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

If you go by what's really happening when we increment i or j in the expression 2^i * 5^j, you are either multiplying by another 2 or another 5. If we restate the problem as - given a particular value of i and j, how would you find the next greater value, the solution becomes apparent.

Here are the rules we can quite intuitively enumerate:

• If there is a pair of 2s (i > 1) in the expression, we should replace them with a 5 to get the next biggest number. Thus, i -= 2 and j += 1.
• Otherwise, if there is a 5 (j > 0), we need to replace it with three 2s. So j -= 1 and i += 3.
• Otherwise, we need to just supply another 2 to increase the value by a minimum. i += 1.

Here's the program in Ruby:

i = j = 0                                                                       
20.times do                                                                     
  puts 2**i * 5**j

  if i > 1                                                                      
    j += 1                                                                      
    i -= 2                                                                      
  elsif j > 0                                                                   
    j -= 1                                                                      
    i += 3                                                                      
  else                                                                          
    i += 1                                                                      
  end                                                                                                                                                               
end