isPrime recursive

#include <iostream>
using namespace std;

int increments[] = { 2, 4 };

// Already beyond the square root? -> true (prime)

// (else)

// Divisible by current divisor?   -> false (not prime)

// (else)

// Calculate next divisor and recurse
bool isPrime(int n, int divisor, int incr) {
   return (divisor * divisor > n ) || 
          ( (n % divisor != 0) && 

            isPrime(n, divisor + incr, increments[incr == 2] )

          );
}
 
bool isPrime(int n) {
    return isPrime(n, 2, 1);
}

int main()
{
    for(int i = 2; i <= 100; i++ ) {
        if( isPrime(i) ) {
            cout << i << " ";
        }
    }
    cout << endl;

    return 0;
}

Other entries:

• isPrime: Naive version 
• isPrime, Optimization 1: Iterate only until the square root of the number
• isPrime, Optimization 2: Only divide by odd numbers, until the square root of the number
• isPrime, Optimization 3: Skip the divisors that are multiple of 2 or 3
• Keep the previosly generated primes and use them to test the following numbers.
• isPrime, Recursive.

Generate random numbers without repetition

Instead of controlling the repetition by inserting the already-generated-number in a set, create the set first, pick from there, and remove it for the next iteration,

e.g.:

import java.util.Random;

public class ControlRepetitionWithoutKeepingScore {

     public static void main(String []args) {

         int choices[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
         int sz = choices.length;
         Random random = new Random();
         
         for(int i = 0; i < choices.length; i++ ) {
             int pos = random.nextInt(sz);
             print(choices[pos]);
             
             choices[pos] = choices[sz-1];
             sz--;
         }
     }
}

Other entries:

• isPrime: Naive version 
• isPrime, Optimization 1: Iterate only until the square root of the number
• isPrime, Optimization 2: Only divide by odd numbers, until the square root of the number
• isPrime, Optimization 3: Skip the divisors that are multiple of 2 or 3
• Keep the previosly generated primes and use them to test the following numbers.
• isPrime, Recursive.