#include #include using namespace std; #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i #include #include #include #include #include #include #include // Heavy-Light Decomposition of trees // Based on http://beet-aizu.hatenablog.com/entry/2017/12/12/235950 struct HeavyLightDecomposition { int V; int k; int nb_heavy_path; std::vector> e; std::vector par; // par[i] = parent of vertex i (Default: -1) std::vector depth; // depth[i] = distance between root and vertex i std::vector subtree_sz; // subtree_sz[i] = size of subtree whose root is i std::vector heavy_child; // heavy_child[i] = child of vertex i on heavy path (Default: -1) std::vector tree_id; // tree_id[i] = id of tree vertex i belongs to std::vector aligned_id, aligned_id_inv; // aligned_id[i] = aligned id for vertex i (consecutive on heavy edges) std::vector head; // head[i] = id of vertex on heavy path of vertex i, nearest to root std::vector head_ids; // consist of head vertex id's std::vector heavy_path_id; // heavy_path_id[i] = heavy_path_id for vertex [i] HeavyLightDecomposition(int sz = 0) : V(sz), k(0), nb_heavy_path(0), e(sz), par(sz), depth(sz), subtree_sz(sz), heavy_child(sz), tree_id(sz, -1), aligned_id(sz), aligned_id_inv(sz), head(sz), heavy_path_id(sz, -1) {} void add_edge(int u, int v) { e[u].emplace_back(v); e[v].emplace_back(u); } void _build_dfs(int root) { std::stack> st; par[root] = -1; depth[root] = 0; st.emplace(root, 0); while (!st.empty()) { int now = st.top().first; int &i = st.top().second; if (i < (int)e[now].size()) { int nxt = e[now][i++]; if (nxt == par[now]) continue; par[nxt] = now; depth[nxt] = depth[now] + 1; st.emplace(nxt, 0); } else { st.pop(); int max_sub_sz = 0; subtree_sz[now] = 1; heavy_child[now] = -1; for (auto nxt : e[now]) { if (nxt == par[now]) continue; subtree_sz[now] += subtree_sz[nxt]; if (max_sub_sz < subtree_sz[nxt]) max_sub_sz = subtree_sz[nxt], heavy_child[now] = nxt; } } } } void _build_bfs(int root, int tree_id_now) { std::queue q({root}); while (!q.empty()) { int h = q.front(); q.pop(); head_ids.emplace_back(h); for (int now = h; now != -1; now = heavy_child[now]) { tree_id[now] = tree_id_now; aligned_id[now] = k++; aligned_id_inv[aligned_id[now]] = now; heavy_path_id[now] = nb_heavy_path; head[now] = h; for (int nxt : e[now]) if (nxt != par[now] and nxt != heavy_child[now]) q.push(nxt); } nb_heavy_path++; } } void build(std::vector roots = {0}) { int tree_id_now = 0; for (auto r : roots) _build_dfs(r), _build_bfs(r, tree_id_now++); } template std::vector segtree_rearrange(const std::vector &data) const { assert(int(data.size()) == V); std::vector ret; ret.reserve(V); for (int i = 0; i < V; i++) ret.emplace_back(data[aligned_id_inv[i]]); return ret; } // query for vertices on path [u, v] (INCLUSIVE) void for_each_vertex(int u, int v, const std::function &f) const { while (true) { if (aligned_id[u] > aligned_id[v]) std::swap(u, v); f(std::max(aligned_id[head[v]], aligned_id[u]), aligned_id[v]); if (head[u] == head[v]) break; v = par[head[v]]; } } void for_each_vertex_noncommutative( int from, int to, const std::function &fup, const std::function &fdown) const { int u = from, v = to; const int lca = lowest_common_ancestor(u, v), dlca = depth[lca]; while (u >= 0 and depth[u] > dlca) { const int p = (depth[head[u]] > dlca ? head[u] : lca); fup(aligned_id[p] + (p == lca), aligned_id[u]), u = par[p]; } static std::vector> lrs; int sz = 0; while (v >= 0 and depth[v] >= dlca) { const int p = (depth[head[v]] >= dlca ? head[v] : lca); if (int(lrs.size()) == sz) lrs.emplace_back(0, 0); lrs.at(sz++) = {p, v}, v = par.at(p); } while (sz--) fdown(aligned_id[lrs.at(sz).first], aligned_id[lrs.at(sz).second]); } // query for edges on path [u, v] void for_each_edge(int u, int v, const std::function &f) const { while (true) { if (aligned_id[u] > aligned_id[v]) std::swap(u, v); if (head[u] != head[v]) { f(aligned_id[head[v]], aligned_id[v]); v = par[head[v]]; } else { if (u != v) f(aligned_id[u] + 1, aligned_id[v]); break; } } } // lowest_common_ancestor: O(log V) int lowest_common_ancestor(int u, int v) const { assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0); while (true) { if (aligned_id[u] > aligned_id[v]) std::swap(u, v); if (head[u] == head[v]) return u; v = par[head[v]]; } } int distance(int u, int v) const { assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0); return depth[u] + depth[v] - 2 * depth[lowest_common_ancestor(u, v)]; } // Level ancestor, O(log V) // if k-th parent is out of range, return -1 int kth_parent(int v, int k) const { if (k < 0) return -1; while (v >= 0) { int h = head.at(v), len = depth.at(v) - depth.at(h); if (k <= len) return aligned_id_inv.at(aligned_id.at(v) - k); k -= len + 1, v = par.at(h); } return -1; } // Jump on tree, O(log V) int s_to_t_by_k_steps(int s, int t, int k) const { if (k < 0) return -1; if (k == 0) return s; int lca = lowest_common_ancestor(s, t); if (k <= depth.at(s) - depth.at(lca)) return kth_parent(s, k); return kth_parent(t, depth.at(s) + depth.at(t) - depth.at(lca) * 2 - k); } }; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); int N, Q; cin >> N >> Q; vector A(N); for (auto &a : A) cin >> a; atcoder::fenwick_tree fw(N); HeavyLightDecomposition hld(N); REP(i, N - 1) { int a, b; cin >> a >> b; --a, --b; hld.add_edge(a, b); } const int root = 0; hld.build({root}); REP(i, N) { if (i != root) { int p = hld.par.at(i); fw.add(hld.aligned_id.at(p), A.at(i)); } } while (Q--) { int tp; cin >> tp; if (tp == 0) { int v, x; cin >> v >> x; --v; A.at(v) += x; if (v != root) fw.add(hld.aligned_id.at(hld.par.at(v)), x); } else if (tp == 1) { int u, v; cin >> u >> v; --u, --v; const auto lca = hld.lowest_common_ancestor(u, v); auto ret = A.at(lca); if (lca != root) ret += A.at(hld.par.at(lca)); hld.for_each_vertex(u, v, [&](int a, int b) { ret += fw.sum(a, b + 1); }); cout << ret << '\n'; } else { assert(false); } } }