There are many sudoku variants where exactly the same solving techniques are used as in classical sudoku.
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I'm wondering that no of the many solvers for classical sudoku supports these sudoku variants.
You are correct in saying that classical sudoku techniques also apply apply to many variant puzzles. With a lot of programming effort, some of the variants you mention could be combined into a unified solver.
Puzzle specification is a big problem. That is, what makes a particular variant different? For example, though Samauri Soduko is just a bigger version of the standard puzzle, how do you specify "shape" in a reasonable way? For even/odd puzzles, you need be able to specify non-standard regions. Every new constraint, however small, defines a new class of puzzle.
There are several programs available to solve standard soduko in a non-brute force manner. In my opinion, only a few are slick, where 1)presentation (input/output) is nice, 2) techniques are good, and 3) and it works in a timely manner without error.
Many people who have some programming ability, when they see the standard soduko for the first time, say "I can program a solution to that." This is fine. They know there is a large number of potential users. There goal is to "solve the problem", not to spend time making it pretty. In many cases, the end-user turns out to be only themself.
In summary, what you suggest -- to write a
good solver in a way to suit a large class of soduko puzzles -- is hard to do.
This is not to say that it won't be done. Your question has merit.