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#include "graph/others/block-cut-tree.hpp"
#pragma once
#include "../graph-template.hpp"
#include "../connected-components/bi-connected-components.hpp"
/**
* @brief Block Cut Tree
* @see https://ei1333.hateblo.jp/entry/2020/03/25/010057
*/
template< typename T = int >
struct BlockCutTree : BiConnectedComponents< T > {
public:
using BiConnectedComponents< T >::BiConnectedComponents;
using BiConnectedComponents< T >::g;
using BiConnectedComponents< T >::articulation;
using BiConnectedComponents< T >::bc;
vector< int > rev;
vector< vector< int > > group;
Graph< T > tree;
explicit BlockCutTree(const Graph< T > &g) : Graph< T >(g) {}
int operator[](const int &k) const {
return rev[k];
}
void build() override {
BiConnectedComponents< T >::build();
rev.assign(g.size(), -1);
int ptr = (int) bc.size();
for(auto &idx : articulation) {
rev[idx] = ptr++;
}
vector< int > last(ptr, -1);
tree = Graph< T >(ptr);
for(int i = 0; i < (int) bc.size(); i++) {
for(auto &e : bc[i]) {
for(auto &ver : {e.from, e.to}) {
if(rev[ver] >= (int) bc.size()) {
if(exchange(last[rev[ver]], i) != i) {
tree.add_edge(rev[ver], i, e.cost);
}
} else {
rev[ver] = i;
}
}
}
}
group.resize(ptr);
for(int i = 0; i < (int) g.size(); i++) {
group[rev[i]].emplace_back(i);
}
}
};
#line 2 "graph/others/block-cut-tree.hpp"
#line 2 "graph/graph-template.hpp"
/**
* @brief Graph Template(グラフテンプレート)
*/
template< typename T = int >
struct Edge {
int from, to;
T cost;
int idx;
Edge() = default;
Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {}
operator int() const { return to; }
};
template< typename T = int >
struct Graph {
vector< vector< Edge< T > > > g;
int es;
Graph() = default;
explicit Graph(int n) : g(n), es(0) {}
size_t size() const {
return g.size();
}
void add_directed_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es++);
}
void add_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
void read(int M, int padding = -1, bool weighted = false, bool directed = false) {
for(int i = 0; i < M; i++) {
int a, b;
cin >> a >> b;
a += padding;
b += padding;
T c = T(1);
if(weighted) cin >> c;
if(directed) add_directed_edge(a, b, c);
else add_edge(a, b, c);
}
}
inline vector< Edge< T > > &operator[](const int &k) {
return g[k];
}
inline const vector< Edge< T > > &operator[](const int &k) const {
return g[k];
}
};
template< typename T = int >
using Edges = vector< Edge< T > >;
#line 2 "graph/others/low-link.hpp"
#line 4 "graph/others/low-link.hpp"
/**
* @brief Low Link(橋/関節点)
* @see http://kagamiz.hatenablog.com/entry/2013/10/05/005213
*
*/
template< typename T = int >
struct LowLink : Graph< T > {
public:
using Graph< T >::Graph;
vector< int > ord, low, articulation;
vector< Edge< T > > bridge;
using Graph< T >::g;
virtual void build() {
used.assign(g.size(), 0);
ord.assign(g.size(), 0);
low.assign(g.size(), 0);
int k = 0;
for(int i = 0; i < (int) g.size(); i++) {
if(!used[i]) k = dfs(i, k, -1);
}
}
explicit LowLink(const Graph< T > &g) : Graph< T >(g) {}
private:
vector< int > used;
int dfs(int idx, int k, int par) {
used[idx] = true;
ord[idx] = k++;
low[idx] = ord[idx];
bool is_articulation = false, beet = false;
int cnt = 0;
for(auto &to : g[idx]) {
if(to == par && !exchange(beet, true)) {
continue;
}
if(!used[to]) {
++cnt;
k = dfs(to, k, idx);
low[idx] = min(low[idx], low[to]);
is_articulation |= par >= 0 && low[to] >= ord[idx];
if(ord[idx] < low[to]) bridge.emplace_back(to);
} else {
low[idx] = min(low[idx], ord[to]);
}
}
is_articulation |= par == -1 && cnt > 1;
if(is_articulation) articulation.push_back(idx);
return k;
}
};
#line 3 "graph/connected-components/bi-connected-components.hpp"
template< typename T = int >
struct BiConnectedComponents : LowLink< T > {
public:
using LowLink< T >::LowLink;
using LowLink< T >::g;
using LowLink< T >::ord;
using LowLink< T >::low;
vector< vector< Edge< T > > > bc;
void build() override {
LowLink< T >::build();
used.assign(g.size(), 0);
for(int i = 0; i < (int)used.size(); i++) {
if(!used[i]) dfs(i, -1);
}
}
explicit BiConnectedComponents(const Graph< T > &g) : Graph< T >(g) {}
private:
vector< int > used;
vector< Edge< T > > tmp;
void dfs(int idx, int par) {
used[idx] = true;
bool beet = false;
for(auto &to : g[idx]) {
if(to == par && !exchange(beet, true)) continue;
if(!used[to] || ord[to] < ord[idx]) {
tmp.emplace_back(to);
}
if(!used[to]) {
dfs(to, idx);
if(low[to] >= ord[idx]) {
bc.emplace_back();
for(;;) {
auto e = tmp.back();
bc.back().emplace_back(e);
tmp.pop_back();
if(e.idx == to.idx) break;
}
}
}
}
}
};
#line 5 "graph/others/block-cut-tree.hpp"
/**
* @brief Block Cut Tree
* @see https://ei1333.hateblo.jp/entry/2020/03/25/010057
*/
template< typename T = int >
struct BlockCutTree : BiConnectedComponents< T > {
public:
using BiConnectedComponents< T >::BiConnectedComponents;
using BiConnectedComponents< T >::g;
using BiConnectedComponents< T >::articulation;
using BiConnectedComponents< T >::bc;
vector< int > rev;
vector< vector< int > > group;
Graph< T > tree;
explicit BlockCutTree(const Graph< T > &g) : Graph< T >(g) {}
int operator[](const int &k) const {
return rev[k];
}
void build() override {
BiConnectedComponents< T >::build();
rev.assign(g.size(), -1);
int ptr = (int) bc.size();
for(auto &idx : articulation) {
rev[idx] = ptr++;
}
vector< int > last(ptr, -1);
tree = Graph< T >(ptr);
for(int i = 0; i < (int) bc.size(); i++) {
for(auto &e : bc[i]) {
for(auto &ver : {e.from, e.to}) {
if(rev[ver] >= (int) bc.size()) {
if(exchange(last[rev[ver]], i) != i) {
tree.add_edge(rev[ver], i, e.cost);
}
} else {
rev[ver] = i;
}
}
}
}
group.resize(ptr);
for(int i = 0; i < (int) g.size(); i++) {
group[rev[i]].emplace_back(i);
}
}
};