Detailed Component Design

relational database is used to store the mapping we have 3 columns -> ID (which we generate using some methods), LongUrl, ShortUrl (to use some hash functions to generate short url)
client makes a POST call to web server with long url. It checks if it exists in cache if it is short url is returned. In case it does not exist makes a call to DB if entry exists corresponding short url is returned if no entry exists a new entry is created. It is cached and returned back to the client.
Load balancer to distribute the load to handle traffic
Cache like reddis can be used to store frequently accessed with TTL not being to short or too long
client makes a GET call to web server with short url if it exists in the cache response is returned otherwise a call is made to the db to get the corresponding long url it is cached and the response is returned.