from math import sqrt

# Returns a distance-based similarity score for person1 and person2
def sim_distance(prefs,person1,person2):

  # Get the list of shared_items
  si={}
  for item in prefs[person1]:
    if item in prefs[person2]:
      si[item]=1

  # if they have no ratings in common, return 0
  if len(si)==0: return 0

  # Add up the squares of all the differences
  sum_of_squares=sum([pow(prefs[person1][item]-prefs[person2][item],2)
                      for item in prefs[person1] if item in prefs[person2]])

  return 1/(1+sum_of_squares)