That's what I preach, you can't mess with the birthday paradox without losing efficiency, if your software doesn't do this right for you, at least you're not looking for a fish in the sky. My comments are directed towards @ktimesg's crazy proposals. If you read the context you'll understand.
In fact, it is wrong to increase the jumps, you only lose efficiency, it is an exact science, I demonstrate it in my previous script.
What do you understand by "efficiency"? It's not the same thing as "speed" or "complexity", rather a more overall indicator that accounts for a multitude of factors, of which one is the practical techniques that are being used; another one is what problem you are trying to solve.
Why is it wrong to increase the jump (I guess you meant average jump size)? You're pretty much dismissing all existing research with this statement, and the math looks pretty legit IMHO (with well defined proofs for why it's
optimal to use a specific average jump size to
minimize the expected number of operations, etc.). By your (assumed) logic, and continuing it in reverse, we should basically run a brute-force search, one point after the other, right? So as not to mess with the damn birthday paradox, losing efficiency... am I wrong? But the joke's on you: messing around with the way you intend to use some theory, only ends up to decrease the efficiency. If you want better "birthday paradox" results, then you lose efficiency, because you do more operations. It does not matter the way you split the interval, or whether you make the jump sizes smaller or larger, or if you increase the DP to abnormal magnitude, or if you decide to go with storing trillions of points in the cloud, or if you decide to randomize starting points instead of having a central database of working state, the end result is the same:
sub-optimal. And this is an objective measurable metric, not some personal opinion.
Maybe, enlighten us about your exact science. Let's talk theory, not "you'll never find 135 using this or that", this is not the main point here anymore. Let's have some fun on the realm of exact science!
ok, explain to me why here the first script is more efficient than the second, and we will talk about math.
1- same resources.
2- same range
only difference x10 in jumps.
