Prime Number Generator in C

Question

This is the Link to the problem: http://www.spoj.com/problems/PRIME1/

Basically we get two limits and we have to print out all the primes between them...

Here is my Code (Language == C) :

#include <stdio.h>

void IsPrime(int test){
    for(int i= 2; i<test; i++){
        if(test%i==0){
            return;
        }
    }
    printf("%d\n",test);
}

int main(){
    int T,lower,upper;
    scanf("%d",&T);

    while(T--){
        scanf("%d",&lower);
        scanf("%d",&upper);

        for(int i = lower;i<=upper;i++){
            if(i>1){
            IsPrime(i);
            }
        }  
    }
return 0;
}

On my local machine I ran this and it works for the simple test cases... My message from the website is timeout error so I was wondering if there is a more efficient way to solve this problem because apparently I am not solving it fast enough?

Answer 1

To begin with, you don't have to go checking every number up to n to determine if n is prime, only to its square root (there is a mathematical proof, not going to give it now). So:

void IsPrime(int test){
    // i <= sqrt(test)
    // but to avoid sqrt you can do i * i <= test
    for(int i= 2; i * i <= test; i++){
        if(test%i==0){
            return;
        }
    }
    printf("%d\n",test);
}

Next, we know that after 2, all other prime numbers are odd, so we can loop by 2 if we treat 2 as special case:

// Do greater than one check only once
if (lower > 1) {
    // Special case - lower is 2
    if (lower == 2) {
        printf("%d\n", 2);
        ++lower;
    }

    for(int i = lower; i <= upper; i += 2){
        IsPrime(i);
    }
}

---

However since you have to do it T times, you will end up doing the checks a lot more than needed. Also, the problem has limits on n and m so it's basically perfect for a sieve, as @HennoBrandsma said.

Using these optimizations, you should go find all prime numbers to the limit, and store them in a container. Then, when prompted with a range, simply traverse the sieve and print out the numbers.

(That will require you to change up the IsPrime function a bit more - instead of printing the number right away, let it return true or false, and then based on that, add the number to the container)

Answer 2

You can try the following which has a slight optimization on the number of tests as well as skipping any even values greater than 2:

int isprime (int v)
{
    int i;

    if (v < 0) v = -v;                          /* insure v non-negative */
    if (v < 2 || !((unsigned)v & 1))    /* 0, 1 + even > 2 are not prime */
        return 0;

    if (v == 2) return 1;

    for (i = 3; i * i <= v; i+=2)
        if (v % i == 0)
            return 0;

    return 1;
}

If you can use the math library and math.h, the following may be faster:

int isprime (int v)
{
    int i;

    if (v < 0) v = -v;                          /* insure v non-negative */
    if (v < 2 || !((unsigned)v & 1))    /* 0, 1 + even > 2 are not prime */
        return 0;

    if (v == 2) return 1;

    for (i = 3; i <= sqrt (v); i+=2)
        if (v % i == 0)
            return 0;

    return 1;
}

I timed both versions over the int range for values between 1-2 million and they are close.

Note: In actual testing with repetitive calls, the version with i * i <= v (isprime2 below) is consistently faster than the call with i <= sqrt (v) (isprime3 below). e.g.:

$ ./bin/isprimetst2
  isprime  (1.650138 sec) - 78497 primes
  isprime2 (0.805816 sec) - 78497 primes
  isprime3 (0.983928 sec) - 78497 primes

The short driver iterated over all primes from 0-2000000, e.g.:

r = 0;
t1 = clock ();
for (v = 0; v < 2000000 - 1; v++) r += isprime2 (v);
t2 = clock ();
printf (" isprime2 (%lf sec) - %u primes\n", (t2-t1)/CLOCKS_PER_SEC, r);

r = 0;
t1 = clock ();
for (v = 0; v < 2000000 - 1; v++) r += isprime3 (v);
t2 = clock ();
printf (" isprime3 (%lf sec) - %u primes\n", (t2-t1)/CLOCKS_PER_SEC, r);

Answer 3

You can use a library maths.h in C and use sqrt function to calculate the square root of given number. So the program might be like this:

#include <stdio.h>
#include <maths.h>

int isPrime(int number){
    int i;
    if(number % 2 == 0){
        return;
    }

    for(i=3; i<=sqrt(number); i++){
        if(number % i == 0){
            return;
    }
    printf("%d\n",number);
}

int main(){
    int lower,upper,i;
    if(lower >1){
        if(lower == 2){
            printf("2\n");
        }

        for(i=lower; i<=upper; i++){
            isPrime(i);
        }
    return 0;
}

In short you can use some extra checks (like if(number % 2 == 0)) using if-else condition to decrease the time complexity of the program.For example a new if condition may be if(number % 5 ==0) etc. ,so with the help of these conditions check won't go in for loop in many of the cases, and that would decrease the time of the program.