Q. Write a O(N^2) function that takes as input an array of N integers, return a bool to indicate whether there are three integers in the array such that the sum of the three is zero.

TheSumOfThree.rb

1. Sort the array A[1..n] incrementally.
2.
process ( A[1..n])
begin
  if(n < 3)
    return false
  else if (A[1] > 0 or A[n] < 0 )
    return false
  else if (A[1] + 2A[n] < 0)
    return process(A[2..n])
  else if ( 2A[1] + A[n] > 0)
    return process(A[1..n-1])
  else
    loop from i = n to 3
      begin
        if( A[1] + 2A[i] >= 0)
          loop from k = 2 to i-1
            begin
              if( A[1] + A[k] + A[i] > 0)
                break
              else if(A[1] + A[k] + A[i] == 0)
                return true
              else continue
            end          
        else
          process( A[2..n] )          
      end
end