from math import sqrt 
from collections import defaultdict 

def ngrams(s,n):
  """
  >>> ngrams('abcde', 2)
  ['ab', 'bc', 'cd', 'de']
  """
  return  [''.join(s[i:i+n]) for i in range(len(s)-n+1)] 

def freq(seq):
  fq = defaultdict(int)
  for elem in seq: fq[elem] += 1
  return fq
  
def scalar(vec):
  return sqrt(sum([k*k for v,k in vec.items()]))

def sim(v, w):
  total = 0 
  for elem in v:
    if elem in w:
      total += v[elem] * w[elem]
  return float(total) / (scalar(v) * scalar(w))