We have to print alternate prime numbers till N.
Examples:
Input : N = 10
Output : 2 5
Input : N = 15
Output : 2 5 11
Naive Approach:We can just simply iterate over N and check whether the number is prime or not and print the alternate number just by keeping a simple altering flag variable.
C++
#include<bits/stdc++.h>
using namespace std;
int prime( int num)
{
int i, flag = 0;
for (i = 2; i<= num / 2; i++)
{
if (num % i == 0)
{
flag = 1;
break ;
}
}
if (flag == 0)
return 1;
else
return 0;
}
void print_alternate_prime( int n)
{
int counter = 0;
for ( int num = 2; num < n; num++)
{
if (prime(num) == 1)
{
if (counter % 2 == 0)
cout << num << " " ;
counter ++;
}
}
}
int main()
{
int n = 15;
cout << "Following are the alternate prime"
<< " number smaller than or equal to "
<< n << endl;
print_alternate_prime(n);
}
|
Java
class GFG
{
static int prime( int num)
{
int i, flag = 0 ;
for (i = 2 ; i<= num / 2 ; i++)
{
if (num % i == 0 )
{
flag = 1 ;
break ;
}
}
if (flag == 0 )
return 1 ;
else
return 0 ;
}
static void print_alternate_prime( int n)
{
int counter = 0 ;
for ( int num = 2 ; num < n; num++)
{
if (prime(num) == 1 )
{
if (counter % 2 == 0 )
System.out.print(num + " " );
counter ++;
}
}
}
public static void main(String[] args)
{
int n = 15 ;
System.out.println( "Following are the alternate " +
"prime number smaller than " +
"or equal to " + n);
print_alternate_prime(n);
}
}
|
Python3
def prime(num) :
flag = 0
for i in range ( 2 ,num / / 2 + 1 ) :
if num % i = = 0 :
flag = 1
break
if flag = = 0 :
return 1
else :
return 0
def print_alternate_prime(n):
counter = 0
for num in range ( 2 ,n) :
if prime(num) = = 1 :
if counter % 2 = = 0 :
print (num,end = " " )
counter + = 1
if __name__ = = "__main__" :
n = 15
print ( "Following are the alternate prime"
+ "number smaller than or equal to" ,n)
print_alternate_prime(n)
|
C#
using System;
class GFG
{
static int prime( int num)
{
int i, flag = 0;
for (i = 2; i <= num / 2; i++)
{
if (num % i == 0)
{
flag = 1;
break ;
}
}
if (flag == 0)
return 1;
else
return 0;
}
static void print_alternate_prime( int n)
{
int counter = 0;
for ( int num = 2; num < n; num++)
{
if (prime(num) == 1)
{
if (counter % 2 == 0)
Console.Write(num + " " );
counter ++;
}
}
}
public static void Main()
{
int n = 15;
Console.Write( "Following are the alternate " +
"prime number smaller than " +
"or equal to " + n + "\n" );
print_alternate_prime(n);
}
}
|
PHP
<?php
function prime( $num )
{
$flag = 0;
for ( $i = 2; $i <= $num / 2; $i ++)
{
if ( $num % $i == 0)
{
$flag = 1;
break ;
}
}
if ( $flag == 0)
return 1;
else
return 0;
}
function print_alternate_prime( $n )
{
$counter = 0;
for ( $num = 2; $num < $n ; $num ++)
{
if (prime( $num ) == 1)
{
if ( $counter % 2 == 0 )
echo $num . " " ;
$counter += 1;
}
}
}
$n = 15;
echo "Following are the alternate prime " .
"number smaller than or equal to " .
$n . "\n" ;
print_alternate_prime( $n );
?>
|
Javascript
<script>
function prime(num) {
var i, flag = 0;
for (i = 2; i <= num / 2; i++) {
if (num % i == 0) {
flag = 1;
break ;
}
}
if (flag == 0)
return 1;
else
return 0;
}
function print_alternate_prime(n)
{
var counter = 0;
for (num = 2; num < n; num++)
{
if (prime(num) == 1)
{
if (counter % 2 == 0)
document.write(num + " " );
counter++;
}
}
}
var n = 15;
document.write( "Following are the alternate " + "prime number smaller than " + "or equal to " + n+ "<br/>" );
print_alternate_prime(n);
</script>
|
Output: Following are the alternate prime numbers smaller than or equal to 15
2 5 11
Time Complexity: O(N * )
Efficient approach: Using Sieve of Eratosthenes we can just print all the alternate true values in the sieve.
C++
#include <bits/stdc++.h>
using namespace std;
void SieveOfEratosthenes( int n)
{
bool prime[n + 1];
memset (prime, true , sizeof (prime));
for ( int p = 2; p * p <= n; p++) {
if (prime[p] == true ) {
for ( int i = p * 2; i <= n; i += p)
prime[i] = false ;
}
}
bool flag = true ;
for ( int p = 2; p <= n; p++) {
if (prime[p]) {
if (flag) {
cout << p << " " ;
flag = false ;
}
else {
flag = true ;
}
}
}
}
int main()
{
int n = 15;
cout << "Following are the alternate"
<< " prime numbers smaller "
<< " than or equal to " << n << endl;
SieveOfEratosthenes(n);
return 0;
}
|
Java
class GFG
{
static void SieveOfEratosthenes( int n)
{
boolean []prime = new boolean [n + 1 ];
for ( int i = 0 ; i < prime.length; i++)
prime[i] = true ;
for ( int p = 2 ; p * p <= n; p++)
{
if (prime[p] == true )
{
for ( int i = p * 2 ;
i <= n; i += p)
prime[i] = false ;
}
}
boolean flag = true ;
for ( int p = 2 ; p <= n; p++)
{
if (prime[p])
{
if (flag)
{
System.out.print(p + " " );
flag = false ;
}
else
{
flag = true ;
}
}
}
}
public static void main(String[] args)
{
int n = 15 ;
System.out.println( "Following are the alternate" +
" prime numbers smaller " +
"than or equal to " + n );
SieveOfEratosthenes(n);
}
}
|
Python 3
def SieveOfEratosthenes(n):
prime = [ None ] * (n + 1 )
for i in range ( len (prime)):
prime[i] = True
p = 2
while p * p < = n:
if (prime[p] = = True ):
for i in range (p * 2 , n + 1 , p):
prime[i] = False
p + = 1
flag = True
for p in range ( 2 , n + 1 ):
if (prime[p]):
if (flag):
print ( str (p), end = " " )
flag = False
else :
flag = True
if __name__ = = "__main__" :
n = 15
print ( "Following are the alternate" +
" prime numbers smaller " +
"than or equal to " + str (n))
SieveOfEratosthenes(n)
|
C#
using System;
class GFG
{
static void SieveOfEratosthenes( int n)
{
bool [] prime = new bool [n + 1];
for ( int i = 0; i < prime.Length; i++)
prime[i] = true ;
for ( int p = 2; p * p <= n; p++)
{
if (prime[p] == true )
{
for ( int i = p * 2;
i <= n; i += p)
prime[i] = false ;
}
}
bool flag = true ;
for ( int p = 2; p <= n; p++)
{
if (prime[p])
{
if (flag)
{
Console.Write(p + " " );
flag = false ;
}
else
{
flag = true ;
}
}
}
}
public static void Main()
{
int n = 15;
Console.Write( "Following are the alternate" +
" prime numbers smaller " +
"than or equal to " + n + "\n" );
SieveOfEratosthenes(n);
}
}
|
PHP
<?php
function SieveOfEratosthenes( $n )
{
$prime = array ();
for ( $i = 0; $i <= $n ; $i ++)
$prime [ $i ] = true;
for ( $p = 2; $p * $p <= $n ; $p ++)
{
if ( $prime [ $p ] == true)
{
for ( $i = $p * 2;
$i <= $n ; $i += $p )
$prime [ $i ] = false;
}
}
$flag = true;
for ( $p = 2; $p <= $n ; $p ++)
{
if ( $prime [ $p ])
{
if ( $flag )
{
echo $p . " " ;
$flag = false;
}
else
{
$flag = true;
}
}
}
}
$n = 15;
echo "Following are the alternate" .
" prime numbers smaller " .
"than or equal to " . $n . "\n" ;
SieveOfEratosthenes( $n );
?>
|
Javascript
<script>
function SieveOfEratosthenes(n)
{
let prime = new Array(n + 1);
for (let i = 0; i < prime.length; i++)
prime[i] = true ;
for (let p = 2; p * p <= n; p++)
{
if (prime[p] == true )
{
for (let i = p * 2;
i <= n; i += p)
prime[i] = false ;
}
}
let flag = true ;
for (let p = 2; p <= n; p++)
{
if (prime[p])
{
if (flag)
{
document.write(p + " " );
flag = false ;
}
else
{
flag = true ;
}
}
}
}
let n = 15;
document.write( "Following are the alternate" +
" prime numbers smaller " +
"than or equal to " + n + "<br>" );
SieveOfEratosthenes(n);
</script>
|
Output: Following are the alternate prime numbers smaller than or equal to 15
2 5 11
Time complexity: O(n log log n).
Auxilitary Space Complexity : O(n).
Last Updated :
13 Apr, 2023
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