Meta E4 Phone Screen - Cut Wood and Random pick

I recently completed a Meta E4 phone screen interview. The questions were from a list of previously asked questions:

1. Cut Wood: I began with a binary search solution, but the interviewer asked for a brute-force approach first, followed by optimization. I successfully solved it and discussed the time complexities of both approaches.
2. Random Pick with Weight: Given a map of city names and populations, the task was to return a random city name weighted by population. I initially used the bisectright method in Python, but the interviewer asked me to implement it without using the library function. I developed a solution but experienced some initial panic when testing an example. However, the code appeared correct. I discussed the time and space complexities.

I solved both problems within the allotted time. The interviewer ended the call promptly at the 45-minute mark, leaving me unsure of my performance.

I received positive feedback from the recruiter on Monday, indicating that I had advanced to the virtual onsite interview stage.

I am seeking advice on preparing for the onsite interview, particularly regarding system design.