I have Nikon D5100. I like to buy lens 18-200mm. Nikon lens is very costly?

Any third party lens is available to my D5100?

I want 18-200mm with auto focus.

Tamron and Sigma make the 18-200 in Nikon mount.

I think you may find this a disappointing combination. The 18-200mm is nice and versatile, and when placed on the 6MP or 10 MP bodies that most people had when it was introduced, the image quality usually looked adequate. Viewed at 16 MP the deficiencies may be more annoying. The third party 18-200mm's are not as good as the Nikon, so those would be less money wasted, but a bigger waste as you might be a little dissatisfied with the Nikon 18-200, but you will surely be dissatisfied with the others.

They're costly because they are very high quality. Sure there are third party lenses but I can virtually guarntee you they're not nearly the quality and that's obvious by the price point.

Keep in mind there's no such thing as cheap quality - it doesn't exist. Even in this economy you still get what you pay for. If you buy that Nikon lens it will last you many decades if you take care of it properly.

Your choice, cheap will get you cheap and nothing more.

Sigma are a very good option when it comes to buying lenses. They do not have as good image quality as Nikon but it is still rather impressive. 18-200s are lenses that suffer from the big zoom but sigma copes pretty well and are a dam sight cheper than nikons lenses but money no object go nikon but on a buget go sigma or Tamron. Tamron are also high good quality.

The lens matters as much or more than the camera.

You must realize that the 18-200mm lens offers versatility, bur you give up some optical quality compared to lenses such as 18-105mm or 55-200mm.

You really need to be able to test the lenses you are interested in, and be able to return them if you are not satisfied. Or be prepared to resell them yourself.