I want to know whether the experience of research programmer is useful to one who want to become a real programmer. I am working as a intern in a company, the daily work gets mainly to do with
designing and implementing algorithm,
change the environment of a program and get the corresponding result by using different tools.
write the similar program using different method and compare the performance
Some of them make me really bored.
Do these things help me to become a real programmer?
A programmer, certainly. There is a lot more for a software development engineer, though. For that you need to know how to elicit requirements, create a project plan, establish estimates, allocate resources, have a test plan, and so forth.
In my opinion, the biggest thing you'll be missing experience in is coding for maintainability.
But of course, experience in any part of the job is better than none at all. No one job is going to include everything.
In my experience, I would've thought that being a research programmer is more interesting than being a software development engineer.
Very generally speaking, as a research programmer your tasks will be a lot more open-ended. Perhaps you would be given a very vague task and you would need to use a lot more of your own initiative in order to investigate and find a solution.
Whereas as a software development engineer your tasks will hopefully be better specified and will be of narrower scope.
Probably it would be best if you can get a job where you do both types of programming, as it can both types can be rewarding in different ways.