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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;
}
};