m math import sqrt 

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 = {}
    for elem in seq:
        try: fq[elem] += 1
        except KeyError: fq[elem] = 1
    return fq

def scalar(vec):
    total = 0 
    for elem in vec:
        total += vec[elem] * vec[elem]
    return sqrt(total)

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))