Do all the routers have backup table to maintain routing info?. If there is any corruption on routing table how do they resolve it?. Does router smart enough to find the error?. Is any error code chech happen in real time?. If you have any idea plase share with me.
No. Typically you've got smaller routers or layer 3 switches which have only a few entries in their routing tables, say a few hundred at most. Most of this information comes from the router's configuration file, or from routing protocol advertisements from a similarly small, nearby router.
Then you've got BGP speaking routers which have over 140K routes all the time. The majority of those routes come from external BGP neighbors, and that data is updated in real time.
Generally this information doesn't get corrupted. Though, you may have heard of folks experiencing problems because their router's CEF table doesn't have the routes installed that it should. That' is a case of route table corruption, and is basically due to Cisco IOS being a piece of junk. Many newer Cisco platforms have features to allow you to correct these problems in a hitless manner, and it is not such a big deal on modern IOS releases as it used to be. In any case, the corruption isn't something that is fixed with "backups" so much as clearing the CEF information and letting the router repopulate it from its main memory; or rebooting it (hopefullly not!) and letting it learn the routes again from its configuration file and nearby routers / external neighbors.