Check if number is Prime - Primality Test
Sun Feb 06 2022 04:24:25 GMT+0000 (Coordinated Universal Time)
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@Uttam
#java
#mathematics
#lecture
#gfg
#geeksforgeeks
#efficientmethod
#naivemethod
#isprime
#primalitytest
// Time Complexity: O(N^1/2), Auxilliary Space: O(1)
//More Efficient Code(for large numbers)
//Almost 3x faster than Efficient Solution
import java.io.*;
import java.util.*;
public class Main {
static boolean isPrime(int n)
{
if(n==1)
return false;
if(n==2 || n==3)
return true;
if(n%2==0 || n%3==0)
return false;
for(int i=5; i*i<=n; i=i+6)
{
if(n % i == 0 || n % (i + 2) == 0)
return false;
}
return true;
}
//DRIVER CODE
public static void main (String[] args) {
//taking input using Scanner class
Scanner sc=new Scanner(System.in);
int T=sc.nextInt();//input testcases
while(T-->0)//while testcase have not been exhausted
{
Solution obj=new Solution ();
int N;
N=sc.nextInt();//input n
if(obj.isPrime(N))
System.out.println("Yes");
else
System.out.println("No");
}
}
}
//Efficient Code : Time Complexity : O(sqrt(n))
static boolean isPrime(int n)
{
if(n==1)
return false;
for(int i=2; i*i<=n; i++)
{
if(n % i == 0)
return false;
}
return true;
}
// Naive Method : Time Complexity : O(n)
static boolean isPrime(int n)
{
if(n == 1)
return false;
for(int i=2; i<n; i++)
{
if(n%i == 0)
return false;
}
return true;
}
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7. Primality Test
A prime number is a number which is only divisible by 1 and itself.
Given number N check if it is prime or not.
Example 1:
Input:
N = 5
Output: Yes
Explanation: 5 is only divisible by 1
and itself. So, 5 is a prime number.
Example 2:
Input:
N = 4
Output: No
Explanation: 4 is divisible by 2.
So, 4 is not a prime number.
Your Task:
You don't need to read input or print anything. Your task is to complete the function isPrime() that takes N as input parameter and returns True if N is prime else returns False.
Expected Time Complexity: O(N^1/2)
Expected Auxilliary Space: O(1)
Constraints:
1 <= N <= 10^9
https://practice.geeksforgeeks.org/problems/primality-test/1/?track=DSASP-Mathematics&batchId=190
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