New hashing exercise

[AlexisEnglebert]

Hello,

Here is a new exercise about polynomial hash.

The solution idea is to compute the hash for each row with polynomial hash for e.g the string "hello" we have

hash = (h · a⁰ + e · a¹ + l · a² + l · a³ + o · a⁴) mod m (where a is the base and m the modulo)

and then we can rotate the string by simply doing some math operation on the already hashed string so to get "ohell" we remove the o from "hello"

hash = (h · a⁰ + e · a¹ + l · a² + l · a³ ) mod m

Then we multiply the hash by the basis (a)

hash = (h · a⁰ + e · a¹ + l · a² + l · a³ ) · a = (h · a¹ + e · a² + l · a³ + l · a⁴ ) mod m

And finally we add the o at the start:

(h · a¹ + e · a² + l · a³ + l · a⁴ ) + o · a⁰ = ( o· a⁰ + h · a¹ + e · a² + l · a³ + l · a⁴ ) mod m

And now we have the hash for "ohell" in O(1).

[haroldks]

Hello Alexis,

Thank you for your exercise. It is a very interesting one. In general, there is too much to do for the students in my opinion. The challenge here should only focus on think about rolling hash to compute the hash of the word rotations.

I would suggest :

• Giving the student a method or function to compute the hash of the base word
• In you solution extract the rotation par in a method with relevant comments so when looking at the solution we know what is happening
• maybe use digit instead of char as input for the solve method to simplify test writings
• Add a comment for the base exponent precomputation

I also think that it can be possible to track the best while avoiding using pair and comparable in the end. I've add an idea in the comments but we can discuss it further.

[AlexisEnglebert]

Hey @haroldks,

I've taken account the proposed modifications for the exercise, I've moved the hashing logic into a separate function and removed the minimum pair things. Now only a valid pair is required.