// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } /** * Union-Find tree. * Verified by https://atcoder.jp/contests/pakencamp-2019-day3/submissions/9253305 */ struct UnionFind { disj: Vec, rank: Vec } impl UnionFind { fn new(n: usize) -> Self { let disj = (0..n).collect(); UnionFind { disj: disj, rank: vec![1; n] } } fn root(&mut self, x: usize) -> usize { if x != self.disj[x] { let par = self.disj[x]; let r = self.root(par); self.disj[x] = r; } self.disj[x] } fn unite(&mut self, x: usize, y: usize) { let mut x = self.root(x); let mut y = self.root(y); if x == y { return } if self.rank[x] > self.rank[y] { std::mem::swap(&mut x, &mut y); } self.disj[x] = y; self.rank[y] += self.rank[x]; } #[allow(unused)] fn is_same_set(&mut self, x: usize, y: usize) -> bool { self.root(x) == self.root(y) } #[allow(unused)] fn size(&mut self, x: usize) -> usize { let x = self.root(x); self.rank[x] } } /// Tarjan's offline LCA algorithm. /// https://github.com/spaghetti-source/algorithm/blob/master/graph/least_common_ancestor_tarjan.cc /// g should represent a forest and roots should be a list of vertices, /// each of which is the designated root of exactly one connected component. /// qs is a Vec /// where qs[i] should contain the i-th query (a, b), /// meaning the LCA of a and b is asked for. /// This function returns out: Vec, /// i-th of which contains the output for qs[i]. /// Depends on: UnionFind.rs /// Verified by: https://yukicoder.me/submissions/430909 fn offline_lca( g: &[Vec], roots: &[usize], qs: &[(usize, usize)] ) -> Vec { fn visit(g: &[Vec], u: usize, w: usize, q_map: &[Vec<(usize, usize)>], col: &mut [bool], out: &mut [usize], anc: &mut [usize], uf: &mut UnionFind) { for &v in &g[u] { if v == w { continue; } visit(g, v, u, q_map, col, out, anc, uf); uf.unite(u, v); anc[uf.root(u)] = u; } col[u] = true; for &(target, idx) in &q_map[u] { if col[target] { out[idx] = anc[uf.root(target)] } } } let n = g.len(); let mut uf = UnionFind::new(n); let mut col = vec![false; n]; let mut anc = vec![0; n]; let mut q_map = vec![vec![]; n]; let mut out = vec![usize::max_value(); qs.len()]; for i in 0..qs.len() { let (a, b) = qs[i]; if a != b { q_map[a].push((b, i)); q_map[b].push((a, i)); } else { out[i] = a; } } for &r in roots { visit(g, r, n, &q_map, &mut col, &mut out, &mut anc, &mut uf); } out } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); } fn dfs(v: usize, par: usize, g: &[Vec], c: &[i64], dp: &mut [i64], x: i64) { let x = x + c[v]; dp[v] = x; for &w in &g[v] { if w == par { continue; } dfs(w, v, g, c, dp, x); } } fn solve() { input! { n: usize, ab: [(usize, usize); n - 1], u: [i64; n], m: usize, abc: [(usize, usize, i64); m], } let mut g = vec![vec![]; n]; for &(a, b) in &ab { g[a].push(b); g[b].push(a); } let mut ev = vec![]; for &(a, b, _) in &abc { ev.push((a, b)); } let lcas = offline_lca(&g, &[0], &ev); let mut dp = vec![0; n]; dfs(0, n, &g, &u, &mut dp, 0); let mut tot = 0; for i in 0..m { let (a, b, c) = abc[i]; tot += (dp[a] + dp[b] - 2 * dp[lcas[i]] + u[lcas[i]]) * c; } println!("{}", tot); }