Prime Numbers

221910304057VIVEK — Mon, 25 Oct 2021 17:56:16 +0000

To find prime numbers in a fast and efficient way in O(sqrt(n)) time complexity.

To check prime numbers efficiently any number is a prime number if it is not divisible by any number less than or equal to the square root of the given number.

First we take an input n to check whether it is prime or not.
then the number is checked whether it is a valid number or not as numbers less than or equal to 1 are not prime in which case our function prime return -1 .

Then divisibility by 2 or 3 is checked ,if it is divisible by 2 or 3 then 0 is returned.

Then we check for all numbers below square root of the given number if it is divisible or not.
To check that more efficiently we iterate the variable i starting from 5 and increment it by 6 and we check it is divisible by i and i+2 if it is then 0 is returned else the given number is a prime number.

This program checks for prime numbers in o(sqrt(n)) time complexity.

import java.util.*;
public class Prime {
    static int prime(int n){
        if(n<=1){
            return -1;
        }
        if(n==2||n==3){
            return 1;
        }
        if(n%2==0||n%3==0){
            return 0;
        }
        for(int i=5;i*i<=n;i=i+6){
            if(n%i==0||n%(i+2)==0){
                return 0;
            }
        }
        return 1;
    }
    public static void main(String args[]) {
        Scanner sc=new Scanner(System.in);
        int n,r ;
        System.out.println("Enter the number to check");
        n=sc.nextInt();
        r=prime(n);
        System.out.println(r);
        if(r==-1){
        System.out.println("Please enter a valid number");
        }
        else if(r==0){
            System.out.println(""+n+" is not a prime number");
        }
        else{
            System.out.println("It is a prime number");
        }
    }
}

How to convert string to binary in python

221910304057VIVEK — Fri, 07 May 2021 16:09:14 +0000

Strings are an array of Unicode code characters.

Binary is a base-2 number system consisting of 0's and 1's. The computer understands binary. The computer sees the string in binary format i.e 'H'=1001000.

The string as seen by the computer is a binary number which is an ASCCI value( Decimal number) of the string converted to binary.

String to binary

To convert a string to binary we first append( join ) the string's individual ASCII values to a list l by using the function ord(_string).

The function ord(_string) gives the ASCII value of the string. i.e ord(H) = 72 , ord(e) = 101.

Then from the list of ASCII values we convert them to binary by using the function bin(_integer).

The function bin(_integer) converts decimal number to a binary number.
i.e bin(72) = 1001000

Then append(add) these binary values to a list m. Then the list m now consists of the binary numbers from the strings given and can be returned or printed.


import math

def toBinary(a):
  l,m=[],[]
  for i in a:
    l.append(ord(i))
  for i in l:
    m.append(int(bin(i)[2:]))
  return m

print("''Hello world'' in binary is ") 
print(toBinary("Hello world"))

DEV Community: 221910304057VIVEK

Prime Numbers

To find prime numbers in a fast and efficient way in O(sqrt(n)) time complexity.

How to convert string to binary in python

String to binary