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// AC | ||
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// https://atcoder.jp/contests/abc327/tasks/abc327_e | ||
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fn main() { | ||
// n ~ 5000 | ||
let n: usize = read_vec()[0]; | ||
let ls: Vec<f64> = read_vec(); | ||
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const C1: f64 = 0.9; | ||
const C2: f64 = 1200.0; | ||
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// dp(n, k) = (optimal of "∑ (0.9)^(k - i) Qi" when picking "k" out of "P1" .. "Pn") | ||
let mut dp: Vec<Vec<f64>> = vec![vec![f64::MIN; n + 1]; n + 1]; | ||
dp[0][0] = 0.0; | ||
for i in 0..n { | ||
dp[i + 1][0] = 0.0; | ||
for k in 0..=i { | ||
let next = C1 * dp[i][k] + ls[i]; | ||
dp[i + 1][k + 1] = next.max(dp[i][k + 1]); | ||
} | ||
} | ||
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let mut result = f64::MIN; | ||
for k in 1..=n { | ||
let denom = (1.0 - C1.powf(k as f64)) / (1.0 - C1); | ||
let next = dp[n][k] / denom - C2 / (k as f64).sqrt(); | ||
result = result.max(next); | ||
} | ||
println!("{}", result); | ||
} | ||
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/* | ||
python misc/run.py atcoder/abc327/e/main.rs | ||
%%%% begin | ||
3 | ||
1000 600 1200 | ||
%%%% | ||
256.735020470879931 | ||
%%%% end | ||
%%%% begin | ||
3 | ||
600 1000 1200 | ||
%%%% | ||
261.423219407873489 | ||
%%%% end | ||
%%%% begin | ||
1 | ||
100 | ||
%%%% | ||
-1100.000000000000000 | ||
%%%% end | ||
*/ | ||
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// | ||
// utils | ||
// | ||
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#[allow(dead_code)] | ||
fn read_vec<T: std::str::FromStr>() -> Vec<T> { | ||
let mut line = String::new(); | ||
std::io::stdin().read_line(&mut line).unwrap(); | ||
line.split_whitespace() | ||
.map(|s| s.parse().ok().unwrap()) | ||
.collect() | ||
} | ||
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#[allow(dead_code)] | ||
fn read_array<T: std::str::FromStr, const LEN: usize>() -> [T; LEN] { | ||
#[allow(unused_imports)] | ||
use std::convert::TryInto; | ||
read_vec::<T>().try_into().ok().unwrap() | ||
} |