Problem
In this problem, we shall simulate the "popular elements" algorithm of Section 4.7.3, which uses an exponentially decaying window. We use the unrealistically large decay parameter c=0.1, so we multiply by 0.9 at each stage. We use a threshold of 0.6, in place of the 0.5 suggested in that section. The sequence of elements arriving on the stream is:
a b c a d e a c b b
Simulate the computation of the popularity score on this stream. When computing scores, you should round to 3 decimal places after each step. What are the popularity scores of a, b, c, d, e at the end of the stream? Please show your work.