Tricky Google interview question

Question

A friend of mine is interviewing for a job. One of the interview questions got me thinking, just wanted some feedback.

There are 2 non-negative integers: i and j. Gi

Answer 1

This is very easy to do O(n) in functional languages. The list l of 2^i*5^j numbers can be simply defined as 1 and then 2*l and 5*l merged. Here is how it looks in Haskell:

merge :: [Integer] -> [Integer] -> [Integer]
merge (a:as) (b:bs)   
  | a < b   = a : (merge as (b:bs))
  | a == b  = a : (merge as bs)
  | b > a   = b : (merge (a:as) bs)

xs :: [Integer]
xs = 1 : merge (map(2*)xs) (map(5*)xs)

The merge function gives you a new value in constant time. So does map and hence so does l.