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#include "graph/tree/heavy-light-decomposition.hpp"
#pragma once
#include "../graph-template.hpp"
/**
* @brief Heavy-Light-Decomposition(HL分解)
* @see https://smijake3.hatenablog.com/entry/2019/09/15/200200
*/
template <typename T = int>
struct HeavyLightDecomposition : Graph<T> {
public:
using Graph<T>::Graph;
using Graph<T>::g;
vector<int> sz, in, out, head, rev, par, dep;
void build() {
sz.assign(g.size(), 0);
in.assign(g.size(), 0);
out.assign(g.size(), 0);
head.assign(g.size(), 0);
rev.assign(g.size(), 0);
par.assign(g.size(), 0);
dep.assign(g.size(), 0);
dfs_sz(0, -1, 0);
int t = 0;
dfs_hld(0, -1, t);
}
/* k: 0-indexed */
int la(int v, int k) {
while (1) {
int u = head[v];
if (in[v] - k >= in[u]) return rev[in[v] - k];
k -= in[v] - in[u] + 1;
v = par[u];
}
}
int lca(int u, int v) const {
for (;; v = par[head[v]]) {
if (in[u] > in[v]) swap(u, v);
if (head[u] == head[v]) return u;
}
}
int dist(int u, int v) const { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; }
template <typename E, typename Q, typename F, typename S>
E query(int u, int v, const E &ti, const Q &q, const F &f, const S &s,
bool edge = false) {
E l = ti, r = ti;
for (;; v = par[head[v]]) {
if (in[u] > in[v]) swap(u, v), swap(l, r);
if (head[u] == head[v]) break;
l = f(q(in[head[v]], in[v] + 1), l);
}
return s(f(q(in[u] + edge, in[v] + 1), l), r);
}
template <typename E, typename Q, typename F>
E query(int u, int v, const E &ti, const Q &q, const F &f,
bool edge = false) {
return query(u, v, ti, q, f, f, edge);
}
template <typename Q>
void add(int u, int v, const Q &q, bool edge = false) {
for (;; v = par[head[v]]) {
if (in[u] > in[v]) swap(u, v);
if (head[u] == head[v]) break;
q(in[head[v]], in[v] + 1);
}
q(in[u] + edge, in[v] + 1);
}
/* {parent, child} */
vector<pair<int, int> > compress(vector<int> &remark) {
auto cmp = [&](int a, int b) { return in[a] < in[b]; };
sort(begin(remark), end(remark), cmp);
remark.erase(unique(begin(remark), end(remark)), end(remark));
int K = (int)remark.size();
for (int k = 1; k < K; k++)
remark.emplace_back(lca(remark[k - 1], remark[k]));
sort(begin(remark), end(remark), cmp);
remark.erase(unique(begin(remark), end(remark)), end(remark));
vector<pair<int, int> > es;
stack<int> st;
for (auto &k : remark) {
while (!st.empty() && out[st.top()] <= in[k]) st.pop();
if (!st.empty()) es.emplace_back(st.top(), k);
st.emplace(k);
}
return es;
}
explicit HeavyLightDecomposition(const Graph<T> &g) : Graph<T>(g) {}
private:
void dfs_sz(int idx, int p, int d) {
dep[idx] = d;
par[idx] = p;
sz[idx] = 1;
if (g[idx].size() && g[idx][0] == p) swap(g[idx][0], g[idx].back());
for (auto &to : g[idx]) {
if (to == p) continue;
dfs_sz(to, idx, d + 1);
sz[idx] += sz[to];
if (sz[g[idx][0]] < sz[to]) swap(g[idx][0], to);
}
}
void dfs_hld(int idx, int p, int ×) {
in[idx] = times++;
rev[in[idx]] = idx;
for (auto &to : g[idx]) {
if (to == p) continue;
head[to] = (g[idx][0] == to ? head[idx] : to);
dfs_hld(to, idx, times);
}
out[idx] = times;
}
};
#line 2 "graph/tree/heavy-light-decomposition.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 4 "graph/tree/heavy-light-decomposition.hpp"
/**
* @brief Heavy-Light-Decomposition(HL分解)
* @see https://smijake3.hatenablog.com/entry/2019/09/15/200200
*/
template <typename T = int>
struct HeavyLightDecomposition : Graph<T> {
public:
using Graph<T>::Graph;
using Graph<T>::g;
vector<int> sz, in, out, head, rev, par, dep;
void build() {
sz.assign(g.size(), 0);
in.assign(g.size(), 0);
out.assign(g.size(), 0);
head.assign(g.size(), 0);
rev.assign(g.size(), 0);
par.assign(g.size(), 0);
dep.assign(g.size(), 0);
dfs_sz(0, -1, 0);
int t = 0;
dfs_hld(0, -1, t);
}
/* k: 0-indexed */
int la(int v, int k) {
while (1) {
int u = head[v];
if (in[v] - k >= in[u]) return rev[in[v] - k];
k -= in[v] - in[u] + 1;
v = par[u];
}
}
int lca(int u, int v) const {
for (;; v = par[head[v]]) {
if (in[u] > in[v]) swap(u, v);
if (head[u] == head[v]) return u;
}
}
int dist(int u, int v) const { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; }
template <typename E, typename Q, typename F, typename S>
E query(int u, int v, const E &ti, const Q &q, const F &f, const S &s,
bool edge = false) {
E l = ti, r = ti;
for (;; v = par[head[v]]) {
if (in[u] > in[v]) swap(u, v), swap(l, r);
if (head[u] == head[v]) break;
l = f(q(in[head[v]], in[v] + 1), l);
}
return s(f(q(in[u] + edge, in[v] + 1), l), r);
}
template <typename E, typename Q, typename F>
E query(int u, int v, const E &ti, const Q &q, const F &f,
bool edge = false) {
return query(u, v, ti, q, f, f, edge);
}
template <typename Q>
void add(int u, int v, const Q &q, bool edge = false) {
for (;; v = par[head[v]]) {
if (in[u] > in[v]) swap(u, v);
if (head[u] == head[v]) break;
q(in[head[v]], in[v] + 1);
}
q(in[u] + edge, in[v] + 1);
}
/* {parent, child} */
vector<pair<int, int> > compress(vector<int> &remark) {
auto cmp = [&](int a, int b) { return in[a] < in[b]; };
sort(begin(remark), end(remark), cmp);
remark.erase(unique(begin(remark), end(remark)), end(remark));
int K = (int)remark.size();
for (int k = 1; k < K; k++)
remark.emplace_back(lca(remark[k - 1], remark[k]));
sort(begin(remark), end(remark), cmp);
remark.erase(unique(begin(remark), end(remark)), end(remark));
vector<pair<int, int> > es;
stack<int> st;
for (auto &k : remark) {
while (!st.empty() && out[st.top()] <= in[k]) st.pop();
if (!st.empty()) es.emplace_back(st.top(), k);
st.emplace(k);
}
return es;
}
explicit HeavyLightDecomposition(const Graph<T> &g) : Graph<T>(g) {}
private:
void dfs_sz(int idx, int p, int d) {
dep[idx] = d;
par[idx] = p;
sz[idx] = 1;
if (g[idx].size() && g[idx][0] == p) swap(g[idx][0], g[idx].back());
for (auto &to : g[idx]) {
if (to == p) continue;
dfs_sz(to, idx, d + 1);
sz[idx] += sz[to];
if (sz[g[idx][0]] < sz[to]) swap(g[idx][0], to);
}
}
void dfs_hld(int idx, int p, int ×) {
in[idx] = times++;
rev[in[idx]] = idx;
for (auto &to : g[idx]) {
if (to == p) continue;
head[to] = (g[idx][0] == to ? head[idx] : to);
dfs_hld(to, idx, times);
}
out[idx] = times;
}
};