combinations | Go lang combination package

Firstly, you can use a list comprehension to give you all of the possible combinations (regardless of the duplicates):

We can use ego like below

Using chartr, you can do (although this might crash for larger vectors):

Series.value_counts + Series.unstack to convert to dataframe

The following works by subclassing the relevant class, and duplicating code with the relevant changes. We also have to subclass the Client class, to overwrite the place where the gateway/websocket class is used. This results in a lot of duplicated code, however it does work, and requires neither dirty monkey-patching nor editing the library source code.

However, it does come with many of the same problems as editing the library source code - mainly that as the library is updated, this code will become out of date (if you're using the archived and obsolete version of the library, you have bigger problems instead).

Attention:

Here is an inspiring idea which is not fully satisfy OP's requirement (e.g., ID.new and number order) but I think it worth to be recoreded here.

You can turn DT into long format by melt firstly. Then to shift value with the step -nrow(DT) in order to do the minus operation, i.e. NAME1 - NAME2, NAME2 - NAME3, NAME3 - NAME1.

This is what you need:

The structure that you want your data in is very messy, so this is probably the best method given the data you want.

This looks like a combinatorial problem where its "messiness" suggests no mathematical answer can be formulated. The cheer number of allowed combinations makes it ever more likely that each n has a valid solution, especially given that for small n you already found solutions.

Finding solutions for larger n can be tricky. One approach is called "simulated annealing", where you would take a random set of equations, I try to improve it step by step. "Bad equations" (i.e. equations that have numbers overlapping with others in the set) get removed, and new equations are tried.

Whatever approach is used, it probably can be speed up with heuristics. Such as start creating equations for numbers that show up in the least number of possible equations.

A somewhat related problem is called "graceful labeling", which has no definite answer and for which similar algorithms are appropriate.

Here is an approach using z3py, a library which implements a sat/smt solver.

First, for each number, a list of possible expressions is made. For each possible expression, a symbolic boolean indicates whether the expression will be used in the solution. To have a valid solution, for each number, exactly one of its possible expressions should be True.