How can one prepare to know a company's products, product strategy and user goals inside and out?

To prepare for the unexpected in a tough job interview, you should thoroughly research the company and its products, understand their product strategy and user goals, and practice making decisions with incomplete data. You should also brush up on your technical skills, as you may be asked to design algorithms or write code on the spot.

During an interview, you can demonstrate your ability to make sound business decisions by showcasing your analytical skills, your understanding of the company's products and strategy, and your ability to make decisions under pressure. You can also share examples from your past experiences where you made critical business decisions with incomplete data. Additionally, demonstrating your product instincts and your ability to design algorithms or write code on the spot can also be beneficial.

You can demonstrate your understanding of algorithms during an interview by explaining the logic behind the algorithm, discussing its time and space complexity, and providing examples of its application. You could also write pseudocode or actual code to illustrate how the algorithm works. If possible, discuss how you have used algorithms in your past projects or how you would apply them in the context of the company's products or services.