cplib

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:heavy_check_mark: tree/hld.cpp

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#pragma once

#include "template.cpp"
#include "graph/graph.cpp"

class HLD {
 private:
  VI index, sz, par, rev;
  // last vertex in ascending heavy path
  VI nxt;

 public:
  HLD(Graph& graph)
      : index(graph.size()), sz(graph.size(), 1),
        par(graph.size(), -1), rev(graph.size()), nxt(graph.size()) {
    dfs_sz(graph, 0);
    dfs_hld(graph, 0);
  }

 private:
  void dfs_sz(Graph& graph, int v) {
    if (graph[v].size() >= 2 and graph[v][0] == par[v])
      swap(graph[v][0], graph[v][1]);
    for (auto& c : graph[v])
      if (c != par[v]) {
        par[c] = v;
        dfs_sz(graph, c);
        sz[v] += sz[c];
        if (sz[c] > sz[graph[v][0]]) swap(c, graph[v][0]);
      }
  }

  void dfs_hld(const Graph& graph, int v) {
    static int t = 0;
    index[v] = t++;
    rev[index[v]] = v;
    for (auto c : graph[v])
      if (c != par[v]) {
        nxt[c] = (c.to == graph[v][0].to ? nxt[v] : c.to);
        dfs_hld(graph, c);
      }
    assert(sz[v] == t - index[v]);
  }

 public:
  template <typename F>
  void path_vertex(int u, int v, F f) {
    while (true) {
      if (index[u] > index[v]) swap(u, v);
      // debug(u); debug(v);
      // debug(nxt[u]); debug(index[u]);
      f(max(index[nxt[v]], index[u]), index[v] + 1);
      if (nxt[u] != nxt[v])
        v = par[nxt[v]];
      else
        break;
    }
  }

  template <typename F>
  void path_edge(int u, int v, F f) {
    while (true) {
      if (index[u] > index[v]) swap(u, v);
      if (nxt[u] != nxt[v]) {
        f(index[nxt[v]], index[v] + 1);
        v = par[nxt[v]];
      } else {
        if (u != v) f(index[u] + 1, index[v] + 1);
        break;
      }
    }
  }

  template <typename F>
  void subtree_vertex(int v, F f) {
    f(index[v], index[v] + sz[v]);
  }

  template <typename F>
  void subtree_edge(int v, F f) {
    f(index[v] + 1, index[v] + sz[v]);
  }

  int lca(int u, int v) {
    while (1) {
      if (index[u] > index[v]) swap(u, v);
      if (nxt[u] == nxt[v]) return u;
      v = par[nxt[v]];
    }
  }

  int subtree_size(int v) { return sz[v]; }

  int vertex(int v) { return index[v]; }

  int parent(int v) { return par[v]; }

  int restore(int ix) { return rev[ix]; }
};
#line 2 "tree/hld.cpp"

#line 2 "template.cpp"

#ifndef LOCAL
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx")
#endif
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using VI = vector<int>;
using VVI = vector<vector<int>>;
using VLL = vector<ll>;
using VVLL = vector<vector<ll>>;
using VB = vector<bool>;
using PII = pair<int, int>;
using PLL = pair<ll, ll>;
constexpr int INF = 1000000007;
constexpr ll INF_LL = 1'000'000'000'000'000'007;
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define newl '\n'

// loops rep(until) / rep(var, until) / rep(var, from, until) / repr (reversed order)
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define rep(...) OVERLOAD3(__VA_ARGS__, REPEAT_FROM_UNTIL, REPEAT_UNTIL, REPEAT)(__VA_ARGS__)
#define REPEAT(times) REPEAT_CNT(_repeat, __COUNTER__, times)
#define REPEAT_CNT(_repeat, cnt, times) REPEAT_CNT_CAT(_repeat, cnt, times)
#define REPEAT_CNT_CAT(_repeat, cnt, times) REPEAT_FROM_UNTIL(_repeat ## cnt, 0, times)
#define REPEAT_UNTIL(name, times) REPEAT_FROM_UNTIL(name, 0, times)
#define REPEAT_FROM_UNTIL(name, from, until) for (int name = from, name ## __until = (until); name < name ## __until; name++)
#define repr(...) OVERLOAD3(__VA_ARGS__, REPR_FROM_UNTIL, REPR_UNTIL, REPEAT)(__VA_ARGS__)
#define REPR_UNTIL(name, times) REPR_FROM_UNTIL(name, 0, times)
#define REPR_FROM_UNTIL(name, from, until) for (int name = (until)-1, name ## __from = (from); name >= name ## __from; name--)

template <typename T, typename U>
bool chmin(T& var, U x) { if (var > x) { var = x; return true; } else return false; }
template <typename T, typename U>
bool chmax(T& var, U x) { if (var < x) { var = x; return true; } else return false; }
ll power(ll e, ll t, ll mod = INF_LL) {
  ll res = 1; for (; t; t >>= 1, (e *= e) %= mod) if (t & 1) (res *= e) %= mod; return res;
}
ll choose(ll n, int r) {
  chmin(r, n-r); if (r < 0) return 0; ll res = 1; rep(i, r) res *= n-i, res /= i+1; return res;
}
template <typename T, typename U> T divceil(T m, U d) { return (m + d - 1) / d; }
template <typename T> vector<T> make_v(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}

// debugging stuff
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wmisleading-indentation"
#define repi(it, ds) for (auto it = ds.begin(); it != ds.end(); it++)
class DebugPrint { public: template <typename T> DebugPrint& operator <<(const T& v) {
#ifdef LOCAL
    cerr << v;
#endif
return *this; } } debugos; template <typename T> DebugPrint& operator<<(DebugPrint& os, const
vector<T>& vec) { os << "{"; for (int i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 ==
vec.size() ? "" : ", "); os << "}"; return os; } template <typename T, typename U> DebugPrint&
operator<<(DebugPrint& os, const map<T, U>& map_var) { os << "{"; repi(itr, map_var) { os << *
itr; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } template <
typename T> DebugPrint& operator<<(DebugPrint& os, const set<T>& set_var) { os << "{"; repi(
itr, set_var) { os << *itr; itr++; if (itr != set_var.end()) os << ", "; itr--; } os << "}";
return os; } template <typename T, typename U> DebugPrint& operator<<(DebugPrint& os, const
pair<T, U>& p) { os << "(" << p.first << ", " << p.second << ")"; return os; } void dump_func(
) { debugos << newl; } template <class Head, class... Tail> void dump_func(Head &&head, Tail
&&... tail) { debugos << head; if (sizeof...(Tail) > 0) { debugos << ", "; } dump_func(forward
<Tail>(tail)...); }
#ifdef LOCAL
#define dump(...) debugos << "  " << string(#__VA_ARGS__) << ": " << "[" << to_string(__LINE__) \
<< ":" << __FUNCTION__ << "]" << newl << "    ", dump_func(__VA_ARGS__)
#else
#define dump(...) ({})
#endif
#pragma GCC diagnostic pop


#line 2 "graph/graph.cpp"

#line 4 "graph/graph.cpp"

struct Edge {
  int to; ll cost;
  Edge(int _to) : to(_to), cost(1) {}
  Edge(int _to, ll _cost) : to(_to), cost(_cost) {}
  operator int() const { return to; }
};

using Graph = vector<vector<Edge>>;
#line 5 "tree/hld.cpp"

class HLD {
 private:
  VI index, sz, par, rev;
  // last vertex in ascending heavy path
  VI nxt;

 public:
  HLD(Graph& graph)
      : index(graph.size()), sz(graph.size(), 1),
        par(graph.size(), -1), rev(graph.size()), nxt(graph.size()) {
    dfs_sz(graph, 0);
    dfs_hld(graph, 0);
  }

 private:
  void dfs_sz(Graph& graph, int v) {
    if (graph[v].size() >= 2 and graph[v][0] == par[v])
      swap(graph[v][0], graph[v][1]);
    for (auto& c : graph[v])
      if (c != par[v]) {
        par[c] = v;
        dfs_sz(graph, c);
        sz[v] += sz[c];
        if (sz[c] > sz[graph[v][0]]) swap(c, graph[v][0]);
      }
  }

  void dfs_hld(const Graph& graph, int v) {
    static int t = 0;
    index[v] = t++;
    rev[index[v]] = v;
    for (auto c : graph[v])
      if (c != par[v]) {
        nxt[c] = (c.to == graph[v][0].to ? nxt[v] : c.to);
        dfs_hld(graph, c);
      }
    assert(sz[v] == t - index[v]);
  }

 public:
  template <typename F>
  void path_vertex(int u, int v, F f) {
    while (true) {
      if (index[u] > index[v]) swap(u, v);
      // debug(u); debug(v);
      // debug(nxt[u]); debug(index[u]);
      f(max(index[nxt[v]], index[u]), index[v] + 1);
      if (nxt[u] != nxt[v])
        v = par[nxt[v]];
      else
        break;
    }
  }

  template <typename F>
  void path_edge(int u, int v, F f) {
    while (true) {
      if (index[u] > index[v]) swap(u, v);
      if (nxt[u] != nxt[v]) {
        f(index[nxt[v]], index[v] + 1);
        v = par[nxt[v]];
      } else {
        if (u != v) f(index[u] + 1, index[v] + 1);
        break;
      }
    }
  }

  template <typename F>
  void subtree_vertex(int v, F f) {
    f(index[v], index[v] + sz[v]);
  }

  template <typename F>
  void subtree_edge(int v, F f) {
    f(index[v] + 1, index[v] + sz[v]);
  }

  int lca(int u, int v) {
    while (1) {
      if (index[u] > index[v]) swap(u, v);
      if (nxt[u] == nxt[v]) return u;
      v = par[nxt[v]];
    }
  }

  int subtree_size(int v) { return sz[v]; }

  int vertex(int v) { return index[v]; }

  int parent(int v) { return par[v]; }

  int restore(int ix) { return rev[ix]; }
};
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