Dynamic Connectivity Algorithm
コードについての説明(個人的メモ)
一般のグラフを対象に辺の追加, 削除, 頂点間の連結性判定を効率よく行うことのできるアルゴリズム. Link Cut Tree, Euler Tour Tree などは森を対象にしていたためそれの一般化にあたる.
元論文は "Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spannning tree, 2-edge, and biconnectivity" [Holm, Lichtenberg, Thorup 1998]
グラフは単純グラフであることを仮定している(多重辺, 自己ループがあっても外部で適切に処理すれば問題ない).
(追記 1)
高速な自作 Unordered Map, Unordered Set を用いた高速版も一応用意した.
ただ unordered_map, unordered_set 自体がそこまでボトルネックになっていないので速度はあまり速くならない. あとコードが長くなるので前者のほうがおすすめ.
(関数)
link$(a, b)$ : 辺$(a, b)$ を追加(連結成分が減るかどうか(true / false) を返す)
cut$(a, b)$ : 辺$(a, b)$ を削除(連結成分が増えるかどうか(true / false) を返す)
connected$(a, b)$ : 頂点 $a$, $b$ が同じ連結成分内に属するかどうかを判定する(true / false)
時間計算量: link, cut ならし $\O (\log^2 n)$, connected $\O (\log n)$ (厳密には以下の実装では "ならし" $\O (\log n)$)
コード
class BSTNode {
public:
const int from, to;
int sz;
bool subtree_edge, subofftree_edge, exact_level;
BSTNode *left, *right, *par;
unordered_set<int> adjacent;
BSTNode(const int _ver) noexcept :
from(_ver), to(_ver), sz(1), subtree_edge(false), subofftree_edge(false),
exact_level(false), left(nullptr), right(nullptr), par(nullptr){}
BSTNode(const int _from, const int _to, const bool _flag) noexcept :
from(_from), to(_to), sz(0), subtree_edge(false), subofftree_edge(false),
exact_level((from < to) && _flag), left(nullptr), right(nullptr), par(nullptr){}
inline bool IsRoot() const noexcept { return !par; }
inline bool IsVertex() const noexcept { return (from == to); }
inline void eval() noexcept {
if(IsVertex()) sz = 1, subtree_edge = false, subofftree_edge = !adjacent.empty();
else sz = 0, subtree_edge = exact_level, subofftree_edge = false;
if(left){
sz += left->sz, subtree_edge |= left->subtree_edge, subofftree_edge |= left->subofftree_edge;
}
if(right){
sz += right->sz, subtree_edge |= right->subtree_edge, subofftree_edge |= right->subofftree_edge;
}
}
inline void subtree_edge_eval(){
subtree_edge = exact_level;
if(left) subtree_edge |= left->subtree_edge;
if(right) subtree_edge |= right->subtree_edge;
}
inline void subofftree_edge_eval(){
subofftree_edge = !adjacent.empty();
if(left) subofftree_edge |= left->subofftree_edge;
if(right) subofftree_edge |= right->subofftree_edge;
}
inline bool subofftree_check(){
return !adjacent.empty() ||
(left ? left->subofftree_edge : false) || (right ? right->subofftree_edge : false);
}
inline bool offtree_check(){
return adjacent.empty() ||
(left ? left->subofftree_edge : false) || (right ? right->subofftree_edge : false);
}
void rotate(const bool right_) noexcept {
BSTNode *p = par, *g = p->par;
if(right_){
if((p->left = right)) right->par = p;
right = p, p->par = this;
}else{
if((p->right = left)) left->par = p;
left = p, p->par = this;
}
p->eval(), eval();
if(!(par = g)) return;
if(g->left == p) g->left = this;
if(g->right == p) g->right = this;
g->eval();
}
};
BSTNode *splay(BSTNode *u) noexcept {
if(!u) return nullptr;
while(!(u->IsRoot())){
BSTNode *p = u->par, *gp = p->par;
if(p->IsRoot()){
u->rotate((u == p->left));
}else{
bool flag = (u == p->left);
if((u == p->left) == (p == gp->left)){
p->rotate(flag), u->rotate(flag);
}else{
u->rotate(flag), u->rotate(!flag);
}
}
}
return u;
}
BSTNode *join(BSTNode *root1, BSTNode *root2) noexcept {
if(!root1 || !root2) return root1 ? root1 : root2;
BSTNode *cur = nullptr, *nx = root1;
do{ cur = nx, nx = cur->right; }while(nx);
BSTNode *ver = splay(cur);
ver->right = root2, ver->eval(), root2->par = ver;
return ver;
}
class EulerTourTree {
public:
struct pair_hash {
template <class T1, class T2>
size_t operator() (const pair<T1, T2>& p) const {
size_t lhs = hash<T1>()(p.first), rhs = hash<T2>()(p.second);
return lhs^(rhs+0x9e3779b9+(lhs<<6)+(lhs>>2));
}
};
const int V;
BSTNode** vertex_set;
unordered_map<pair<int, int>, pair<BSTNode*, BSTNode*>, pair_hash> edge_set;
private:
void dfs(const int u, const int p, const BSTNode *cur,
bool *visit, vector<BSTNode*>& nodes, const vector<vector<int> >& G) noexcept {
visit[u] = true;
nodes.push_back(vertex_set[u]);
for(auto& v : G[u]){
if(!visit[v]){
BSTNode* e1 = new BSTNode(u, v, true);
nodes.push_back(e1);
dfs(v, u, cur, visit, nodes, G);
BSTNode* e2 = new BSTNode(v, u, true);
if(u < v) edge_set[{u, v}] = {e1, e2};
else edge_set[{v, u}] = {e2, e1};
nodes.push_back(e2);
}else if(v != p){
vertex_set[u]->adjacent.insert(v);
vertex_set[u]->subofftree_edge = true;
}
}
}
void bst_build(vector<BSTNode*>& nodes) noexcept {
int i, n = (int)nodes.size(), st = 2, isolate = ((n % 4 == 1) ? (n-1) : -1);
while(st <= n){
for(i = st-1; i < n; i += 2*st){
nodes[i]->left = nodes[i-st/2], nodes[i-st/2]->par = nodes[i];
if(i+st/2 < n) nodes[i]->right = nodes[i+st/2], nodes[i+st/2]->par = nodes[i];
else if(isolate >= 0) nodes[i]->right = nodes[isolate], nodes[isolate]->par = nodes[i];
nodes[i]->eval();
}
isolate = ((n % (4*st) >= st && (n % (4*st) < 2*st)) ? (i-2*st): isolate);
st <<= 1;
}
}
void build_forest(const vector<vector<int> >& G){
bool *visit = new bool[V]();
for(int i = 0; i < V; ++i){
if(!visit[i]){
vector<BSTNode*> nodes;
BSTNode *cur = nullptr;
dfs(i, -1, cur, visit, nodes, G);
bst_build(nodes);
}
}
}
BSTNode *reroot(BSTNode *ver) noexcept {
BSTNode *res = splay(ver)->left;
if(!res) return ver;
ver->left = nullptr, ver->eval();
while(ver->right) ver = ver->right;
splay(ver), ver->right = res, ver->eval(), res->par = ver;
return ver;
}
void link(BSTNode *ver1, BSTNode *ver2, const bool flag) noexcept {
BSTNode *e1 = new BSTNode(ver1->from, ver2->from, flag);
BSTNode *e2 = new BSTNode(ver2->from, ver1->from, flag);
edge_set[{ver1->from, ver2->from}] = {e1, e2};
join(join(reroot(ver1), e1), join(reroot(ver2), e2));
}
void cut(BSTNode *edge1, BSTNode *edge2) noexcept {
splay(edge1), splay(edge2);
BSTNode *p = edge1->par;
bool _right = (edge1 == edge2->right);
if(p != edge2){
_right = (p == edge2->right);
p->par = nullptr, edge1->rotate((edge1 == p->left));
}
if(edge1->left) edge1->left->par = nullptr;
if(edge1->right) edge1->right->par = nullptr;
if(_right){
if(edge2->left) edge2->left->par = nullptr;
join(edge2->left, edge1->right);
}else{
if(edge2->right) edge2->right->par = nullptr;
join(edge1->left, edge2->right);
}
delete edge1; delete edge2;
}
bool connected(BSTNode *ver1, BSTNode *ver2) noexcept {
splay(ver1), splay(ver2);
return ver1->par;
}
int component_size(BSTNode *ver) noexcept { return splay(ver)->sz; }
public:
EulerTourTree(const int node_size) : V(node_size), vertex_set(new BSTNode*[V]){
for(int i = 0; i < V; i++) vertex_set[i] = new BSTNode(i);
}
EulerTourTree(const vector<vector<int> >& G) : V((int)G.size()), vertex_set(new BSTNode*[V]){
for(int i = 0; i < V; i++) vertex_set[i] = new BSTNode(i);
build_forest(G);
}
// ~EulerTourTree(){
// for(auto it : edge_set){
// delete (it.second).first;
// delete (it.second).second;
// }
// for(int i = 0; i < V; ++i) delete vertex_set[i];
// delete[] vertex_set;
// }
void reroot(const int node_id) noexcept { reroot(vertex_set[node_id]); }
void link(int node1_id, int node2_id, bool flag=true) noexcept {
if(node1_id > node2_id) swap(node1_id, node2_id);
link(vertex_set[node1_id], vertex_set[node2_id], flag);
}
void cut(int node1_id, int node2_id){
if(node1_id > node2_id) swap(node1_id, node2_id);
auto it = edge_set.find({node1_id, node2_id});
assert(it != edge_set.end());
BSTNode *edge1 = (it->second).first, *edge2 = (it->second).second;
edge_set.erase(it);
cut(edge1, edge2);
}
bool connected(const int node1_id, const int node2_id) noexcept {
if(node1_id == node2_id) return true;
return connected(vertex_set[node1_id], vertex_set[node2_id]);
}
int component_size(int node_id) noexcept { return component_size(vertex_set[node_id]); }
void check_dfs(const BSTNode* cur) const noexcept {
if(cur->left) check_dfs(cur->left);
cout << "{" << (cur->from) << "," << (cur->to) << "} ";
if(cur->right) check_dfs(cur->right);
}
};
class DynamicConnectivity {
private:
BSTNode *level_up_dfs(BSTNode *cur, const int layer) noexcept {
if(cur->exact_level){
splay(cur)->exact_level = false, cur->subtree_edge_eval();
detect_layer[{cur->from, cur->to}]++, et[layer+1].link(cur->from, cur->to);
return cur;
}
if(cur->left && cur->left->subtree_edge) return level_up_dfs(cur->left, layer);
if(cur->right && cur->right->subtree_edge) return level_up_dfs(cur->right, layer);
return nullptr;
}
BSTNode *search_edge_dfs
(BSTNode *cur, const int layer, const int another, bool& flag, pair<int, int>& rep_edge) noexcept {
if(!cur->adjacent.empty()){
bool state = et[layer+1].vertex_set[cur->from]->adjacent.empty();
for(auto it = cur->adjacent.begin(); it != cur->adjacent.end();){
pair<int, int> e = {min(cur->from, *it), max(cur->from, *it)};
BSTNode *correspond = et[layer].vertex_set[*it];
if(et[layer].connected(another, *it)){
flag = true, rep_edge = e;
cur->adjacent.erase(it), correspond->adjacent.erase(cur->from);
if(!correspond->subofftree_check()){
splay(correspond)->subofftree_edge_eval();
}
break;
}else{
if(!et[layer+1].vertex_set[*it]->subofftree_check()){
splay(et[layer+1].vertex_set[*it])->subofftree_edge = true;
}
et[layer+1].vertex_set[cur->from]->adjacent.insert(*it);
et[layer+1].vertex_set[*it]->adjacent.insert(cur->from);
detect_layer[e]++, it = cur->adjacent.erase(it);
correspond->adjacent.erase(cur->from);
if(!correspond->subofftree_check()){
splay(correspond)->subofftree_edge_eval();
}
}
}
if(state && !et[layer+1].vertex_set[cur->from]->offtree_check()){
splay(et[layer+1].vertex_set[cur->from])->subofftree_edge = true;
}
splay(cur)->subofftree_edge_eval();
return cur;
}
if(cur->left && cur->left->subofftree_edge){
return search_edge_dfs(cur->left, layer, another, flag, rep_edge);
}
if(cur->right && cur->right->subofftree_edge){
return search_edge_dfs(cur->right, layer, another, flag, rep_edge);
}
return nullptr;
}
bool replace(const int from, const int to, const int layer) noexcept {
if(layer < 0) return true;
int u, v;
if(et[layer].component_size(from) <= et[layer].component_size(to)) u = from, v = to;
else u = to, v = from;
BSTNode *ver = splay(et[layer].vertex_set[u]);
while(ver->subtree_edge) ver = level_up_dfs(ver, layer);
pair<int, int> rep_edge = {-1, -1};
bool flag = false;
while(ver->subofftree_edge){
ver = search_edge_dfs(ver, layer, v, flag, rep_edge);
if(flag) break;
}
if(flag){
et[layer].link(rep_edge.first, rep_edge.second);
for(int i = 0; i < layer; i++) et[i].link(rep_edge.first, rep_edge.second, false);
return false;
}else return replace(from, to, layer-1);
}
public:
const int V;
int depth;
vector<EulerTourTree> et;
unordered_map<pair<int, int>, int, EulerTourTree::pair_hash> detect_layer;
DynamicConnectivity(const int node_size) noexcept : V(node_size), depth(1){
et.emplace_back(V);
}
DynamicConnectivity(const vector<vector<int> >& G) noexcept : V((int)G.size()), depth(1){
for(int i = 0; i < V; ++i){
for(const int j : G[i]){
if(i < j) detect_layer[{i, j}] = 0;
}
}
et.emplace_back(G);
}
bool link(int node1_id, int node2_id) noexcept {
if(node1_id > node2_id) swap(node1_id, node2_id);
detect_layer[{node1_id, node2_id}] = 0;
if(et[0].connected(node1_id, node2_id)){
BSTNode *ver1 = et[0].vertex_set[node1_id], *ver2 = et[0].vertex_set[node2_id];
splay(ver1)->subofftree_edge = true, ver1->adjacent.insert(node2_id);
splay(ver2)->subofftree_edge = true, ver2->adjacent.insert(node1_id);
return false;
}else{
et[0].link(node1_id, node2_id);
return true;
}
}
bool cut(int node1_id, int node2_id) noexcept {
if(node1_id > node2_id) swap(node1_id, node2_id);
auto it = detect_layer.find({node1_id, node2_id});
assert(it != detect_layer.end());
int layer = it->second;
detect_layer.erase(it);
auto& st = et[layer].vertex_set[node1_id]->adjacent;
if(st.find(node2_id) == st.end()){
for(int i = 0; i <= layer; i++) et[i].cut(node1_id, node2_id);
if(layer + 1 == depth) ++depth, et.emplace_back(V);
return replace(node1_id, node2_id, layer);
}else{
et[layer].vertex_set[node1_id]->adjacent.erase(node2_id);
if(!et[layer].vertex_set[node1_id]->subofftree_check()){
splay(et[layer].vertex_set[node1_id])->subofftree_edge_eval();
}
et[layer].vertex_set[node2_id]->adjacent.erase(node1_id);
if(!et[layer].vertex_set[node2_id]->subofftree_check()){
splay(et[layer].vertex_set[node2_id])->subofftree_edge_eval();
}
return false;
}
}
bool connected(const int node1_id, const int node2_id) noexcept {
return et[0].connected(node1_id, node2_id);
}
};
コード(高速版)
template<class _Key, class _Hash, bool DOWNSIZE> class UnorderedSetIterator;
template<class _Key, class _Hash = hash<_Key>, bool DOWNSIZE = false>
class UnorderedSet
{
private:
using iterator = UnorderedSetIterator<_Key, _Hash, DOWNSIZE>;
friend UnorderedSetIterator<_Key, _Hash, DOWNSIZE>;
struct bucket {
_Key _key;
short int _dist;
bool _last, _end;
bucket() noexcept : _dist(-1), _last(false), _end(false){}
bucket& operator=(const bucket& another) = default;
~bucket(){ if(!empty()) _key.~_Key(); }
inline void clear() noexcept { _dist = -1; }
inline void _delete(){ _dist = -1, _key.~_Key(); }
inline bool empty() const noexcept { return (_dist == -1); }
};
inline static unsigned int ceilpow2(unsigned int u) noexcept {
if(u == 0u) return 0u;
--u, u |= u >> 1, u |= u >> 2, u |= u >> 4, u |= u >> 8;
return (u | (u >> 16)) + 1;
}
inline static bucket *increment(bucket *cur) noexcept {
for(++cur; !cur->_end; ++cur){
if(!cur->empty()) break;
}
return cur;
}
inline bucket *next_bucket(bucket *cur) const noexcept {
return cur->_last ? _buckets : cur + 1;
}
inline unsigned int make_hash(const _Key& key) const noexcept {
return _Hash()(key);
}
inline float load_rate() const noexcept {
return (float)_data_count / _bucket_count;
}
bucket *insert(bucket *cur, short int dist, _Key&& key){
bucket *ret = cur;
bool flag = false;
while(true){
if(cur->empty()){
cur->_key = move(key), cur->_dist = dist;
if(!flag) ret = cur, flag = true;
break;
}else if(dist > cur->_dist){
swap(key, cur->_key), swap(dist, cur->_dist);
if(!flag) ret = cur, flag = true;
}
++dist;
cur = next_bucket(cur);
}
return ret;
}
bucket *_find(const _Key& key) const {
bucket *cur = _buckets + (make_hash(key) & _mask);
int dist = 0;
while(dist <= cur->_dist){
if(key == cur->_key) return cur;
++dist, cur = next_bucket(cur);
}
return _buckets + _bucket_count;
}
template<class Key>
bucket *find_insert(Key&& key){
unsigned int hash = make_hash(key);
bucket *cur = _buckets + (hash & _mask);
int dist = 0;
while(dist <= cur->_dist){
if(key == cur->_key) return cur;
++dist, cur = next_bucket(cur);
}
++_data_count;
if(rehash_check()){
cur = _buckets + (hash & _mask), dist = 0;
}
_Key new_key = forward<Key>(key);
return insert(cur, dist, move(new_key));
}
template<typename... Args>
bucket *emplace(Args&&... args){
return find_insert(_Key(forward<Args>(args)...));
}
bucket *backward_shift(bucket *cur, bool next_ret){
bucket *next = next_bucket(cur), *ret = cur;
if(next->_dist < 1) return next_ret ? increment(cur) : cur;
do {
cur->_key = next->_key, cur->_dist = next->_dist - 1;
cur = next, next = next_bucket(cur);
}while(next->_dist >= 1);
cur->clear();
return ret;
}
bucket *erase_impl(bucket *cur, bool next_ret){
assert(static_cast<size_t>(cur - _buckets) != _bucket_count);
cur->_delete();
--_data_count;
return backward_shift(cur, next_ret);
}
bucket *erase_itr(bucket *cur, bool next_ret = true){
const _Key key = cur->_key;
return erase_impl(rehash_check() ? _find(key) : cur, next_ret);
}
bucket *erase_key(const _Key& key, bool next_ret = true){
rehash_check();
return erase_impl(_find(key), next_ret);
}
bool rehash_check(){
if(_bucket_count == 0){
rehash(1u);
return true;
}else if(load_rate() >= MAX_LOAD_RATE){
rehash(_bucket_count * 2u);
return true;
}else if(DOWNSIZE){
if(load_rate() <= MIN_LOAD_RATE && _bucket_count >= DOWNSIZE_THRESHOLD){
rehash(_bucket_count / 2u);
return true;
}
}
return false;
}
void move_data(bucket *cur){
insert(_buckets + (make_hash(cur->_key) & _mask), 0, move(cur->_key));
}
void rehash(unsigned int new_bucket_count){
UnorderedSet new_unordered_set(new_bucket_count);
new_unordered_set._data_count = _data_count;
for(bucket *cur = _buckets; !cur->_end; ++cur){
if(!cur->empty()){
new_unordered_set.move_data(cur);
}
}
swap(*this, new_unordered_set);
}
friend void swap(UnorderedSet& ust1, UnorderedSet& ust2){
swap(ust1._bucket_count, ust2._bucket_count);
swap(ust1._mask, ust2._mask);
swap(ust1._data_count, ust2._data_count);
swap(ust1._buckets, ust2._buckets);
}
private:
unsigned int _bucket_count, _mask, _data_count;
bucket *_buckets;
public:
const float MAX_LOAD_RATE = 0.5f;
const float MIN_LOAD_RATE = 0.1f;
const unsigned int DOWNSIZE_THRESHOLD = 16u;
UnorderedSet(unsigned int bucket_size = 0u)
: _bucket_count(ceilpow2(bucket_size)), _mask(_bucket_count - 1),
_data_count(0u), _buckets(new bucket[_bucket_count + 1]){
if(_bucket_count > 0) _buckets[_bucket_count - 1]._last = true;
else _mask = 0;
_buckets[_bucket_count]._end = true;
}
UnorderedSet(const UnorderedSet& another)
: _bucket_count(another._bucket_count), _mask(another._mask), _data_count(another._data_count){
_buckets = new bucket[_bucket_count + 1u];
for(unsigned int i = 0u; i <= _bucket_count; ++i){
_buckets[i] = another._buckets[i];
}
}
UnorderedSet(UnorderedSet&& another)
: _bucket_count(move(another._bucket_count)), _mask(move(another._mask)),
_data_count(move(another._data_count)), _buckets(another._buckets){
another._buckets = nullptr;
}
UnorderedSet& operator=(const UnorderedSet& another){
delete[] _buckets;
_bucket_count = another._bucket_count;
_mask = another._mask;
_data_count = another._data_count;
_buckets = new bucket[_bucket_count + 1u];
for(unsigned int i = 0u; i <= _bucket_count; ++i){
_buckets[i] = another._buckets[i];
}
return *this;
}
UnorderedSet& operator=(UnorderedSet&& another){
delete[] _buckets;
_bucket_count = move(another._bucket_count);
_mask = move(another._mask);
_data_count = move(another._data_count);
_buckets = another._buckets;
another._buckets = nullptr;
return *this;
}
void allocate(unsigned int element_size){
rehash(ceilpow2(ceil(element_size / MAX_LOAD_RATE) + 1));
}
~UnorderedSet(){ delete[] _buckets; }
friend ostream& operator<< (ostream& os, UnorderedSet& ust) noexcept {
for(_Key& val : ust) os << val << " ";
return os;
}
void clear(){
UnorderedSet new_unordered_set(0u);
swap(*this, new_unordered_set);
}
size_t size() const noexcept { return _data_count; }
size_t bucket_count() const noexcept { return _bucket_count; }
bool empty() const noexcept { return (_data_count == 0); }
iterator begin() noexcept {
return (_buckets->empty() && _bucket_count > 0) ? iterator(increment(_buckets)) : iterator(_buckets);
}
iterator end() noexcept { return iterator(_buckets + _bucket_count); }
iterator find(const _Key& key) const { return iterator(_find(key)); }
size_t count(const _Key& key) const { return (_find(key) != _buckets + _bucket_count); }
iterator insert(const _Key& key){ return iterator(find_insert(key)); }
iterator insert(_Key&& key){ return iterator(find_insert(move(key))); }
template<typename... Args>
iterator emplace(Args&&... args){ return iterator(_emplace(forward<Args>(args)...)); }
iterator erase(const _Key& key){ return iterator(erase_key(key)); }
iterator erase(const iterator& itr){ return iterator(erase_itr(itr.bucket_ptr)); }
void simple_erase(const _Key& key){ erase_key(key, false); }
void simple_erase(const iterator& itr){ erase_itr(itr.bucket_ptr, false); }
// DEBUG 用
short int maximum_distance() const noexcept {
short int ret = -1;
for(bucket *cur = _buckets; !cur->_end; ++cur){
ret = max(ret, cur->_dist);
}
return ret;
}
};
template<class _Key, class _Hash, bool DOWNSIZE>
class UnorderedSetIterator {
private:
friend UnorderedSet<_Key, _Hash, DOWNSIZE>;
typename UnorderedSet<_Key, _Hash, DOWNSIZE>::bucket *bucket_ptr;
using iterator_category = forward_iterator_tag;
using value_type = _Key;
using difference_type = ptrdiff_t;
using pointer = _Key*;
using reference = _Key&;
private:
UnorderedSetIterator(typename UnorderedSet<_Key, _Hash, DOWNSIZE>::bucket *_bucket_ptr)
noexcept : bucket_ptr(_bucket_ptr){}
public:
UnorderedSetIterator() noexcept : bucket_ptr(){}
UnorderedSetIterator(const UnorderedSetIterator& itr) noexcept : bucket_ptr(itr.bucket_ptr){}
UnorderedSetIterator& operator=(const UnorderedSetIterator& itr)
& noexcept { return bucket_ptr = itr.bucket_ptr, *this; }
UnorderedSetIterator& operator=(const UnorderedSetIterator&& itr)
& noexcept { return bucket_ptr = itr.bucket_ptr, *this; }
reference operator*() const noexcept { return bucket_ptr->_key; }
pointer operator->() const noexcept { return &(bucket_ptr->_key); }
UnorderedSetIterator& operator++() noexcept {
return bucket_ptr = UnorderedSet<_Key, _Hash, DOWNSIZE>::increment(bucket_ptr), *this;
}
UnorderedSetIterator operator++(int) const noexcept {
return UnorderedSetIterator(UnorderedSet<_Key, _Hash, DOWNSIZE>::increment(this->bucket_ptr));
}
bool operator==(const UnorderedSetIterator& itr) const noexcept { return !(*this != itr); };
bool operator!=(const UnorderedSetIterator& itr) const noexcept { return bucket_ptr != itr.bucket_ptr; }
};
template<class _Key, class _Tp, class _Hash, bool DOWNSIZE> class UnorderedMapIterator;
template<class _Key, class _Tp, class _Hash = hash<_Key>, bool DOWNSIZE = false>
class UnorderedMap
{
private:
using iterator = UnorderedMapIterator<_Key, _Tp, _Hash, DOWNSIZE>;
using value_type = _Tp;
using data_type = pair<_Key, _Tp>;
using aligned_pointer = typename aligned_storage<sizeof(value_type), alignof(value_type)>::type;
friend UnorderedMapIterator<_Key, _Tp, _Hash, DOWNSIZE>;
struct bucket {
_Key _key;
short int _dist;
bool _last, _end;
aligned_pointer _value_ptr;
bucket() noexcept : _dist(-1), _last(false), _end(false){}
bucket& operator=(const bucket& another) noexcept {
_key = another._key, _dist = another._dist, _last = another._last, _end = another._end;
if(!another.empty()){
new(&_value_ptr) value_type(*reinterpret_cast<const value_type*>(&another._value_ptr));
}
return *this;
}
~bucket(){ if(!empty()) _delete(); }
inline void clear() noexcept { _dist = -1; }
inline void _delete(){ _dist = -1, value_ptr()->~value_type(); }
inline bool empty() const noexcept { return (_dist == -1); }
inline value_type& value() noexcept {
return *reinterpret_cast<value_type*>(&_value_ptr);
}
inline value_type* value_ptr() noexcept {
return reinterpret_cast<value_type*>(&_value_ptr);
}
inline void new_value(value_type&& value){
new(&_value_ptr) value_type(move(value));
}
};
inline static unsigned int ceilpow2(unsigned int u) noexcept {
if(u == 0u) return 0u;
--u, u |= u >> 1, u |= u >> 2, u |= u >> 4, u |= u >> 8;
return (u | (u >> 16)) + 1u;
}
inline static bucket *increment(bucket *cur) noexcept {
for(++cur; !cur->_end; ++cur){
if(!cur->empty()) break;
}
return cur;
}
inline bucket *next_bucket(bucket *cur) const noexcept {
return cur->_last ? _buckets : cur + 1;
}
inline unsigned int make_hash(const _Key& key) const noexcept {
return _Hash()(key);
}
inline float load_rate() const noexcept {
return (float)_data_count / _bucket_count;
}
bucket *insert(bucket *cur, _Key&& key, short int dist, value_type&& value){
bucket *ret = cur;
bool flag = false;
while(true){
if(cur->empty()){
cur->_key = move(key), cur->_dist = dist, cur->new_value(move(value));
if(!flag) ret = cur, flag = true;
break;
}else if(dist > cur->_dist){
swap(key, cur->_key), swap(dist, cur->_dist), swap(value, cur->value());
if(!flag) ret = cur, flag = true;
}
++dist;
cur = next_bucket(cur);
}
return ret;
}
template<class Key>
bucket *_find(Key&& key, bool push = false){
unsigned int hash = make_hash(key);
bucket *cur = _buckets + (hash & _mask);
short int dist = 0;
while(dist <= cur->_dist){
if(key == cur->_key) return cur;
++dist, cur = next_bucket(cur);
}
if(!push) return _buckets + _bucket_count;
++_data_count;
if(rehash_check()){
cur = _buckets + (hash & _mask), dist = 0;
}
value_type new_value = value_type();
_Key new_key = forward<Key>(key);
return insert(cur, move(new_key), dist, move(new_value));
}
template<class Data>
bucket *find_insert(Data&& data){
const _Key& key = data.first;
unsigned int hash = make_hash(key);
bucket *cur = _buckets + (hash & _mask);
short int dist = 0;
while(dist <= cur->_dist){
if(key == cur->_key) return cur;
++dist, cur = next_bucket(cur);
}
++_data_count;
if(rehash_check()){
cur = _buckets + (hash & _mask), dist = 0;
}
data_type new_data = forward<Data>(data);
return insert(cur, move(new_data.first), dist, move(new_data.second));
}
template<typename... Args>
bucket *emplace(Args&&... args){
return find_insert(data_type(forward<Args>(args)...));
}
bucket *backward_shift(bucket *cur, bool next_ret){
bucket *next = next_bucket(cur), *ret = cur;
if(next->_dist < 1) return next_ret ? increment(cur) : cur;
do {
cur->_key = next->_key, cur->_dist = next->_dist - 1;
cur->new_value(move(next->value()));
cur = next, next = next_bucket(cur);
}while(next->_dist >= 1);
cur->clear();
return ret;
}
bucket *erase_impl(bucket *cur, bool next_ret){
assert(static_cast<size_t>(cur - _buckets) != _bucket_count);
cur->_delete();
--_data_count;
return backward_shift(cur, next_ret);
}
bucket *erase_itr(bucket *cur, bool next_ret = true){
const _Key key = cur->_key;
return erase_impl(rehash_check() ? _find(key) : cur, next_ret);
}
bucket *erase_key(const _Key& key, bool next_ret = true){
rehash_check();
return erase_impl(_find(key), next_ret);
}
bool rehash_check(){
if(_bucket_count == 0){
rehash(1u);
return true;
}else if(load_rate() >= MAX_LOAD_RATE){
rehash(_bucket_count * 2u);
return true;
}else if(DOWNSIZE){
if(load_rate() <= MIN_LOAD_RATE && _bucket_count >= DOWNSIZE_THRESHOLD){
rehash(_bucket_count / 2u);
return true;
}
}
return false;
}
void move_data(bucket *cur){
insert(_buckets + (make_hash(cur->_key) & _mask), move(cur->_key), 0, move(cur->value()));
}
void rehash(unsigned int new_bucket_count){
UnorderedMap new_unordered_map(new_bucket_count);
new_unordered_map._data_count = _data_count;
for(bucket *cur = _buckets; !cur->_end; ++cur){
if(!cur->empty()){
new_unordered_map.move_data(cur);
}
}
swap(*this, new_unordered_map);
}
friend void swap(UnorderedMap& ump1, UnorderedMap& ump2){
swap(ump1._bucket_count, ump2._bucket_count);
swap(ump1._mask, ump2._mask);
swap(ump1._data_count, ump2._data_count);
swap(ump1._buckets, ump2._buckets);
}
private:
unsigned int _bucket_count, _mask, _data_count;
bucket *_buckets;
public:
const float MAX_LOAD_RATE = 0.5f;
const float MIN_LOAD_RATE = 0.1f;
const unsigned int DOWNSIZE_THRESHOLD = 16u;
UnorderedMap(unsigned int bucket_size = 0u)
: _bucket_count(ceilpow2(bucket_size)), _mask(_bucket_count - 1),
_data_count(0u), _buckets(new bucket[_bucket_count + 1]){
if(_bucket_count > 0) _buckets[_bucket_count - 1]._last = true;
else _mask = 0;
_buckets[_bucket_count]._end = true;
}
UnorderedMap(const UnorderedMap& another)
: _bucket_count(another._bucket_count), _mask(another._mask), _data_count(another._data_count){
_buckets = new bucket[_bucket_count + 1u];
for(unsigned int i = 0u; i <= _bucket_count; ++i){
_buckets[i] = another._buckets[i];
}
}
UnorderedMap(UnorderedMap&& another)
: _bucket_count(move(another._bucket_count)), _mask(move(another._mask)),
_data_count(move(another._data_count)), _buckets(another._buckets){
another._buckets = nullptr;
}
UnorderedMap& operator=(const UnorderedMap& another){
delete[] _buckets;
_bucket_count = another._bucket_count;
_mask = another._mask;
_data_count = another._data_count;
_buckets = new bucket[_bucket_count + 1u];
for(unsigned int i = 0u; i <= _bucket_count; ++i){
_buckets[i] = another._buckets[i];
}
return *this;
}
UnorderedMap& operator=(UnorderedMap&& another){
delete[] _buckets;
_bucket_count = move(another._bucket_count);
_mask = move(another._mask);
_data_count = move(another._data_count);
_buckets = another._buckets;
another._buckets = nullptr;
return *this;
}
void allocate(unsigned int element_size){
rehash(ceilpow2(ceil(element_size / MAX_LOAD_RATE) + 1));
}
~UnorderedMap(){ delete[] _buckets; }
friend ostream& operator<< (ostream& os, UnorderedMap& ump) noexcept {
for(auto val : ump) os << '{' << val.first << ',' << val.second << "} ";
return os;
}
_Tp& operator[](const _Key& key){ return _find(key, true)->value(); }
_Tp& operator[](_Key&& key){ return _find(move(key), true)->value(); }
const _Tp& at(const _Key& key){
bucket *res = _find(key);
if(res == _buckets + _bucket_count) __throw_out_of_range(__N("Unordered_Map::at"));
return res->value();
}
void clear(){
UnorderedMap new_unordered_map(0u);
swap(*this, new_unordered_map);
}
size_t size() const noexcept { return _data_count; }
size_t bucket_count() const noexcept { return _bucket_count; }
bool empty() const noexcept { return (_data_count == 0); }
iterator begin() noexcept {
return (_buckets->empty() && _bucket_count > 0) ? iterator(increment(_buckets)) : iterator(_buckets);
}
iterator end() noexcept { return iterator(_buckets + _bucket_count); }
iterator find(const _Key& key){ return iterator(_find(key)); }
iterator insert(const data_type& data){ return iterator(find_insert(data)); }
iterator insert(data_type&& data){ return iterator(find_insert(move(data))); }
template<typename... Args>
iterator emplace(Args&&... args){ return iterator(_emplace(forward<Args>(args)...)); }
iterator erase(const _Key& key){ return iterator(erase_key(key)); }
iterator erase(const iterator& itr){ return iterator(erase_itr(itr.bucket_ptr)); }
void simple_erase(const _Key& key){ erase_key(key, false); }
void simple_erase(const iterator& itr){ erase_itr(itr.bucket_ptr, false); }
// DEBUG 用
short int maximum_distance() const noexcept {
short int ret = -1;
for(bucket *cur = _buckets; !cur->_end; ++cur){
ret = max(ret, cur->_dist);
}
return ret;
}
};
template<class _Key, class _Tp, class _Hash, bool DOWNSIZE>
class UnorderedMapIterator {
private:
friend UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>;
typename UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::bucket *bucket_ptr;
using iterator_category = forward_iterator_tag;
using value_type = pair<const _Key, _Tp>;
using difference_type = ptrdiff_t;
using reference = pair<const _Key&, _Tp&>;
private:
UnorderedMapIterator(typename UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::bucket *_bucket_ptr)
noexcept : bucket_ptr(_bucket_ptr){}
public:
UnorderedMapIterator() noexcept : bucket_ptr(){}
UnorderedMapIterator(const UnorderedMapIterator& itr) noexcept : bucket_ptr(itr.bucket_ptr){}
UnorderedMapIterator& operator=(const UnorderedMapIterator& itr)
& noexcept { return bucket_ptr = itr.bucket_ptr, *this; }
UnorderedMapIterator& operator=(const UnorderedMapIterator&& itr)
& noexcept { return bucket_ptr = itr.bucket_ptr, *this; }
reference operator*() const noexcept { return {bucket_ptr->_key, bucket_ptr->value()}; }
UnorderedMapIterator& operator++() noexcept {
return bucket_ptr = UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::increment(bucket_ptr), *this;
}
UnorderedMapIterator operator++(int) const noexcept {
return UnorderedMapIterator(UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::increment(this->bucket_ptr));
}
bool operator==(const UnorderedMapIterator& itr) const noexcept { return !(*this != itr); };
bool operator!=(const UnorderedMapIterator& itr) const noexcept { return bucket_ptr != itr.bucket_ptr; }
};
// 多重辺は無いと仮定する
class BSTNode {
public:
struct murmur_hash32 {
unsigned int operator()(int p) const {
const unsigned int m = 0x5bd1e995; p *= m;
unsigned int h = (p^(p>>24))*m;
return h = (h^(h>>13))*m, (h^(h>>15));
}
};
const int from, to;
int sz;
bool subtree_edge, subofftree_edge, exact_level;
BSTNode *left, *right, *par;
UnorderedSet<int, murmur_hash32, true> adjacent;
BSTNode(const int _ver) noexcept :
from(_ver), to(_ver), sz(1), subtree_edge(false), subofftree_edge(false),
exact_level(false), left(nullptr), right(nullptr), par(nullptr){}
BSTNode(const int _from, const int _to, const bool _flag) noexcept :
from(_from), to(_to), sz(0), subtree_edge(false), subofftree_edge(false),
exact_level((from < to) && _flag), left(nullptr), right(nullptr), par(nullptr){}
inline bool IsRoot() const noexcept { return !par; }
inline bool IsVertex() const noexcept { return (from == to); }
inline void eval() noexcept {
if(IsVertex()) sz = 1, subtree_edge = false, subofftree_edge = !adjacent.empty();
else sz = 0, subtree_edge = exact_level, subofftree_edge = false;
if(left){
sz += left->sz, subtree_edge |= left->subtree_edge, subofftree_edge |= left->subofftree_edge;
}
if(right){
sz += right->sz, subtree_edge |= right->subtree_edge, subofftree_edge |= right->subofftree_edge;
}
}
inline void subtree_edge_eval(){
subtree_edge = exact_level;
if(left) subtree_edge |= left->subtree_edge;
if(right) subtree_edge |= right->subtree_edge;
}
inline void subofftree_edge_eval(){
subofftree_edge = !adjacent.empty();
if(left) subofftree_edge |= left->subofftree_edge;
if(right) subofftree_edge |= right->subofftree_edge;
}
inline bool subofftree_check(){
return !adjacent.empty() ||
(left ? left->subofftree_edge : false) || (right ? right->subofftree_edge : false);
}
inline bool offtree_check(){
return adjacent.empty() ||
(left ? left->subofftree_edge : false) || (right ? right->subofftree_edge : false);
}
void rotate(const bool right_) noexcept {
BSTNode *p = par, *g = p->par;
if(right_){
if((p->left = right)) right->par = p;
right = p, p->par = this;
}else{
if((p->right = left)) left->par = p;
left = p, p->par = this;
}
p->eval(), eval();
if(!(par = g)) return;
if(g->left == p) g->left = this;
if(g->right == p) g->right = this;
g->eval();
}
};
BSTNode *splay(BSTNode *u) noexcept {
if(!u) return nullptr;
while(!(u->IsRoot())){
BSTNode *p = u->par, *gp = p->par;
if(p->IsRoot()){
u->rotate((u == p->left));
}else{
bool flag = (u == p->left);
if((u == p->left) == (p == gp->left)){
p->rotate(flag), u->rotate(flag);
}else{
u->rotate(flag), u->rotate(!flag);
}
}
}
return u;
}
BSTNode *join(BSTNode *root1, BSTNode *root2) noexcept {
if(!root1 || !root2) return root1 ? root1 : root2;
BSTNode *cur = nullptr, *nx = root1;
do{ cur = nx, nx = cur->right; }while(nx);
BSTNode *ver = splay(cur);
ver->right = root2, ver->eval(), root2->par = ver;
return ver;
}
class EulerTourTree {
public:
struct murmur_hash64 {
unsigned long long operator()(unsigned long long p) const {
const unsigned long long m = 0xc6a4a7935bd1e995; p *= m;
unsigned long long h = (p^(p>>47))*m;
return h = (h^(h>>47))*m, (h^(h>>47));
}
};
inline static unsigned long long pair_to_ll(const int u, const int v){
return ((unsigned long long)(u) << 32) | v;
}
const int V;
BSTNode** vertex_set;
UnorderedMap<unsigned long long, pair<BSTNode*, BSTNode*>, murmur_hash64> edge_set;
private:
void dfs(const int u, const int p, const BSTNode *cur,
bool *visit, vector<BSTNode*>& nodes, const vector<vector<int> >& G) noexcept {
visit[u] = true;
nodes.push_back(vertex_set[u]);
for(auto& v : G[u]){
if(!visit[v]){
BSTNode* e1 = new BSTNode(u, v, true);
nodes.push_back(e1);
dfs(v, u, cur, visit, nodes, G);
BSTNode* e2 = new BSTNode(v, u, true);
if(u < v) edge_set[pair_to_ll(u, v)] = {e1, e2};
else edge_set[pair_to_ll(v, u)] = {e2, e1};
nodes.push_back(e2);
}else if(v != p){
vertex_set[u]->adjacent.insert(v);
vertex_set[u]->subofftree_edge = true;
}
}
}
void bst_build(vector<BSTNode*>& nodes) noexcept {
int i, n = (int)nodes.size(), st = 2, isolate = ((n % 4 == 1) ? (n-1) : -1);
while(st <= n){
for(i = st-1; i < n; i += 2*st){
nodes[i]->left = nodes[i-st/2], nodes[i-st/2]->par = nodes[i];
if(i+st/2 < n) nodes[i]->right = nodes[i+st/2], nodes[i+st/2]->par = nodes[i];
else if(isolate >= 0) nodes[i]->right = nodes[isolate], nodes[isolate]->par = nodes[i];
nodes[i]->eval();
}
isolate = ((n % (4*st) >= st && (n % (4*st) < 2*st)) ? (i-2*st): isolate);
st <<= 1;
}
}
void build_forest(const vector<vector<int> >& G){
bool *visit = new bool[V]();
for(int i = 0; i < V; ++i){
if(!visit[i]){
vector<BSTNode*> nodes;
BSTNode *cur = nullptr;
dfs(i, -1, cur, visit, nodes, G);
bst_build(nodes);
}
}
}
BSTNode *reroot(BSTNode *ver) noexcept {
BSTNode *res = splay(ver)->left;
if(!res) return ver;
ver->left = nullptr, ver->eval();
while(ver->right) ver = ver->right;
splay(ver), ver->right = res, ver->eval(), res->par = ver;
return ver;
}
void link(BSTNode *ver1, BSTNode *ver2, const bool flag) noexcept {
BSTNode *e1 = new BSTNode(ver1->from, ver2->from, flag);
BSTNode *e2 = new BSTNode(ver2->from, ver1->from, flag);
edge_set[pair_to_ll(ver1->from, ver2->from)] = {e1, e2};
join(join(reroot(ver1), e1), join(reroot(ver2), e2));
}
void cut(BSTNode *edge1, BSTNode *edge2) noexcept {
splay(edge1), splay(edge2);
BSTNode *p = edge1->par;
bool _right = (edge1 == edge2->right);
if(p != edge2){
_right = (p == edge2->right);
p->par = nullptr, edge1->rotate((edge1 == p->left));
}
if(edge1->left) edge1->left->par = nullptr;
if(edge1->right) edge1->right->par = nullptr;
if(_right){
if(edge2->left) edge2->left->par = nullptr;
join(edge2->left, edge1->right);
}else{
if(edge2->right) edge2->right->par = nullptr;
join(edge1->left, edge2->right);
}
delete edge1; delete edge2;
}
bool connected(BSTNode *ver1, BSTNode *ver2) noexcept {
splay(ver1), splay(ver2);
return ver1->par;
}
int component_size(BSTNode *ver) noexcept { return splay(ver)->sz; }
public:
EulerTourTree(const int node_size) : V(node_size), vertex_set(new BSTNode*[V]){
for(int i = 0; i < V; i++) vertex_set[i] = new BSTNode(i);
}
EulerTourTree(const vector<vector<int> >& G) : V((int)G.size()), vertex_set(new BSTNode*[V]){
for(int i = 0; i < V; i++) vertex_set[i] = new BSTNode(i);
build_forest(G);
}
// ~EulerTourTree(){
// for(auto it : edge_set){
// delete (it.second).first;
// delete (it.second).second;
// }
// for(int i = 0; i < V; ++i) delete vertex_set[i];
// delete[] vertex_set;
// }
void reroot(const int node_id) noexcept { reroot(vertex_set[node_id]); }
void link(int node1_id, int node2_id, bool flag=true) noexcept {
if(node1_id > node2_id) swap(node1_id, node2_id);
link(vertex_set[node1_id], vertex_set[node2_id], flag);
}
void cut(int node1_id, int node2_id){
if(node1_id > node2_id) swap(node1_id, node2_id);
auto it = edge_set.find(pair_to_ll(node1_id, node2_id));
assert(it != edge_set.end());
BSTNode *edge1 = ((*it).second).first, *edge2 = ((*it).second).second;
edge_set.simple_erase(it);
cut(edge1, edge2);
}
bool connected(const int node1_id, const int node2_id) noexcept {
if(node1_id == node2_id) return true;
return connected(vertex_set[node1_id], vertex_set[node2_id]);
}
int component_size(const int node_id) noexcept { return component_size(vertex_set[node_id]); }
void check_dfs(const BSTNode* cur) const noexcept {
if(cur->left) check_dfs(cur->left);
cout << "{" << (cur->from) << "," << (cur->to) << "} ";
if(cur->right) check_dfs(cur->right);
}
};
class DynamicConnectivity {
private:
BSTNode *level_up_dfs(BSTNode *cur, const int layer) noexcept {
if(cur->exact_level){
splay(cur)->exact_level = false, cur->subtree_edge_eval();
detect_layer[EulerTourTree::pair_to_ll(cur->from, cur->to)]++;
et[layer+1].link(cur->from, cur->to);
return cur;
}
if(cur->left && cur->left->subtree_edge) return level_up_dfs(cur->left, layer);
if(cur->right && cur->right->subtree_edge) return level_up_dfs(cur->right, layer);
return nullptr;
}
BSTNode *search_edge_dfs
(BSTNode *cur, const int layer, const int another, bool& flag, pair<int, int>& rep_edge) noexcept {
if(!cur->adjacent.empty()){
bool state = et[layer+1].vertex_set[cur->from]->adjacent.empty();
for(auto it = cur->adjacent.begin(); it != cur->adjacent.end();){
pair<int, int> e = {min(cur->from, *it), max(cur->from, *it)};
BSTNode *correspond = et[layer].vertex_set[*it];
if(et[layer].connected(another, *it)){
flag = true, rep_edge = e;
cur->adjacent.simple_erase(it), correspond->adjacent.simple_erase(cur->from);
if(!correspond->subofftree_check()){
splay(correspond)->subofftree_edge_eval();
}
break;
}else{
if(!et[layer+1].vertex_set[*it]->subofftree_check()){
splay(et[layer+1].vertex_set[*it])->subofftree_edge = true;
}
et[layer+1].vertex_set[cur->from]->adjacent.insert(*it);
et[layer+1].vertex_set[*it]->adjacent.insert(cur->from);
detect_layer[EulerTourTree::pair_to_ll(e.first, e.second)]++;
it = cur->adjacent.erase(it);
correspond->adjacent.simple_erase(cur->from);
if(!correspond->subofftree_check()){
splay(correspond)->subofftree_edge_eval();
}
}
}
if(state && !et[layer+1].vertex_set[cur->from]->offtree_check()){
splay(et[layer+1].vertex_set[cur->from])->subofftree_edge = true;
}
splay(cur)->subofftree_edge_eval();
return cur;
}
if(cur->left && cur->left->subofftree_edge){
return search_edge_dfs(cur->left, layer, another, flag, rep_edge);
}
if(cur->right && cur->right->subofftree_edge){
return search_edge_dfs(cur->right, layer, another, flag, rep_edge);
}
return nullptr;
}
bool replace(const int from, const int to, const int layer) noexcept {
if(layer < 0) return true;
int u, v;
if(et[layer].component_size(from) <= et[layer].component_size(to)) u = from, v = to;
else u = to, v = from;
BSTNode *ver = splay(et[layer].vertex_set[u]);
while(ver->subtree_edge) ver = level_up_dfs(ver, layer);
pair<int, int> rep_edge = {-1, -1};
bool flag = false;
while(ver->subofftree_edge){
ver = search_edge_dfs(ver, layer, v, flag, rep_edge);
if(flag) break;
}
if(flag){
et[layer].link(rep_edge.first, rep_edge.second);
for(int i = 0; i < layer; i++) et[i].link(rep_edge.first, rep_edge.second, false);
return false;
}else return replace(from, to, layer-1);
}
public:
const int V;
int depth;
vector<EulerTourTree> et;
UnorderedMap<unsigned long long, int, EulerTourTree::murmur_hash64> detect_layer;
DynamicConnectivity(const int node_size) noexcept : V(node_size), depth(1){
et.emplace_back(V);
}
DynamicConnectivity(const vector<vector<int> >& G) noexcept : V((int)G.size()), depth(1){
for(int i = 0; i < V; ++i){
for(const int j : G[i]){
if(i < j) detect_layer[EulerTourTree::pair_to_ll(i, j)] = 0;
}
}
et.emplace_back(G);
}
bool link(int node1_id, int node2_id) noexcept {
if(node1_id > node2_id) swap(node1_id, node2_id);
detect_layer[EulerTourTree::pair_to_ll(node1_id, node2_id)] = 0;
if(et[0].connected(node1_id, node2_id)){
BSTNode *ver1 = et[0].vertex_set[node1_id], *ver2 = et[0].vertex_set[node2_id];
splay(ver1)->subofftree_edge = true, ver1->adjacent.insert(node2_id);
splay(ver2)->subofftree_edge = true, ver2->adjacent.insert(node1_id);
return false;
}else{
et[0].link(node1_id, node2_id);
return true;
}
}
bool cut(int node1_id, int node2_id) noexcept {
if(node1_id > node2_id) swap(node1_id, node2_id);
auto it = detect_layer.find(EulerTourTree::pair_to_ll(node1_id, node2_id));
assert(it != detect_layer.end());
int layer = (*it).second;
detect_layer.simple_erase(it);
auto& st = et[layer].vertex_set[node1_id]->adjacent;
if(st.find(node2_id) == st.end()){
for(int i = 0; i <= layer; i++) et[i].cut(node1_id, node2_id);
if(layer + 1 == depth) ++depth, et.emplace_back(V);
return replace(node1_id, node2_id, layer);
}else{
et[layer].vertex_set[node1_id]->adjacent.simple_erase(node2_id);
if(!et[layer].vertex_set[node1_id]->subofftree_check()){
splay(et[layer].vertex_set[node1_id])->subofftree_edge_eval();
}
et[layer].vertex_set[node2_id]->adjacent.simple_erase(node1_id);
if(!et[layer].vertex_set[node2_id]->subofftree_check()){
splay(et[layer].vertex_set[node2_id])->subofftree_edge_eval();
}
return false;
}
}
bool connected(const int node1_id, const int node2_id) noexcept {
return et[0].connected(node1_id, node2_id);
}
};
verify 用の問題
AOJ : Graph Construction
提出コード
(同じ問題で高速版の方は提出コード長制限に引っかかってしまいましたがテストケースをスクレイピングしてきて正答することを確認しました.)