// ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- fn run() { input! { n: usize, w: f64, p: [(f64, f64, f64, f64, f64); n], } let pi = std::f64::consts::PI / 180.0; // s から時刻tに出発してpをとる最小の時刻 let calc = |p: (f64, f64, f64, f64, f64), s: (f64, f64), t: f64| -> f64 { let (x, y, r, v, a) = p; let mut ng = t; let mut ok = t + 100000.0; for _ in 0..50 { let m = (ok + ng) * 0.5; let pos = (x + r * ((v * m + a) * pi).cos(), y + r * ((v * m + a) * pi).sin()); if ((pos.0 - s.0).powi(2) + (pos.1 - s.1).powi(2)).sqrt() / w <= m - t { ok = m; } else { ng = m; } } ok }; let inf = 10000000000f64; let mut dp = vec![vec![inf; 1 << n]; n]; for (i, p) in p.iter().enumerate() { dp[i][1 << i] = calc(*p, (0f64, 0f64), 0f64); } for bit in 1..(1 << n) { for i in 0..n { if dp[i][bit] > inf / 10.0 { continue; } let t = dp[i][bit]; let (x, y, r, v, a) = p[i]; let pos = (x + r * ((v * t + a) * pi).cos(), y + r * ((v * t + a) * pi).sin()); for j in 0..n { if bit >> j & 1 == 0 { let po = &mut dp[j][bit | (1 << j)]; *po = calc(p[j], pos, t).min(*po); } } } } let mut ans = inf; for dp in dp { ans = ans.min(dp[(1 << n) - 1]); } println!("{:.6}", ans); } fn main() { run(); }