Write a program to find 100 largest numbers out of an array of 1 billion numbers

Question

I recently attended an interview where I was asked \"write a program to find 100 largest numbers out of an array of 1 billion numbers.\"

I was only able to give a br

Answer 1

I see a lot of O(N) discussions, so I propose something different just for the thought exercise.

Is there any known information about the nature of these numbers? If it's random in nature, then go no further and look at the other answers. You won't get any better results than they do.

However! See if whatever list-populating mechanism populated that list in a particular order. Are they in a well-defined pattern where you can know with certainty that the largest magnitude of numbers will be found in a certain region of the list or on a certain interval? There may be a pattern to it. If that is so, for example if they are guaranteed to be in some sort of normal distribution with the characteristic hump in the middle, always have repeating upward trends among defined subsets, have a prolonged spike at some time T in the middle of the data set like perhaps an incidence of insider trading or equipment failure, or maybe just have a "spike" every Nth number as in analysis of forces after a catastrophe, you can reduce the number of records you have to check significantly.

There's some food for thought anyway. Maybe this will help you give future interviewers a thoughtful answer. I know I would be impressed if someone asked me such a question in response to a problem like this - it would tell me that they are thinking of optimization. Just recognize that there may not always be a possibility to optimize.