How to find the value for a given key if a hash function is chosen randomly from Universal family of hash functions?

Question

I am taking a course on data structures in coursera and I read recently about Universal family of hash functions. If i choose a hash function randomly from a universal family of hash functions, How will i exactly remap it to look up for a value. If i have to remember the function chosen for each key, then i should maintain a list for it. And this evaluation of finding the correct hash function for a key itself will take linear time violating the constant time look up of hash tables. How should i proceed implementing it?

Answer 1

When making one hash map, you use one function from the family. When you rehash the entire map (typically because of lack of capacity or too many collisions) or create a separate map, you can then choose a different hashing function from the family. You wouldn't use two different functions to attempt to create the same hash map.