Submit Info #4838

Problem Lang User Status Time Memory
Dynamic Tree Vertex Add Path Sum cpp niuez AC 1119 ms 169.54 MiB

ケース詳細
Name Status Time Memory
example_00 AC 77 ms 155.07 MiB
max_random_00 AC 1119 ms 169.54 MiB
max_random_01 AC 1118 ms 169.53 MiB
max_random_02 AC 1109 ms 169.53 MiB
random_00 AC 695 ms 164.42 MiB
random_01 AC 783 ms 166.03 MiB
random_02 AC 382 ms 159.16 MiB
random_03 AC 483 ms 166.66 MiB
random_04 AC 228 ms 156.42 MiB
small_00 AC 77 ms 155.17 MiB
small_01 AC 79 ms 155.05 MiB
small_02 AC 76 ms 155.02 MiB

#include <utility> #include <array> #include <cassert> using i64 = long long; struct cluster { i64 length; using V = i64; cluster(i64 l): length(l) {} static cluster identity() { return cluster(0); } static cluster compress(const cluster& a, const cluster& b, V, V, V cv) { return cluster( a.length + b.length + cv ); } static cluster rake(const cluster& a, const cluster&, V, V, V) { return cluster( a.length ); } static cluster reverse(const cluster& c) { return c; } static std::size_t select(const cluster&, const cluster&, V, V, V) { return 0; } }; class vertex; class node; int parent_dir(node*); node* link(vertex, vertex, cluster); void test_comp_set(node* n); class vertex_raw { cluster::V val; node* hand; public: vertex_raw(cluster::V val): val(val), hand(nullptr) {} node* handle() const { return this->hand; } void set_handle(node* hand) { this->hand = hand; } const cluster::V& value() const { return this->val; } void set_value(cluster::V val) { this->val = val; } }; class vertex { vertex_raw* ver; private: public: static vertex dangling() { return vertex(); } vertex(): ver(nullptr) {} vertex(cluster::V val): ver( new vertex_raw(val)) { vertex dummy; dummy.ver = new vertex_raw(cluster::V()); link(*this, dummy, cluster::identity()); } bool operator==(const vertex& other) { return this->ver == other.ver; } inline node* handle() const { return this->ver->handle(); } inline void set_handle(node* hand) { this->ver->set_handle(hand); } inline const cluster::V& value() const { return this->ver->value(); } inline void set_value(cluster::V val) { this->ver->set_value(val); } }; enum class Type { Compress, Rake, Edge, None }; static std::size_t ni = 0; extern node ns[2020202]; class node { node* ch[2]; node* par; node* ra; node* me; bool rev; cluster fo; vertex v[2]; Type ty; public: node(): par(nullptr), ra(nullptr), me(nullptr), rev(false), fo(cluster::identity()), ty(Type::None) {} static node* new_edge(vertex v, vertex u, cluster val) { //node* n = new node(); node* n = ns + (ni++); n->v[0] = v; n->v[1] = u; n->fo = val; n->me = n; n->ty = Type::Edge; n->fix(); return n; } static node* new_compress(node* left, node* right) { //node* n = new node(); node* n = ns + (ni++); n->ch[0] = left; n->ch[1] = right; n->me = n; n->ty = Type::Compress; n->fix(); return n; } static node* new_rake(node* left, node* right) { //node * n = new node(); node* n = ns + (ni++); n->ch[0] = left; n->ch[1] = right; n->me = n; n->ty = Type::Rake; n->fix(); return n; } inline void fix() { if(this->ty == Type::Edge) { if(!this->parent()) { this->endpoint(0).set_handle(this->me); this->endpoint(1).set_handle(this->me); } else if(this->parent()->ty == Type::Compress) { if(parent_dir(this->me) == -1) { this->endpoint(0).set_handle(this->me); } } else if(this->parent()->ty == Type::Rake) { this->endpoint(0).set_handle(this->me); } } else if(this->ty == Type::Compress) { this->push(); this->v[0] = this->child(0)->endpoint(0); this->v[1] = this->child(1)->endpoint(1); assert(this->child(0)->endpoint(1) == this->child(1)->endpoint(0)); cluster left = this->child(0)->fold(); node* l = this->child(0); if(this->rake()) { node* r = this->rake(); left = cluster::rake(l->fold(), r->fold(), l->endpoint(0).value(), r->endpoint(0).value(), l->endpoint(1).value()); } node* r = this->child(1); this->fo= cluster::compress(left, r->fold(), l->endpoint(0).value(), r->endpoint(1).value(), l->endpoint(1).value()); this->child(0)->endpoint(1).set_handle(this->me); if(!this->parent()) { this->endpoint(0).set_handle(this->me); this->endpoint(1).set_handle(this->me); } else if(this->parent()->ty == Type::Compress) { if(parent_dir(this->me) == -1) { this->endpoint(0).set_handle(this->me); } } else if(this->parent()->ty == Type::Rake) { this->endpoint(0).set_handle(this->me); } } else if(this->ty == Type::Rake) { this->push(); this->v[0] = this->child(0)->endpoint(0); this->v[1] = this->child(0)->endpoint(1); this->fo = cluster::rake(this->child(0)->fold(), this->child(1)->fold(), this->child(0)->endpoint(0).value(), this->child(1)->endpoint(0).value(), this->child(0)->endpoint(1).value()); } else { assert(false); } } inline void push() { if(this->ty == Type::Compress) { if(this->rev) { std::swap(this->ch[0], this->ch[1]); this->child(0)->reverse(); this->child(1)->reverse(); this->rev = false; } } } inline void reverse() { if(this->ty == Type::Edge) { std::swap(this->v[0], this->v[1]); this->fo = cluster::reverse(this->fold()); } else if(this->ty == Type::Compress) { std::swap(this->v[0], this->v[1]); this->fo = cluster::reverse(this->fold()); this->rev ^= true; } else if(this->ty == Type::Rake) { } else { assert(false); } } inline node* parent() const { return this->par; } inline void set_parent(node* par) { this->par = par; } inline node* rake() const { return this->ra; } inline void set_rake(node* rake) { this->ra = rake; } inline node* child(std::size_t dir) const { return this->ch[dir]; } inline void set_child(node* ch, std::size_t dir) { this->ch[dir] = ch; } inline vertex endpoint(std::size_t dir) { return this->v[dir]; } inline Type type() const { return this->ty; } cluster fold() const { return this->fo; } bool guard; }; int parent_dir(node* child) { node* par = child->parent(); if(par) { if(par->guard) { return -1; } else if(par->child(0) == child) { return 0; } else if(par->child(1) == child) { return 1; } else { return -1; } } else { return -1; } } int parent_dir_guard(node* child) { node* par = child->parent(); if(par) { if(par->child(0) == child) { return 0; } else if(par->child(1) == child) { return 1; } else { return -1; } } else { return -1; } } void rotate(node* t, node* x, std::size_t dir) { node* y = x->parent(); int par = parent_dir_guard(x); t->child(dir)->push(); x->set_child(t->child(dir), dir ^ 1); t->child(dir)->set_parent(x); t->set_child(x, dir); x->set_parent(t); t->set_parent(y); if(par != -1) { y->set_child(t, par); } else if(y && y->type() == Type::Compress) { y->set_rake(t); } x->fix(); t->fix(); if(y && !y->guard) { y->fix(); } } void splay(node* t) { assert(t->type() != Type::Edge); t->push(); while(parent_dir(t) != -1) { node* q = t->parent(); if(q->type() != t->type()) break; if(parent_dir(q) != -1 && q->parent() && q->parent()->type() == q->type()) { node* r = q->parent(); if(r->parent()) r->parent()->push(); r->push(); q->push(); t->push(); int qt_dir = parent_dir(t); int rq_dir = parent_dir(q); if(rq_dir == qt_dir) { rotate(q, r, rq_dir ^ 1); rotate(t, q, qt_dir ^ 1); } else { rotate(t, q, qt_dir ^ 1); rotate(t, r, rq_dir ^ 1); } } else { if(q->parent()) q->parent()->push(); q->push(); t->push(); int qt_dir = parent_dir(t); rotate(t, q, qt_dir ^ 1); } } } node* expose_raw(node* t) { while(true) { assert(t->type() != Type::Rake); if(t->type() == Type::Compress) { splay(t); } node* n = nullptr; { node* par = t->parent(); if(!par) { break; } else if(par->type() == Type::Rake) { par->push(); splay(par); n = par->parent(); } else if(par->type() == Type::Compress) { par->push(); if(par->guard && parent_dir_guard(t) != -1) { break; } n = par; } else { assert(false); } } splay(n); int dir = parent_dir_guard(n); if(dir == -1 || n->parent()->type() == Type::Rake) dir = 0; if(dir == 1) { n->child(dir)->reverse(); n->child(dir)->push(); t->reverse(); t->push(); } int n_dir = parent_dir(t); if(n_dir != -1) { node* nch = n->child(dir); nch->push(); node* rake = t->parent(); rake->push(); rake->set_child(nch, n_dir); nch->set_parent(rake); n->set_child(t, dir); t->set_parent(n); nch->fix(); rake->fix(); t->fix(); n->fix(); splay(rake); } else { node* nch = n->child(dir); nch->push(); n->set_rake(nch); nch->set_parent(n); n->set_child(t, dir); t->set_parent(n); nch->fix(); t->fix(); n->fix(); } if(t->type() == Type::Edge) { t = n; } } return t; } node* expose(vertex ver) { return expose_raw(ver.handle()); } void soft_expose(vertex v, vertex u) { node* root = expose(v); if(v.handle() == u.handle()) { if(root->endpoint(1) == v || root->endpoint(0) == u) { root->reverse(); root->push(); } return; } root->guard = true; node* soot = expose(u); root->guard = false; root->fix(); if(parent_dir(soot) == 0) { root->reverse(); root->push(); } } node* link(vertex v, vertex u, cluster weight) { if(!v.handle() && !u.handle()) { return node::new_edge(v, u, weight); } else { node* nnu = u.handle(); node* nnv = v.handle(); node* e = node::new_edge(v, u, weight); node* left = nullptr; if(!nnu) { left = e; } else { node* uu = expose_raw(nnu); uu->push(); if(uu->endpoint(1) == u) { uu->reverse(); uu->push(); } if(uu->endpoint(0) == u) { node* nu = node::new_compress(e, uu); e->set_parent(nu); e->fix(); uu->set_parent(nu); uu->fix(); nu->fix(); left = nu; } else { node* nu = uu; node* left_ch = nu->child(0); left_ch->push(); nu->set_child(e, 0); e->set_parent(nu); e->fix(); node* beta = nu->rake(); node* rake = nullptr; if(beta) { beta->push(); rake = node::new_rake(beta, left_ch); beta->set_parent(rake); left_ch->set_parent(rake); beta->fix(); left_ch->fix(); } else { rake = left_ch; } nu->set_rake(rake); rake->set_parent(nu); rake->fix(); nu->fix(); left = nu; } } if(!nnv) {} else { node* vv =expose_raw(nnv); vv->push(); if(vv->endpoint(0) == v) { vv->reverse(); vv->push(); } if(vv->endpoint(1) == v) { node* top = node::new_compress(vv, left); vv->set_parent(top); left->set_parent(top); vv->fix(); left->fix(); top->fix(); } else { node* nv = vv; node* right_ch = nv->child(1); right_ch->reverse(); right_ch->push(); nv->set_child(left, 1); left->set_parent(nv); left->fix(); node* alpha = nv->rake(); node* rake = nullptr; if(alpha) { alpha->push(); rake = node::new_rake(alpha, right_ch); alpha->set_parent(rake); alpha->fix(); right_ch->set_parent(rake); right_ch->fix(); } else { rake = right_ch; } nv->set_rake(rake); rake->set_parent(nv); rake->fix(); nv->fix(); } } return e; } } void bring(node* root) { node* rake = root->rake(); if(!rake) { node* left = root->child(0); //delete root, root = nullptr; left->set_parent(nullptr); left->fix(); } else if(rake->type() == Type::Compress || rake->type() == Type::Edge) { rake->push(); node* new_right = rake; new_right->reverse(); new_right->push(); root->set_child(new_right, 1); new_right->set_parent(root); root->set_rake(nullptr); new_right->fix(); root->fix(); } else if(rake->type() == Type::Rake) { rake->push(); while(rake->child(1)->type() == Type::Rake) { rake->child(1)->push(); rake = rake->child(1); } root->guard = true; splay(rake); root->guard = false; node* new_rake = rake->child(0); node* new_right = rake->child(1); //delete rake, rake = nullptr; new_right->reverse(); new_right->push(); root->set_child(new_right, 1); new_right->set_parent(root); root->set_rake(new_rake); new_rake->set_parent(root); new_rake->fix(); new_right->fix(); root->fix(); } } void cut(vertex v, vertex u) { soft_expose(v, u); node* root = v.handle(); root->push(); node* right = root->child(1); right->set_parent(nullptr); right->reverse(); right->push(); bring(right); bring(root); } cluster path_query(vertex v, vertex u) { soft_expose(v, u); node* root = v.handle(); root->push(); if(root->endpoint(0) == v && root->endpoint(1) == u) { return root->fold(); } else if(root->endpoint(0) == v) { return root->child(0)->fold(); } else if(root->endpoint(1) == u) { return root->child(1)->fold(); } else { root->child(1)->push(); return root->child(1)->child(0)->fold(); } } node ns[2020202]; #include <iostream> #include <vector> #include <tuple> using namespace std; #include <cstdio> namespace niu { char cur; struct FIN { static inline bool is_blank(char c) { return c <= ' '; } inline char next() { return cur = getc_unlocked(stdin); } inline char peek() { return cur; } inline void skip() { while(is_blank(next())){} } #define intin(inttype) \ FIN& operator>>(inttype& n) { \ bool sign = 0; \ n = 0; \ skip(); \ while(!is_blank(peek())) { \ if(peek() == '-') sign = 1; \ else n = (n << 1) + (n << 3) + (peek() & 0b1111); \ next(); \ } \ if(sign) n = -n; \ return *this; \ } intin(int) intin(long long) } fin; char tmp[128]; struct FOUT { static inline bool is_blank(char c) { return c <= ' '; } inline void push(char c) { putc_unlocked(c, stdout); } FOUT& operator<<(char c) { push(c); return *this; } FOUT& operator<<(const char* s) { while(*s) push(*s++); return *this; } #define intout(inttype) \ FOUT& operator<<(inttype n) { \ if(n) { \ char* p = tmp + 127; bool neg = 0; \ if(n < 0) neg = 1, n = -n; \ while(n) *--p = (n % 10) | 0b00110000, n /= 10; \ if(neg) *--p = '-'; \ return (*this) << p; \ } \ else { \ push('0'); \ return *this; \ } \ } intout(int) intout(long long) } fout; } int main() { using niu::fin; using niu::fout; i64 N, Q; fin >> N >> Q; vector<vertex> vs; for(int i = 0;i < N;i++) { i64 a; fin >> a; vs.push_back(vertex(a)); } for(int i = 0;i + 1 < N;i++) { i64 a, b; fin >> a >> b; link(vs[a], vs[b], cluster::identity()); } for(int i = 0;i < Q;i++) { i64 c, a, b; fin >> c >> a >> b; if(c == 0) { i64 d, e; fin >> d >> e; cut(vs[a], vs[b]); link(vs[d], vs[e], cluster::identity()); } else if(c == 1) { auto node = expose(vs[a]); vs[a].set_value(vs[a].value() + b); node->fix(); } else if(a == b) { fout << vs[a].value() << '\n'; } else { fout << path_query(vs[a], vs[b]).length + vs[a].value() + vs[b].value() << '\n'; } } }