study | Learn, Share and Grow | Math library

Ignoring the cases when N is 0 or 1, you want to know if N is representable as a^b for a>1, b>1.

If you knew b, you could find a in O(log(N)) arithmetic operations (using binary search). Each arithmetic operation including exponentiation runs in polynomial time in log(N), so that would be polynomial too.

It's possible to bound b: it can be at most log_2(N)+1, otherwise a will be less than 2.

So simply try each b from 2 to floor(log_2(N)+1). Each try is polynomial in n (n ~= log_2(N)), and there's O(n) trials, so the resulting time is polynomial in n.

because you want

t = append(t, 0)

the data type can be int or float group.

this code should work

I had the same issue and solved it downgrading numpy to version 1.20.3 by:

Not sure if this exactly what you are looking for, but here is my attempt with rowwise and unnest

You can do it in only two regex passes. First extract the monetary amounts with a regex, then remove the thousands separators, finally, join the output by group keeping only the first two occurrences per original row.

The advantage of this solution is that is really only extracts monetary digits, not other possible numbers that would be there if the input is not clean.

Makie.jl, specifically via either the GLMakie.jl or WebGLMakie.jl backends, is a good option for interactive plots. For instance, the following example from the BeautifulMakie gallery

Older versions of libstdc++, like the one shipped by gcc 4.8.5, seem to only optimise function pointers to not allocate (as seen here).

Since the std::function implementation does not have the small object optimisation that you want, you will have to use an alternative implementation. Either upgrade your compiler or use boost::function, which is essentially the same as std::function.

Here is a possible solution.

To use a master password, you can use the loginUsingId function

Search the user by username, then check if the password matches the master password, and if so, log in with the user ID that it found

Redux used to be great but if you have tried none of them, I would highly recommend using Redux-Toolkit. The only case where I may want you to stick to redux is when you're using class-based components, where Redux Toolkit does have some boilerplate (like Redux) and you may miss out decent support.

However with functional components, Redux toolkit is like Redux on steroids.

Reason for using Redux toolkit:

1. A lot lesser boilerplate code is required compared to Redux.

2. Redux hooks like useSelector and useDispatch make things so short and easy to use.

3. You don't need to do manual thunk setup as redux-toolkit comes with out of the box createAsyncThunk which enables you to perform async operations in very hastle free way.

4. getState is also very helpful in obtaining state variables across any of your actions or async operations.

5. Mutability might be considered as advantage or disadvantage, but if you're not too used to writing with spread operators, you might love this feature as well. Do straight assignments and let redux toolkit take care of mutability under the hoods.

6. current can be used to log your state anywhere in case you want to debug and understand where things are going wrong. (Ofcourse, Redux debugger tools are great as well)

7. Prebuilt templates you might want to use npx create-react-app my-app --template redux-typescript or if you're using it with next: yarn create next-app --example with-redux with-redux-app. It gives you a setup ready redux toolkit boiler plate and also contains a boiler plate of most important redux state management applications so that you could refer them to create your own slices very easily.

I have been using a lot of redux and initially it was a bit confusing but once you get a good command over redux toolkit and if you're using a lot of functional components, you probably would never go back to redux again.