我如何在python中获得矢量的点积（列表形式）

Question

we are given 2 sparse vectors v1 and v2 represented as Counters, we need to return their dot products. what i have so far code wise:

import collections 

v1 = collections.Counter('aaabbbcccd')

v2 = collections.Counter('bcdd')

l1=list(v1.items())

l2=list(v2.items())

im not sure how to proceed from here because l1 and l2 contains:

[('b', 3), ('c', 3), ('d', 1), ('a', 3)]

[('b', 1), ('c', 1), ('d', 2)]

and i have no idea how to calculate the dot product from a list of this form. (in this case would be 3*1 + 3*1 + 1*2 + 3*0 = 8)

also this code is suppose to work for vectors of arbitrary length, not just 4

any ideas would be appreciated.

Answer 1

Just iterate over all the keys of either dict and sum the products (returning 0 for values which aren't present):

sum(v1.get(k, 0) * v2.get(k, 0) for k in v1)

I didn't use the lists because it seems to me like it would complicate the problem unnecessarily...

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Also note that the answer I've provide works for any python dict. For Counter instances, the second step gets even a bit simpler/cleaner:

sum(v1[k] * v2[k] for k in v1)