In general to solve an NP complete problem like 3-SAT, you have to spend compute or storage to solve it.
Suppose you solve one 3-SAT problem. If you don’t write down the solution and steps along the way, then you have no way to get the benefit of the work for the next problem. But if you do store the results of the intermediate steps, then you need to store data that’s also polynomial in size.
In practice often you can do much better than that because the problems you’re solving may share certain data or characteristics that lead to shortcuts, but in the general case you have to pay the cost every time you need to solve an NP complete problem.
In general to solve an NP complete problem like 3-SAT, you have to spend compute or storage to solve it.
Suppose you solve one 3-SAT problem. If you don’t write down the solution and steps along the way, then you have no way to get the benefit of the work for the next problem. But if you do store the results of the intermediate steps, then you need to store data that’s also polynomial in size.
In practice often you can do much better than that because the problems you’re solving may share certain data or characteristics that lead to shortcuts, but in the general case you have to pay the cost every time you need to solve an NP complete problem.
So it means that you can’t gain cost advantages in general by solving other same or similarly computationally complex problems?