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#include "graph/centroid_decomposition_old.hpp"
#include "graph/base.hpp"
#include "graph/find_centroid.hpp"
template <typename GT>
struct Centroid_Decomposition {
using edge_type = typename GT::edge_type;
GT& G;
int N;
vc<int> sz;
vc<int> par;
vector<int> cdep; // depth in centroid tree
bool calculated;
Centroid_Decomposition(GT& G)
: G(G), N(G.N), sz(G.N), par(G.N), cdep(G.N, -1) {
calculated = 0;
build();
}
private:
int find(int v) {
vc<int> V = {v};
par[v] = -1;
int p = 0;
while (p < len(V)) {
int v = V[p++];
sz[v] = 0;
for (auto&& e: G[v]) {
if (e.to == par[v] || cdep[e.to] != -1) continue;
par[e.to] = v;
V.eb(e.to);
}
}
while (len(V)) {
int v = V.back();
V.pop_back();
sz[v] += 1;
if (p - sz[v] <= p / 2) return v;
sz[par[v]] += sz[v];
}
return -1;
}
void build() {
assert(G.is_prepared());
assert(!calculated);
calculated = 1;
vc<pair<int, int>> st;
st.eb(0, 0);
while (!st.empty()) {
auto [lv, v] = st.back();
st.pop_back();
auto c = find(v);
cdep[c] = lv;
for (auto&& e: G[c]) {
if (cdep[e.to] == -1) { st.eb(lv + 1, e.to); }
}
}
}
public:
// V, dat, indptr
template <typename T, typename F>
tuple<vc<int>, vc<T>, vc<int>> collect_path_data(int root, T root_val, F f) {
vc<int> V = {root};
vc<T> dp = {root_val};
vc<int> indptr = {0, 1};
for (auto&& e: G[root]) {
int nxt = e.to;
if (cdep[nxt] < cdep[root]) continue;
int p = len(V);
V.eb(nxt);
dp.eb(f(root_val, e));
par[nxt] = root;
while (p < len(V)) {
int v = V[p];
T val = dp[p];
p++;
for (auto&& e: G[v]) {
if (e.to == par[v]) continue;
if (cdep[e.to] < cdep[root]) continue;
par[e.to] = v;
V.eb(e.to);
dp.eb(f(val, e));
}
}
indptr.eb(len(V));
}
return {V, dp, indptr};
}
// V, dist, indptr
tuple<vc<int>, vc<int>, vc<int>> collect_dist(int root) {
auto f = [&](int x, auto e) -> int { return x + 1; };
return collect_path_data(root, 0, f);
}
// (V, H, indptr), (V[i] in G) = (i in H).
// 0,1,2... is a dfs order in H.
tuple<vc<int>, Graph<typename GT::cost_type, true>, vc<int>> get_subgraph(
int root) {
static vc<int> conv;
while (len(conv) < N) conv.eb(-1);
vc<int> V = {root};
vc<int> indptr = {0, 1};
conv[root] = 0;
using cost_type = typename GT::cost_type;
vc<tuple<int, int, cost_type>> edges;
auto dfs = [&](auto& dfs, int v, int p) -> void {
conv[v] = len(V);
V.eb(v);
for (auto&& e: G[v]) {
int to = e.to;
if (to == p) continue;
if (cdep[to] < cdep[root]) continue;
dfs(dfs, to, v);
edges.eb(conv[v], conv[to], e.cost);
}
};
for (auto&& e: G[root]) {
if (cdep[e.to] < cdep[root]) continue;
dfs(dfs, e.to, root);
edges.eb(conv[root], conv[e.to], e.cost);
indptr.eb(len(V));
}
int n = len(V);
Graph<typename GT::cost_type, true> H(n);
for (auto&& [a, b, c]: edges) H.add(a, b, c);
H.build();
for (auto&& v: V) conv[v] = -1;
return {V, H, indptr};
}
};
#line 2 "graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
static constexpr bool is_directed = directed;
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
vc<int> vc_deg, vc_indeg, vc_outdeg;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() { return prepared; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void build(int n) {
N = n, M = 0;
prepared = 0;
edges.clear();
indptr.clear();
csr_edges.clear();
vc_deg.clear();
vc_indeg.clear();
vc_outdeg.clear();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
#ifdef FASTIO
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
#endif
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
}
#endif
vc<int> new_idx;
vc<bool> used_e;
// G における頂点 V[i] が、新しいグラフで i になるようにする
// {G, es}
// sum(deg(v)) の計算量になっていて、
// 新しいグラフの n+m より大きい可能性があるので注意
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
int n = len(V);
FOR(i, n) new_idx[V[i]] = i;
Graph<T, directed> G(n);
vc<int> history;
FOR(i, n) {
for (auto&& e: (*this)[V[i]]) {
if (len(used_e) <= e.id) used_e.resize(e.id + 1);
if (used_e[e.id]) continue;
int a = e.frm, b = e.to;
if (new_idx[a] != -1 && new_idx[b] != -1) {
history.eb(e.id);
used_e[e.id] = 1;
int eid = (keep_eid ? e.id : -1);
G.add(new_idx[a], new_idx[b], e.cost, eid);
}
}
}
FOR(i, n) new_idx[V[i]] = -1;
for (auto&& eid: history) used_e[eid] = 0;
G.build();
return G;
}
Graph<T, true> to_directed_tree(int root = -1) {
if (root == -1) root = 0;
assert(!is_directed && prepared && M == N - 1);
Graph<T, true> G1(N);
vc<int> par(N, -1);
auto dfs = [&](auto& dfs, int v) -> void {
for (auto& e: (*this)[v]) {
if (e.to == par[v]) continue;
par[e.to] = v, dfs(dfs, e.to);
}
};
dfs(dfs, root);
for (auto& e: edges) {
int a = e.frm, b = e.to;
if (par[a] == b) swap(a, b);
assert(par[b] == a);
G1.add(a, b, e.cost);
}
G1.build();
return G1;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
}
};
#line 2 "graph/find_centroid.hpp"
// (v,w) or (v,-1)
template <typename GT>
pair<int, int> find_centroids(GT& G) {
int N = G.N;
vc<int> par(N, -1);
vc<int> V(N);
vc<int> sz(N);
int l = 0, r = 0;
V[r++] = 0;
while (l < r) {
int v = V[l++];
for (auto&& e: G[v])
if (e.to != par[v]) {
par[e.to] = v;
V[r++] = e.to;
}
}
FOR_R(i, N) {
int v = V[i];
sz[v] += 1;
int p = par[v];
if (p != -1) sz[p] += sz[v];
}
int M = N / 2;
auto check = [&](int v) -> bool {
if (N - sz[v] > M) return false;
for (auto&& e: G[v]) {
if (e.to != par[v] && sz[e.to] > M) return false;
}
return true;
};
pair<int, int> ANS = {-1, -1};
FOR(v, N) if (check(v)) {
if (ANS.fi != -1) {
ANS.se = v;
} else {
ANS.fi = v;
}
}
return ANS;
}
#line 3 "graph/centroid_decomposition_old.hpp"
template <typename GT>
struct Centroid_Decomposition {
using edge_type = typename GT::edge_type;
GT& G;
int N;
vc<int> sz;
vc<int> par;
vector<int> cdep; // depth in centroid tree
bool calculated;
Centroid_Decomposition(GT& G)
: G(G), N(G.N), sz(G.N), par(G.N), cdep(G.N, -1) {
calculated = 0;
build();
}
private:
int find(int v) {
vc<int> V = {v};
par[v] = -1;
int p = 0;
while (p < len(V)) {
int v = V[p++];
sz[v] = 0;
for (auto&& e: G[v]) {
if (e.to == par[v] || cdep[e.to] != -1) continue;
par[e.to] = v;
V.eb(e.to);
}
}
while (len(V)) {
int v = V.back();
V.pop_back();
sz[v] += 1;
if (p - sz[v] <= p / 2) return v;
sz[par[v]] += sz[v];
}
return -1;
}
void build() {
assert(G.is_prepared());
assert(!calculated);
calculated = 1;
vc<pair<int, int>> st;
st.eb(0, 0);
while (!st.empty()) {
auto [lv, v] = st.back();
st.pop_back();
auto c = find(v);
cdep[c] = lv;
for (auto&& e: G[c]) {
if (cdep[e.to] == -1) { st.eb(lv + 1, e.to); }
}
}
}
public:
// V, dat, indptr
template <typename T, typename F>
tuple<vc<int>, vc<T>, vc<int>> collect_path_data(int root, T root_val, F f) {
vc<int> V = {root};
vc<T> dp = {root_val};
vc<int> indptr = {0, 1};
for (auto&& e: G[root]) {
int nxt = e.to;
if (cdep[nxt] < cdep[root]) continue;
int p = len(V);
V.eb(nxt);
dp.eb(f(root_val, e));
par[nxt] = root;
while (p < len(V)) {
int v = V[p];
T val = dp[p];
p++;
for (auto&& e: G[v]) {
if (e.to == par[v]) continue;
if (cdep[e.to] < cdep[root]) continue;
par[e.to] = v;
V.eb(e.to);
dp.eb(f(val, e));
}
}
indptr.eb(len(V));
}
return {V, dp, indptr};
}
// V, dist, indptr
tuple<vc<int>, vc<int>, vc<int>> collect_dist(int root) {
auto f = [&](int x, auto e) -> int { return x + 1; };
return collect_path_data(root, 0, f);
}
// (V, H, indptr), (V[i] in G) = (i in H).
// 0,1,2... is a dfs order in H.
tuple<vc<int>, Graph<typename GT::cost_type, true>, vc<int>> get_subgraph(
int root) {
static vc<int> conv;
while (len(conv) < N) conv.eb(-1);
vc<int> V = {root};
vc<int> indptr = {0, 1};
conv[root] = 0;
using cost_type = typename GT::cost_type;
vc<tuple<int, int, cost_type>> edges;
auto dfs = [&](auto& dfs, int v, int p) -> void {
conv[v] = len(V);
V.eb(v);
for (auto&& e: G[v]) {
int to = e.to;
if (to == p) continue;
if (cdep[to] < cdep[root]) continue;
dfs(dfs, to, v);
edges.eb(conv[v], conv[to], e.cost);
}
};
for (auto&& e: G[root]) {
if (cdep[e.to] < cdep[root]) continue;
dfs(dfs, e.to, root);
edges.eb(conv[root], conv[e.to], e.cost);
indptr.eb(len(V));
}
int n = len(V);
Graph<typename GT::cost_type, true> H(n);
for (auto&& [a, b, c]: edges) H.add(a, b, c);
H.build();
for (auto&& v: V) conv[v] = -1;
return {V, H, indptr};
}
};