// ---------- begin chmin, chmax ---------- pub trait ChangeMinMax { fn chmin(&mut self, x: Self) -> bool; fn chmax(&mut self, x: Self) -> bool; } impl ChangeMinMax for T { fn chmin(&mut self, x: Self) -> bool { *self > x && { *self = x; true } } fn chmax(&mut self, x: Self) -> bool { *self < x && { *self = x; true } } } // ---------- end chmin, chmax ---------- // ---------- 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, m: usize, t: usize, e: [(usize1, usize1, u16); m], v: [usize1; t], } assert!(t <= 17); let mut g = vec![vec![]; n]; for (a, b, c) in e { g[a].push((b, c)); g[b].push((a, c)); } let mut v = v; v.sort(); let mut id = vec![None; n]; for (i, v) in v.iter().enumerate() { id[*v] = Some(i); } let inf = 100 * 34 + 1; let mut dp = vec![vec![inf; 1 << t]; n]; for i in 0..n { dp[i][0] = 0; } for bit in 1..(1 << t) { let mut d = vec![inf; n]; for (i, (d, dp)) in d.iter_mut().zip(dp.iter()).enumerate() { *d = dp[bit]; if let Some(v) = id[i] { if bit >> v & 1 == 1 { d.chmin(dp[bit ^ (1 << v)]); } } let mut x = (bit - 1) & bit; while x > 0 { d.chmin(dp[x] + dp[bit ^ x]); x = (x - 1) & bit; } } let mut used = vec![false; n]; for _ in 1..n { let v = (0..n).filter(|v| !used[*v]).min_by_key(|v| d[*v]).unwrap(); used[v] = true; let a = d[v]; for &(u, w) in g[v].iter() { d[u].chmin(a + w); } } for (dp, d) in dp.iter_mut().zip(d) { dp[bit] = d; } } let ans = dp.iter().map(|dp| dp[(1 << t) - 1]).min().unwrap(); println!("{}", ans); } fn main() { run(); }