These days I am looking at skiplist code in Algorithms in C, Parts 1-4, and when insert a new value into skiplist is more complex than I think. During insert, code should ensure that the new value insert into level i with the probability of 1/2^i, and this implement by below code:
static int Rand()
{
int i, j = 0;
uint32_t t = rand();
for (i = 1, j = 2; i < lg_n_max; i ++, j += j)
if (t > RANDMAX / j)
break;
if (i > lg_n)
lg_n = i;
return i;
}
I don't know how the Rand function ensure this, can you explain this for me, thank you.
Presumably RANDMAX is intended to be RAND_MAX.
Neglecting rounding issues, half the return values of rand are above RAND_MAX / 2, and therefore half the time, the loop exits with i = 1.
If the loop continues, it updates i to 2 and j to 4. Then half the remaining return values (¾ of the total) are above RAND_MAX / 4, so, one-quarter of the time, the loop exits with i = 2.
Further iterations continue in the same manner, each iteration exiting with a portion of return values that is half the previous, until the lg_n_max limit is reached.
Thus, neglecting rounding issues and the final limit, the routine returns 1 half the time, 2 one-quarter of the time, 3 one-eighth the time, and so on.
lg_n is not defined in the routine. It appears to be a record of the greatest value returned by the routine so far.