Read each line, and use a random number to choose whether to keep that line or ignore it. For the first line, you want odds of 1:1 to keep; for the second, you want odds of 1:2, etc.
count = 0;
while (fgets(line, length, stream) != NULL)
{
count++;
if ((rand() * count) / RAND_MAX == 0)
strcpy(keptline, line);
}
I haven't verified that this has the proper random qualities, but it seems right at first glance.
It has been pointed out that integer overflow would quickly become a problem with the way the comparison is coded, and I had independently reached the same conclusion myself. There are probably many ways to fix it, but this is the first that comes to mind:
if ((rand() / (float)RAND_MAX) <= (1.0 / count))
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