bearophile wrote:
Andrei Alexandrescu:
I understood that. My problem is that a quadratic algorithm is applied
to 0.9 of the input. That makes overall behavior quadratic even if you
complete the last 10% in no time.
No part of the algorithm I have shown is quadratic, I think.
Your algo is:
=========
- create an array of m bits, set to zero
- Use a random generator to generate integer numbers in [0, m-1], if the
corresponding big is set, extract another random number, if it's not set
then set it, increment a counter, and return the array item that
corresponds to the bit.
- When about 90% of the bits is set, [... alternate impl ...]
==========
Say at some point there are k available (not taken) slots out of "n".
There is a k/n chance that a random selection finds an unoccupied slot.
The average number of random trials needed to find an unoccupied slot is
proportional to 1/(k/n) = n/k. So the total number of random trials to
span the entire array is quadratic. Multiplying that by 0.9 leaves it
quadratic.
Andrei
