Quote from: kTimesG on March 30, 2024, 08:41:09 PM

Quote from: WanderingPhilospher on March 30, 2024, 03:36:38 PM

First thing, I would not be using RAM. All DP info stored in files.

You still think it would require exabytes? To store all of those DPs?

Glad to see some progress. Did you factor in the entire overhead of using a non-O(1) lookup and item storage for DP? Or are you talking in abstract?

You have only 2 options:
a. Insist on a constant time factor to solve the puzzle, with all the assumptions factored in. One of those requirements is a O(1) DP lookup / storage. You will need a few TB of random access memory at a physical level, not in "files".
b. Actually understand how real-life limitations kick in.

Since the DP points are impossible to predict or compute them in "ranges", actual overheads like disk page reads / writes kick in.
Reading to a SSD is thousands of times slower than reading from physical RAM.
Writing to files involves reading entire pages of data, combining it, and writing it back.

Since DP values are uniformly spread out across the entire range, so say goodbye to "fast" SSD speeds when reading and writing even a single DP entry, since it is not sequential, and you have almost 0% chance to even have two same DP points in a close range.

But sure, if you wait like 5 seconds to compute a DP, store it to a file, and using this as your base, sure, it's a 2**65.5 + DP overhead total time. But you'll end up at the end with a broken SSD with an exceeded write failures count.

Just answer the question, how much storage or RAM do you think one would need, solving a 115 bit range key, using a DP of 25? According to your previous calculations...