Old cassette player (2)

Consider an old cassette player, whose only working buttons are “play”
and “rewind”. You have just one cassette, which you always keep
completely rewinded. So, when you want to listen to a particular song s,
you have to press the “play” button and wait until all the songs stored
before s finish. Afterwards, when s ends, you always rewind the
cassette.

You have n songs, which you listen to with the same frequency. You know
the duration d_(i) of every song i. Assume that the cassette is long
enough to store all your songs. Your goal is to choose the order to
store the songs so as to minimize the expected time to listen to a
desired song.

Input

Input is all natural numbers, and consists of several cases. Every case
begins with n, which is followed by the durations of the n songs, all
strictly positive. Assume 1 ≤ n ≤ 10⁵.

Output

For every case, print with four digits after the decimal point the
optimal expected time to listen to a desired song. The input cases have
no precision issues.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:13:05.686Z

© Jutge.org, 2006–2026.
https://jutge.org
