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  • Runtime of optimized Primehunter

    - by Setton
    Ok so I need some serious runtime help here! This method should take in an int value, check its primality, and return true if the number is indeed a prime. I understand why the loop only needs to go up to i squared, I understand that the worst case scenario is the case in which either the number is prime (or a multiple of a prime). But I don't understand how to quantify the actual runtime. I have done the loop myself by hand to try to understand the pattern or correlation of the number (n) and how many loops occur, but I literally feel like I keep falling into the same trap every time. I need a new way of thinking about this! I have a hint: "Think about the SIZE of the integer" which makes me want to quantify the literal number of integers in a number in relation to how many iterations it does in the for loop (floor log(n)) +1). BUT IT'S NOT WORKIIIING?! I KNOW it isn't square root n, obviously. I'm asking for Big O notation. public class PrimeHunter { public static boolean isPrime(int n) { boolean answer = (n > 1) ? true : false; //runtime = linear runtime for (int i = 2; i * i <= n; i++) //runtime = ????? { if (n % i == 0) //doesn't occur if it is a prime { answer = false; break; } } return answer; //runtime = linear runtime } }

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