#include #include using namespace std; using int64 = long long; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 >& p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { explicit FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } #line 1 "structure/develop/super-link-cut-tree.hpp" /** * @brief 何でもできるLCT */ template< typename LInfo, typename Lazy > struct SplayTree { struct Node { Node *l, *r, *p; LInfo info; Lazy lazy, lbuf; explicit Node(const LInfo &info) : info(info), l(nullptr), r(nullptr), p(nullptr), lazy(Lazy()), lbuf(Lazy()) {} }; const LInfo e; SplayTree() : e(LInfo()) {} using NP = Node *; void rotr(NP t) { NP x = t->p, y = x->p; push(x), push(t); if((x->l = t->r)) t->r->p = x; t->r = x, x->p = t; update(x), update(t); if((t->p = y)) { if(y->l == x) y->l = t; if(y->r == x) y->r = t; } } void rotl(NP t) { NP x = t->p, y = x->p; push(x), push(t); if((x->r = t->l)) t->l->p = x; t->l = x, x->p = t; update(x), update(t); if((t->p = y)) { if(y->l == x) y->l = t; if(y->r == x) y->r = t; } } const LInfo &get_info(NP t) { return t ? t->info : e; } void update(NP t) { t->info.update(get_info(t->l), get_info(t->r)); } NP get_right(NP t) { while(t->r) t = t->r; return t; } NP alloc(const LInfo &v) { auto t = new Node(v); update(t); return t; } void propagate(NP t, const Lazy &lazy) { t->info.propagate(lazy); t->lbuf.propagate(lazy); t->lazy.propagate(lazy); } void push(NP t) { if(t->l) propagate(t->l, t->lazy); if(t->r) propagate(t->r, t->lazy); t->lazy = Lazy(); } void splay(NP t) { push(t); while(t->p) { NP q = t->p; if(!q->p) { if(q->l == t) rotr(t); else rotl(t); } else { NP r = q->p; if(r->l == q) { if(q->l == t) rotr(q), rotr(t); else rotl(t), rotr(t); } else { if(q->r == t) rotl(q), rotl(t); else rotr(t), rotl(t); } } } } NP insert(NP t, const LInfo &v) { if(not t) { t = alloc(v); return t; } else { NP cur = get_right(t), z = alloc(v); splay(cur); z->p = cur; cur->r = z; update(cur); splay(z); return z; } } NP erase(NP t) { splay(t); NP x = t->l, y = t->r; delete t; if(not x) { t = y; if(t) t->p = nullptr; } else if(not y) { t = x; t->p = nullptr; } else { x->p = nullptr; t = get_right(x); splay(t); t->r = y; y->p = t; update(t); } return t; } }; template< template< typename, typename > typename _Info, template< typename > typename _LInfo, typename Lazy > struct SuperLinkCutTree { using LInfo = _LInfo< Lazy >; using Info = _Info< LInfo, Lazy >; private: struct Node { Node *l, *r, *p; Info info; typename SplayTree< LInfo, Lazy >::Node *light, *belong; bool rev; Lazy hlazy, llazy; bool is_root() const { return not p or (p->l != this and p->r != this); } explicit Node(const Info &info) : info(info), l(nullptr), r(nullptr), p(nullptr), rev(false), light(nullptr), belong(nullptr), hlazy(Lazy()), llazy(Lazy()) {} }; public: using NP = Node *; SplayTree< LInfo, Lazy > splay_tree; private: const Info e; private: void toggle(NP t) { swap(t->l, t->r); t->info.toggle(); t->rev ^= true; } void rotr(NP t) { NP x = t->p, y = x->p; push(x), push(t); if((x->l = t->r)) t->r->p = x; t->r = x, x->p = t; update(x), update(t); if((t->p = y)) { if(y->l == x) y->l = t; if(y->r == x) y->r = t; } } void rotl(NP t) { NP x = t->p, y = x->p; push(x), push(t); if((x->r = t->l)) t->l->p = x; t->l = x, x->p = t; update(x), update(t); if((t->p = y)) { if(y->l == x) y->l = t; if(y->r == x) y->r = t; } } void propagate_heavy(NP t, const Lazy &hlazy) { t->hlazy.propagate(hlazy); t->info.propagate(hlazy); } void propagate_light(NP t, const Lazy &llazy) { t->llazy.propagate(llazy); t->info.propagate_light(llazy); } void propagate_all(NP t, const Lazy &lazy) { propagate_heavy(t, lazy); propagate_light(t, lazy); } public: SuperLinkCutTree() : e{Info()}, splay_tree{} {} void push(NP t) { if(t->rev) { if(t->l) toggle(t->l); if(t->r) toggle(t->r); t->rev = false; } { if(t->l) { propagate_heavy(t->l, t->hlazy); propagate_light(t->l, t->llazy); } if(t->r) { propagate_heavy(t->r, t->hlazy); propagate_light(t->r, t->llazy); } if(t->light) { splay_tree.propagate(t->light, t->llazy); } t->hlazy = Lazy(); t->llazy = Lazy(); } } void push_rev(NP t) { if(t->rev) { if(t->l) toggle(t->l); if(t->r) toggle(t->r); t->rev = false; } } const Info &get_info(NP t) { return t ? t->info : e; } void update(NP t) { t->info.update(get_info(t->l), get_info(t->r), splay_tree.get_info(t->light)); } void splay(NP t) { push(t); { NP rot = t; while(not rot->is_root()) rot = rot->p; t->belong = rot->belong; if(t != rot) rot->belong = nullptr; } while(not t->is_root()) { NP q = t->p; if(q->is_root()) { push_rev(q), push_rev(t); if(q->l == t) rotr(t); else rotl(t); } else { NP r = q->p; push_rev(r), push_rev(q), push_rev(t); if(r->l == q) { if(q->l == t) rotr(q), rotr(t); else rotl(t), rotr(t); } else { if(q->r == t) rotl(q), rotl(t); else rotr(t), rotl(t); } } } } NP expose(NP t) { NP rp = nullptr; for(NP cur = t; cur; cur = cur->p) { splay(cur); if(cur->r) { cur->light = splay_tree.insert(cur->light, cur->r->info.link()); cur->r->belong = cur->light; } cur->r = rp; if(cur->r) { splay_tree.splay(cur->r->belong); propagate_all(cur->r, cur->r->belong->lbuf); push(cur->r); cur->light = splay_tree.erase(cur->r->belong); } update(cur); rp = cur; } splay(t); return rp; } void link(NP child, NP parent) { expose(parent); expose(child); child->p = parent; parent->r = child; update(parent); } void cut(NP child) { expose(child); NP parent = child->l; child->l = nullptr; parent->p = nullptr; update(child); } void evert(NP t) { expose(t); toggle(t); push(t); } NP alloc(const Info &info) { NP t = new Node(info); update(t); return t; } bool is_connected(NP u, NP v) { expose(u), expose(v); return u == v or u->p; } vector< NP > build(vector< Info > &vs) { vector< NP > nodes(vs.size()); for(int i = 0; i < (int) vs.size(); i++) { nodes[i] = alloc(vs[i]); } return nodes; } NP lca(NP u, NP v) { if(not is_connected(u, v)) return nullptr; expose(u); return expose(v); } void set_key(NP t, const Info &v) { expose(t); t->info = move(v); update(t); } void set_propagate_path(NP t, const Lazy &lazy) { expose(t); propagate_heavy(t, lazy); push(t); update(t); } void set_propagate_path(NP u, NP v, const Lazy &lazy) { evert(u); set_propagate_path(v, lazy); } void set_propagate_all(NP t, const Lazy &lazy) { expose(t); propagate_all(t, lazy); push(t); update(t); } void set_propagate_subtree(NP t, const Lazy &lazy) { expose(t); NP l = t->l; t->l = nullptr; propagate_all(t, lazy); push(t); t->l = l; update(t); } const Info &query(NP u) { expose(u); return get_info(u); } const Info &query_path(NP u, NP v) { evert(u); expose(v); return get_info(v); } Info query_subtree(NP u) { expose(u); NP l = u->l; u->l = nullptr; update(u); auto ret = u->info; u->l = l; update(u); return ret; } }; /* using T = int64_t; // 遅延伝搬をするための作用素 struct Lazy { // 単位元 Lazy() {} // 初期化 Lazy(T v) {} // 遅延伝搬 void propagate(const Lazy &p) {} }; // Light-edge の情報 template< typename Lazy > struct LInfo { // 単位元(キーの値はアクセスしないので未初期化でもよい LInfo() {} // 初期化 LInfo(T v) {} // l, r は Splay-tree の子 (原理上、各ノード区別はない) void update(const LInfo &l, const LInfo &r) {} // 部分木への遅延伝搬 void propagate(const Lazy &p) {} }; // Heavy-edge の情報 template< typename LInfo, typename Lazy > struct Info { // 単位元(キーの値はアクセスしないので未初期化でもよい Info() {} // 初期化 Info(T v) {} // 反転 void toggle() {} // pが親, cがheavy-edgeで結ばれた子, lがそれ以外の子 void update(const Info &p, const Info &c, const LInfo &l) {} // 親と light-edge で繋げる LInfo link() const { return LInfo(); } // 遅延伝搬 void propagate(const Lazy &p) {} // light-edgeに対する遅延伝搬 // pathとsubtreeの遅延伝搬が両方ある場合に実装する void propagate_light(const Lazy &p) {} }; using LCT = SuperLinkCutTree< Info, LInfo, Lazy >; */ #line 2 "structure/develop/vertex-set-path-sum.hpp" /** * @brief Vertex Set Path Sum */ using T = int64_t; // 遅延伝搬をするための作用素 struct Lazy { // 単位元 Lazy() {} // 初期化 Lazy(T v) {} // 遅延伝搬 void propagate(const Lazy &p) {} }; // Light-edge の情報 template< typename Lazy > struct LInfo { T key, val; // 単位元(キーの値はアクセスしないので未初期化でもよい LInfo() : val{0} {} // 初期化 LInfo(T v) : key{v} {} // l, r は Splay-tree の子 (原理上、各ノード区別はない) void update(const LInfo &l, const LInfo &r) { val = l.val + r.val + key; } // 部分木への遅延伝搬 void propagate(const Lazy &p) {} }; // Heavy-edge の情報 template< typename LInfo, typename Lazy > struct Info { T v; T sum; T most_left, most_right; // 単位元(キーの値はアクセスしないので未初期化でもよい Info() : sum{0}, most_left{infll}, most_right{infll} {} // 初期化 Info(T v) : v{v} {} // 反転 void toggle() { swap(most_left, most_right); } // pが親, cがheavy-edgeで結ばれた子, lがそれ以外の子 void update(const Info &p, const Info &c, const LInfo &l) { sum = p.sum + v + c.sum + l.val; most_left = p.most_left; if(most_left == infll) most_left = v; most_right = c.most_right; if(most_right == infll) most_right = v; } // 親と light-edge で繋げる LInfo link() const { return LInfo(most_left == infll ? 0ll : most_left); } // 遅延伝搬 void propagate(const Lazy &p) {} // light-edgeに対する遅延伝搬 // pathとsubtreeの遅延伝搬が両方ある場合に実装する void propagate_light(const Lazy &p) {} }; using LCT = SuperLinkCutTree< Info, LInfo, Lazy >; int main() { int N, Q; cin >> N >> Q; vector< int > A(N); cin >> A; LCT lct; vector< LCT::NP > vs(N); for(int i = 0; i < N; i++) { vs[i] = lct.alloc(A[i]); } for(int i = 1; i < N; i++) { int u, v; cin >> u >> v; --u, --v; lct.evert(vs[u]); lct.link(vs[u], vs[v]); } while(Q--) { int t, u, v; cin >> t >> u >> v; if(t == 0) { --u; lct.set_key(vs[u], vs[u]->info.v + v); } else { --u, --v; cout << lct.query_path(vs[u], vs[v]).sum << "\n"; } } }