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It always seems that beginners have amazing luck. Just last week you showed your friend Liliana
a video game that you had been playing for over a year. On her first try, her score was better than
your average score!!!
Now, you and Liliana have gotten into a discussion about whether beginners really are lucky.
Luckily, you have data about many individuals playing the video game. For each individual, you'd
like to make a claim of the form:
In their first X games, [Insert Name Here] scored an average of Y points per game.
To make the claim as impressive as possible, you'd like to maximize the value of Y, given the
player's full game history, over all possible positive integers for X.
For example, if Michael had gotten the following scores (in this order):
10, 8, 9, 15, 12, 2, 3, 8, 7, 11
we see that the best claim we can make is that in the first 5 games, Michael averaged a score of
(10 + 8 + 9 + 15 + 12)/5 = 10.8 points per game. (Note that each of the running averages, rounded
to one decimal place are 10.0, 9.0, 9.0, 10.5, 10.8, 9.3, 8.4, 8.4, 8.2, and 8.5, respectively.)
Given a list of positive integers, determine the maximum average of any non-empty prefix of the
The first line of input contains a single positive integer, n (n ? 100), the number of input cases to
be processed. Each input cases follows, one per line. For each input case, the first number is a
positive integer, k (k ? 1000000), representing the number of times the player for the input case
has played the video game. The following k space-separated integers represent the player's scores
for each time playing the video game, in order. Each of these integers will be in between 0 and
For each test case, on a line by itself, output the maximal average of any of the first m (1 ? m ? k)
games, rounded to 6 decimal places.
This question was answered on: Dec 18, 2020
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