What problem type the Power Set belong to? - knapsack-problem

I don't seem to find any much resource about "Power Set" problem.
Is Power Set a NP-Complete or NP-Hard problem? And why? Can someone advise me?

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Anyone can help me with SMA* algorithm?

I have to apply the SMA* algorithm for the labyrinth problem in Python. I found just this PDF: pdfSMA, but it didn't help me too much.
I tried to resolve it, but I didn't manage. Any implementation for this algorithm in Python would help me.
The original description of SMA* from the original AIMA book is flawed. If you implement it as described it may not work. The issue is that you need to preserve the ordering of children and be sure to explore unexplored children before re-exploring old children.
Felner introduced the idea of collapse and restore macros which can be very helpful in understanding SMA*. I suggest looking at that paper and then using a similar approach to implement the algorithm.
But, also know that the recent A*+IDA* algorithm may be a better approach than SMA*. (Not much help if it is an assignment.)

Why using method breakpoints in IntelliJ IDEA causes such slowdown?

I've always known that method breakpoints make programme run a lot slower in debugger compared to a normal breakpoint.
Could someone with deep knowledge of debugger explain in relatively layman's language why is it so?
Thank you!
UPDATE
Thank you for the reply. I understand several similar questions have been asked here in the past, but I find none of them offer a detailed explanation and most of the answers point it out as "JVM design" without giving further details.
I know it's not always easy to explain complex subjects such as this in simple terms, but would appreciate if someone with the knowledge could try to explain it. I'd like to have a slightly better understanding of the subject than just knowing to avoid it.
Thanks!
Method breakpoints are extremely expensive to evaluate. According to JetBrains, the JVM isn't set up to handle this efficiently.

How to solve this system in mathematica

I want to solve this system in mathematica and i have applied various functions such as Solve, NSolve, etc. but none of them worked. could you help me how could i find my answer?

Is Computationally-hard is same as NP-hard?

I want to know that is there any difference between NP- hard problems and Computationally hard problems or are these two terms used for the same thing? I have tried to search the solution but cannot get some reasonable answer. Can anybody please help?
As of current knowledge (until that P=NP question is answered):
All NP-hard problems are computationally hard. But not all computationally hard problems are NP-hard (problems in P, with high exponents in the polynome, for example).
Note that "NP-hard" is a well defined class of problems in computer science.
"Computationally hard" on the other hand isn't, as far as I know.

Is there any case where you can't use backtracking algorithm method?

As the title says, I am really really really curious about this.
I've been trying to find the cases where you can't use backtracking to solve them but I can't find them.
Share your knowledge please
If there are too many possibilities to check, backtracking search will be impractical - see e.g. http://en.wikipedia.org/wiki/Lighthill_report. There may also be cases where you cannot state the problem simply and clearly enough to recognize the correct answer when you find it.

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