I am trying to wrap my mind around this problem, and decided to check if I could get some help here.
In an extremely large pool of possibilities, lets say a 256bits long pool.
How do I calculate which of the following algorithms is optimal, or best:
- pure random search
- random, but for each random number, I try 4billion sequential numbers starting on that initial random number and then get the next random to try another 4billion sequential
- pure sequential
Does my chances change if I have different throughput for each algorithm? Lets say on pure random my search is only 20% of the tries per second of the other two methods?
Thank you in advance.
--- Clarification
- Consider that on the pure random, a number is only tried once, never repeating
- Consider on the random-sequential, the ranges never overlap.
The pure sequential search is certainly the most efficient one: with a pure random search you might (and you probably will) try the same number more than once, while the second possibility you proposed has the same problem, and moreover if you search starting from the number $x$, and then with a number $y$ close to $x$, your sequential searches will overlap.