I applied online and was contacted after 3-4 weeks. They asked me to provide several available time slots for a phone interview. A 45-minute phone interview was scheduled.

Choosing a programming language of your choice:

How do you implement a polynomial?

After I suggested an ArrayList, the interviewer presented a very large polynomial and asked how I would handle such a case. Using an ArrayList would consume a significant amount of memory for polynomials of higher degrees.

I responded that I would use a HashMap to store the degrees and coefficients. The interviewer seemed impressed with this answer.

How would you implement the following four functions using a HashMap or ArrayList?

1. Constructor: Details how your polynomial is stored.
2. Adding two polynomials.
3. Printing a polynomial.
4. Finding the derivative of the polynomial.

The interviewer also inquired about my prior work experience and my current Master's thesis project, which I believe I answered well. However, I was only able to implement the first two functions (using an ArrayList) within the allotted time. I received a rejection email within three days.

Implement the above four polynomial functions using a hashmap.