Run-time error occurs when input value is greater than 100000 - c

Question

I am trying to implement the sieve of eratosthenes in C. The code works for small input values, but once the input goes beyond a certain range, a run- time error is thrown. This is the second problem in the classical section of the SPOJ base. What is the mistake?
#include<stdio.h>
#include<math.h>
int prime(unsigned long int, unsigned long int);
int main()
{
int nitem;
unsigned long int sn,fn;
scanf("%d", &nitem);
while(nitem)
{
scanf("%lu", &fn);
//printf("%d",fn);
scanf("%lu", &sn);
prime(fn, sn);
nitem--;
}
return 0;
}
int prime(unsigned long int fn, unsigned long int sn)
{
unsigned long int prim[100000];
int i,j,k;
for(i = 0; i < 100000; i++)
{
prim[i] = 1;
}
prim[0] = 0;
prim[1] = 0;
//printf("%d", sn);
//printf("%d", k);
//printf("%d", (k <= sn));
for(k = 2; k <= sqrt(sn); k++)
{
// printf("alksnc%5d", k);
if(prim[k] == 1)
{
for(j = 2; (k * j) <= sn; j++)
{
//printf("%d", prim[k]);
prim[k * j] = 0;
}
}
}
for(int i = 0; i <= sn; i++)
{
if(prim[i] !=0 && i >= fn)
{
printf("%lu\n", i);
}
}
printf("\n");
return;
}
Input:
1
100000 100345
output:
run time error
Input:
1
3 5
output:
3
5

Answer 1

We can make more efficient use of memory (2x) by only sieving odd numbers as all the even numbers you're processing waste time and space. It's trickier to work out but gives us something like:
#include <math.h>
#include <libc.h>
#define MAX_ODD_PRIMES 1048576
void prime(unsigned long fn, unsigned long sn)
{
unsigned char primes[MAX_ODD_PRIMES];
for (unsigned long i = 0; i < MAX_ODD_PRIMES; i++)
{
primes[i] = TRUE;
}
primes[0] = 0; // preset first odd, '1'
for (unsigned long k = 3; k <= sqrt(sn) + 1; k += 2)
{
if (primes[k / 2])
{
for (unsigned long j = 3; (k * j) <= sn; j += 2)
{
primes[k * j / 2] = FALSE;
}
}
}
if (fn <= 2)
{
printf("2\n");
fn = 3;
}
for (unsigned long i = fn / 2; i * 2 + 1 <= sn; i++)
{
if (primes[i])
{
printf("%lu\n", i * 2 + 1);
}
}
}
EXAMPLE
> ./a.out
1 1999900 2000000
1999957
1999969
1999979
1999993
>

Answer 2

1) Array range error.
By changing code
for (j = 2; (k * j) <= sn; j++) {
if (k * j >= 100000) {
printf("Out of range %d %d\n", k, j);
exit(1);
}
prim[k * j] = 0;
}
}
With input 2, 100000
Output
Out of range 2 50000
By using an array (VLA) sized to the task, this is avoided. Many other optimizations available. Consider also a malloc() array.
void prime(unsigned long int fn, unsigned long int sn) {
unsigned long int prim[sn + 1];
2) int prime() eventually performs return; where return something; is expected. Suggest changing function to void prime()
int prime(unsigned long int fn, unsigned long int sn) {
unsigned long int prim[100000];
...
printf("\n");
return;
}