The recruiter reached out to me, and we scheduled a technical phone call. In the interview, we gave our introductions. I mentioned I have 7 years of experience.

The interviewer asked a good technical question. The question verified if the candidate could gather requirements, solve a problem, and code it. I finished it in time.

He asked a follow-up question; I struggled a bit, and time was over, so we stopped there. I went through with this interview, but they wanted to be sure, so they scheduled another technical phone screen.

In this interview, the interviewer asked in-depth about my current experience, project details, etc. He asked me the difference between an array and a linked list. I fumbled there for a bit since I wasn't expecting a theoretical question for 7 years of experience! Anyway, I could answer it well.

Then, the interviewer asked a technical question based on graphs. I told him that I had never worked with graphs in my career, so I started solving the problem without graphs. I almost reached the solution when he asked me to solve it only using graphs. I told him again that I am not very familiar with all graph concepts and needed to brush up my knowledge. Then he explained the solution, and we ended the call.

There are asteroids with a certain mass moving in space in left/right directions. To the far right is a space station. Write a program to return the number of asteroids that can collide with the space station. Asteroids collide with each other, and the asteroid with a bigger mass destroys the asteroid with a lower mass and continues in its direction.

Follow-up on the above question: Using the method described above, assume that you also have a space station on the far left. Now you need to return the number of asteroids colliding with both the right and left space stations. How can you do that?

Alice has a set of buckets of various sizes and an unlimited water supply. Her task is to measure an exact amount of water in one of the buckets.

Buckets are unmarked, and she only knows their full capacity, which is always an integer (e.g., 5 gallons).

Alice is allowed the following operations:

• Fully fill a bucket.
• Empty a bucket.
• Pour from one bucket into another, up to the other bucket's capacity.

Note that Alice cannot measure water in any other way; for example, she cannot pour half a bucket into another because her measurement would be inaccurate.

Example: Buckets have capacities of 3 and 5 gallons. Alice is asked to measure 4 gallons.

Let's denote the buckets' contents by a tuple (a, b), where 0 <= a <= 3 and 0 <= b <= 5. We start with (0, 0) and can follow these steps:

1. Fill up the big bucket: (0, 5)
2. Pour to the smaller one: (3, 2)
3. Empty the small one: (0, 2)
4. Pour water from the big to the small: (2, 0)
5. Fill up the big one: (2, 5)
6. Pour water from the big to the small: (3, 4)

This sequence took 6 steps to get to 4 gallons of water.

Your task is to help Alice determine the shortest sequence of steps to achieve the desired capacity.