This algorithm finds a cycle by using two pointer. These pointers move over the sequence at different speeds. In each iteration the first pointer advances to the next element, but the second pointer advances two elements. It's not hard to see, that if there exists a cycle, the second pointer will make at least one full cycle and then meet the first pointer during the next few cycle loops.
This algorithm is also known as tortoise and the hare algorithm , based on the tale in which a tortoise here a slow pointer and a hare here a faster pointer make a race.
The algorithm and returns true as soon as it detects a cycle. If the sequence doesn't have a cycle, then the function will never stop.
However this cannot happen during Pollard's rho algorithm. First here is a implementation using the Floyd's cycle-finding algorithm. If GCC is not available, you can using a similar idea as binary exponentiation. Alternatively you can also implement the Montgomery multiplication.
Brent uses a similar algorithm as Floyd. It also uses two pointer. But instead of advancing the pointers by one and two respectably, we advance them in powers of two. These numbers are too large for the most naive approach to work, but small enough that for example an approach based on enumerating the prime numbers starting from 2 would work. Hint - start with the Sieve of Erasthones. Here is very elegant answer - which uses brute force not some fancy algorithm but in a smart way - by lowering the limit as we find primes and devide composite by those primes It also prints only the primes - and just the primes, and if one prime is more then once in the product - it will print it as many times as that prime is in the product.
That's the most naive way to check for primality. As explained above, this is very very slow if the number is large. Also note that this particular number has other, smaller, prime factors. For a brute force search like this, you can save a little work by dividing out the smaller factors as you find them, and then do a prime factorization of the smaller number that results. This has the advantage of only giving prime factors. Otherwise, you'll also get composite factors e. If you want to optimize that a bit, you can use the sieve of Eratosthenes to find the prime numbers up to the square root, and then only attempt division by primes.
In this case, that has little real payoff though -- even a completely naive algorithm will appear to produce results instantly. Going to the square root of the integer in question is a good shortcut. All that remains is checking if the number within that loop divides evenly. There is no reason for your Prime function. Since you are looking for the largest divisor, another trick would be to start from the highest integer less than the square root and go i For those answers which use a method isPrime int : boolean , there is a faster algorithm than the one previously implemented which is something like.
Hence the above algorithm. Wikipedia article on testing for primality. I got a very similar problem for my programming class. In my class it had to calculate for an inputted number. I used a solution very similar to Stijak. I edited my code to do the number from this problem instead of using an input. I don't recalculate the factorLimit until I have divided all instances of the current factor off. I had all the variables declared as long because I wanted the flexibility of using it for very large values of number.
I found the worst case scenario was a very large prime number like , or a very large number with a prime number square root like The more factors a number has the faster the algorithm runs. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Collectives on Stack Overflow. Learn more. Asked 11 years, 1 month ago. Active 3 years, 11 months ago.
Viewed 30k times. What errors do you get? That is, all numbers are divisible by themselves and 1. You're missing the "only" part of the definition. Unfortunately, you're not even close. Your primality algorithm doesn't work, because all numbers are divisible by themselves and zero- it's just that primes aren't divisible by anything else, and you have to implement a check for that.
The Sieve of Erasthones needs GB of RAM to operate up to a value in the B range, so recursive prime factorization is the only practical strategy, and with a large problem space, it will take hours or days.
This is the basis of all modern encryption: prime factorization above the size of RAM is very slow. Yes that was one of the logical errors, how could I fix that?
Adam, I think you mean " divisible by themselves and one ". Show 3 more comments. Printing 3. Friday, January 14, Code with C. C Program for Regula Falsi Method. C Program for Newton Divided Difference. C Program for Newton Forward Interpolation. Thank you. Please enter your comment! Please enter your name here. You have entered an incorrect email address! We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. Do not sell my personal information.
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