed by shubhamsingh10 |
// C program to implement delete operation in a // unsorted array #include <stdio.h> // To search a key to be deleted int findElement( int arr[], int n, int key);
// Function to delete an element int deleteElement( int arr[], int n, int key)
{ // Find position of element to be deleted
int pos = findElement(arr, n, key);
if (pos == -1) {
printf ( "Element not found" );
return n;
}
// Deleting element
int i;
for (i = pos; i < n - 1; i++)
arr[i] = arr[i + 1];
return n - 1;
} // Function to implement search operation int findElement( int arr[], int n, int key)
{ int i;
for (i = 0; i < n; i++)
if (arr[i] == key)
return i;
return -1;
} // Driver's code int main()
{ int i;
int arr[] = { 10, 50, 30, 40, 20 };
int n = sizeof (arr) / sizeof (arr[0]);
int key = 30;
printf ( "Array before deletion\n" );
for (i = 0; i < n; i++)
printf ( "%d " , arr[i]);
// Function call
n = deleteElement(arr, n, key);
printf ( "\nArray after deletion\n" );
for (i = 0; i < n; i++)
printf ( "%d " , arr[i]);
return 0;
} |
// Java program to implement delete // operation in an unsorted array class Main {
// function to search a key to
// be deleted
static int findElement( int arr[], int n, int key)
{
int i;
for (i = 0 ; i < n; i++)
if (arr[i] == key)
return i;
return - 1 ;
}
// Function to delete an element
static int deleteElement( int arr[], int n, int key)
{
// Find position of element to be
// deleted
int pos = findElement(arr, n, key);
if (pos == - 1 ) {
System.out.println( "Element not found" );
return n;
}
// Deleting element
int i;
for (i = pos; i < n - 1 ; i++)
arr[i] = arr[i + 1 ];
return n - 1 ;
}
// Driver's Code
public static void main(String args[])
{
int i;
int arr[] = { 10 , 50 , 30 , 40 , 20 };
int n = arr.length;
int key = 30 ;
System.out.println( "Array before deletion" );
for (i = 0 ; i < n; i++)
System.out.print(arr[i] + " " );
// Function call
n = deleteElement(arr, n, key);
System.out.println( "\n\nArray after deletion" );
for (i = 0 ; i < n; i++)
System.out.print(arr[i] + " " );
}
} |
# Python program to delete an element # from an unsorted array # Driver's code if __name__ = = '__main__' :
# Declaring array and key to delete
arr = [ 10 , 50 , 30 , 40 , 20 ]
key = 30
print ( "Array before deletion:" )
print (arr)
# deletes key if found in the array
# otherwise shows error not in list
arr.remove(key)
print ( "Array after deletion" )
print (arr)
# This code is contributed by Aditi Sharma.
|
// C# program to implement delete // operation in an unsorted array using System;
class main {
// Function to search a
// key to be deleted
static int findElement( int [] arr, int n, int key)
{
int i;
for (i = 0; i < n; i++)
if (arr[i] == key)
return i;
return -1;
}
// Function to delete an element
static int deleteElement( int [] arr, int n, int key)
{
// Find position of element
// to be deleted
int pos = findElement(arr, n, key);
if (pos == -1) {
Console.WriteLine( "Element not found" );
return n;
}
// Deleting element
int i;
for (i = pos; i < n - 1; i++)
arr[i] = arr[i + 1];
return n - 1;
}
// Driver Code
public static void Main()
{
int i;
int [] arr = { 10, 50, 30, 40, 20 };
int n = arr.Length;
int key = 30;
Console.Write( "Array before deletion " );
for (i = 0; i < n; i++)
Console.Write(arr[i] + " " );
Console.WriteLine();
// Function call
n = deleteElement(arr, n, key);
Console.Write( "Array after deletion " );
for (i = 0; i < n; i++)
Console.Write(arr[i] + " " );
}
} // This code is contributed by vt_m. |
// Java script program to implement delete // operation in an unsorted array // function to search a key to
// be deleted
function findElement(arr,n,key)
{
let i;
for (i = 0; i < n; i++)
if (arr[i] == key)
return i;
return -1;
}
// Function to delete an element
function deleteElement(arr,n,key)
{
// Find position of element to be
// deleted
let pos = findElement(arr, n, key);
if (pos == -1)
{
document.write( "Element not found" );
return n;
}
// Deleting element
let i;
for (i = pos; i< n - 1; i++)
arr[i] = arr[i + 1];
return n - 1;
}
// Driver Code
let i;
let arr = [10, 50, 30, 40, 20];
let n = arr.length;
let key = 30;
document.write( "Array before deletion<br>" );
for (i=0; i<n; i++)
document.write(arr[i] + " " );
n = deleteElement(arr, n, key);
document.write( "<br><br>Array after deletion<br>" );
for (i=0; i<n; i++)
document.write(arr[i]+ " " );
// This code is contributed by sravan kumar Gottumukkala |
<?php // PHP program to implement delete // operation in an unsorted array // To search a key to be deleted function findElement(& $arr , $n , $key )
{ for ( $i = 0; $i < $n ; $i ++)
if ( $arr [ $i ] == $key )
return $i ;
return -1;
} // Function to delete an element function deleteElement(& $arr , $n , $key )
{ // Find position of element to
// be deleted
$pos = findElement( $arr , $n , $key );
if ( $pos == -1)
{
echo "Element not found" ;
return $n ;
}
// Deleting element
for ( $i = $pos ; $i < $n - 1; $i ++)
$arr [ $i ] = $arr [ $i + 1];
return $n - 1;
} // Driver code $arr = array (10, 50, 30, 40, 20);
$n = count ( $arr );
$key = 30;
echo "Array before deletion\n" ;
for ( $i = 0; $i < $n ; $i ++)
echo $arr [ $i ] . " " ;
// Function call $n = deleteElement( $arr , $n , $key );
echo "\nArray after deletion\n" ;
for ( $i = 0; $i < $n ; $i ++)
echo $arr [ $i ] . " " ;
// This code is contributed by // Rajput-Ji ?> |
Array before deletion 10 50 30 40 20 Array after deletion 10 50 40 20
Time Complexity: O(N)
Auxiliary Space: O(1)