CareerCup

Find max size of contiguous shape below, where X represents a shape and . is empty:

.XXXXXX....
...X..XX..X
...XXXX....
..X.....X..
..XXX..XX..
.....XX....
/*method stub*/
public int GetMaxShape(char[][] array) {
}

i was able to come up with a recursive solution but i'd love tips on a dp solution

Asked like 8 different behavioral questions that were supposed to exemplify Amazon values. I was unprepared for this, as many people say Amazon doesn't do this.
For example, I was asked "Tell me about a time when you solved a complex problem with a simple solution", "Tell me about a time when you increased efficiency", "Tell me about a time when you made a judgement call to take an unknown risk", "Tell me about a time when you disagreed with your team about something and how you reconciled it"

Find all paths in binary tree that add up to a given sum.
Given a tree like this:

2
 3   5 
4 8 6 -2
           2

return {3,4}, {2,5}, {2, 5, -2, 2}

Design the "what other people bought feature." This was focused on database design/creating an api to lie on top of it, and he asked questions to see if I understood how dbs actually work(like what does group by do). I was given an example table with the schema of like
itemID, purchaseDate, customerID
He asked big O complexity of sql query as well.

Design Amazon Questions and Answers. This question was to see how I code, and how I would modularize things. He wanted me to code every single thing as realistically as possible on a whiteboard.

Design a push notification system for android. Assume that we have 1 million users this year, but next year we will have 15 million. Assume that Google can handle infinite notifications per second.

I would love to see this answered, as I did not answer it well.