问题
What is the time and space complexity of an algorithm, which calculates the dot product between two vectors with the length n?
回答1:
If the 2 vectors are a = [a1, a2, ... , an] and b = [b1, b2, ... , bn], then
The dot-product is given by a.b = a1 * b1 + a2 * b2 + ... + an * bn
To compute this, we must perform n multiplications and (n-1) additions. (I assume that this is the dot-product algorithm you are referring to).
Assuming that multiplication and addition are constant-time operations,
the time-complexity is therefore O(n) + O(n) = O(n).
The only auxiliary space we require during the computation is to hold the 'partial dot-product so far' and the last product computed, i.e. ai * bi.
Assuming we can hold both values in constant-space,
the space complexity is therefore O(1) + O(1) = O(1).
来源：https://stackoverflow.com/questions/3744094/time-and-space-complexity-of-vector-dot-product-computation