How do I generate random numbers without rand() function?

Look at implementing a pseudo-random generator (what's "inside" rand()) of your own, for instance the Mersenne twister is highly-regarded.

For "not too random" integers, you could start with the current UNIX time, then use the recursive formula r = ((r * 7621) + 1) % 32768;. The nth random integer between 0 (inclusive) and M (exclusive) would be r % M after the nth iteration.

This is called a linear congruential generator.

The recursion formula is what bzip2 uses to select the pivot in its quicksort implementation. I wouldn't know about other purposes, but it works pretty well for this particular one...

If you're after an ultra-simple pseudo-random generator, you can just use a Linear Feedback shift Register.

The wikipedia article has some code snippets for you to look at, but basically the code for a 16-bit generator will look something like this (lightly massaged from that page...)

  unsigned short lfsr = 0xACE1u;
  unsigned bit;

  unsigned rand()
  {
    bit  = ((lfsr >> 0) ^ (lfsr >> 2) ^ (lfsr >> 3) ^ (lfsr >> 5) ) & 1;
    return lfsr =  (lfsr >> 1) | (bit << 15);
  }