Tifa's CP Library

:warning: virtual_tree (src/code/tree/virtual_tree.hpp)

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Code

#ifndef TIFALIBS_TREE_VIRTUAL_TREE
#define TIFALIBS_TREE_VIRTUAL_TREE

#include "lca_hld.hpp"
#include "tree.hpp"

namespace tifa_libs::graph {

class virtual_tree {
  tree& tr;
  lca_hld lca_;
  vecu st;

  constexpr void insert(u32 x) {
    u32 lca = lca_(x, st.back());
    if (lca == st.back()) {
      st.push_back(x);
      return;
    }
    while (st.size() > 1 && lca_.info.dep[st[st.size() - 2]] >= lca_.info.dep[lca]) vt.add_arc(st[st.size() - 2], st.back()), st.pop_back();
    if (lca_.info.dep[st.back()] > lca_.info.dep[lca]) vt.add_arc(lca, st.back()), st.pop_back();
    if (st.back() != lca) st.push_back(lca);
    st.push_back(x);
  }

 public:
  tree vt;

  explicit constexpr virtual_tree(tree& tr) : tr(tr), lca_(tr), vt((u32)tr.g.size()) {}

  constexpr void build(vecu& a) {
    std::ranges::sort(a, [&](u32 a, u32 b) { return lca_.info.dfn[a] < lca_.info.dfn[b]; });
    vt.g.clear();
    st.push_back(tr.root);
    for (u32 x : a) insert(x);
    while (st.size() > 1) vt.add_arc(st[st.size() - 2], st.back()), st.pop_back();
    st.pop_back();
  }
};

}  // namespace tifa_libs::graph

#endif
#line 1 "src/code/tree/virtual_tree.hpp"



#line 1 "src/code/tree/lca_hld.hpp"



#line 1 "src/code/tree/dfs_info.hpp"



#line 1 "src/code/graph/dfs.hpp"



#line 1 "src/code/graph/alist.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


#line 5 "src/code/graph/alist.hpp"

namespace tifa_libs::graph {

template <bool with_deg = false>
struct alist {
  using weight_type = u32;
  using value_type = vvecu;
  value_type g;
  u32 cnt_arc;
  vecu deg_in;

  //! vertex ID: [0, n)
  explicit constexpr alist(u32 n = 0) : g(n), cnt_arc(0), deg_in(0) {
    if constexpr (with_deg) deg_in.resize(n);
  }

  constexpr void add_arc(u32 u, u32 v) {
    g[u].push_back(v), ++cnt_arc;
    if constexpr (with_deg) ++deg_in[v];
  }
};
template <class G>
concept is_alist = (std::is_base_of_v<alist<true>, G> || std::is_base_of_v<alist<false>, G>);

}  // namespace tifa_libs::graph


#line 5 "src/code/graph/dfs.hpp"

namespace tifa_libs::graph {
namespace dfs_impl_ {
template <class G, class Fb, class Fp, class Fs, class Fr>
constexpr void dfs_(G const& fg, u32 u, u32 fa, Fb&& init, Fp&& pre_dfs, Fs&& post_dfs, Fr&& before_return) {
  init(u, fa);
  for (auto v : fg.g[u])
    if constexpr (is_alist<G>) {
      if (v != fa) {
        pre_dfs(v, u);
        dfs_(fg, v, u, std::forward<Fb>(init), std::forward<Fp>(pre_dfs), std::forward<Fs>(post_dfs), std::forward<Fr>(before_return));
        post_dfs(v, u);
      }
    } else {
      if (v.first != fa) {
        pre_dfs(v.first, u, v.second);
        dfs_(fg, v.first, u, std::forward<Fb>(init), std::forward<Fp>(pre_dfs), std::forward<Fs>(post_dfs), std::forward<Fr>(before_return));
        post_dfs(v.first, u, v.second);
      }
    }
  before_return(u, fa);
}
}  // namespace dfs_impl_

template <class G, class Fb, class Fp, class Fs, class Fr>
constexpr void dfs(G const& fg, u32 start, Fb&& init, Fp&& pre_dfs, Fs&& post_dfs, Fr&& before_return) { dfs_impl_::dfs_(fg, start, -1_u32, std::forward<Fb>(init), std::forward<Fp>(pre_dfs), std::forward<Fs>(post_dfs), std::forward<Fr>(before_return)); }

}  // namespace tifa_libs::graph


#line 5 "src/code/tree/dfs_info.hpp"

namespace tifa_libs::graph {

enum tree_dfs_info_mask {
  td_dfn = 1,
  td_sz = 2,
  td_fa = 4,
  td_dep = 8,
  td_maxson = 16,
  td_maxdfn = 32,
  td_euler = 64,
  td_go = 128,
  td_dis = 256
};

template <class G>
struct tree_dfs_info {
  using weight_type = typename G::weight_type;

  vecu dfn, sz, fa, dep, maxson, maxdfn, euler;
  vvecu go;
  vec<weight_type> dis;

  template <int state>
  constexpr tree_dfs_info& reset_dfs_info(G const& tree) {
    u32 n = (u32)tree.g.size();
    if constexpr (state & td_dfn) dfn = vecu(n);
    if constexpr (state & (td_sz | td_maxson)) sz = vecu(n);
    if constexpr (state & td_fa) fa = vecu(n);
    if constexpr (state & td_dep) dep = vecu(n);
    if constexpr (state & td_maxson) maxson = vecu(n, n);
    if constexpr (state & td_maxdfn) maxdfn = vecu(n);
    if constexpr (state & td_euler) euler = vecu(n);
    if constexpr (state & td_go) go = vvecu(n, vecu(21u, n));
    if constexpr (state & td_dis) dis = vec<weight_type>(n);

    u32 cnt = 0;
    dfs(
        tree, tree.root,
        [&](u32 u, u32 f) {
          if constexpr (state & td_dfn) dfn[u] = cnt;
          if constexpr (state & td_euler) euler[cnt] = u;
          if constexpr (state & (td_dfn | td_maxdfn | td_euler)) ++cnt;
          if constexpr (state & (td_sz | td_maxson)) sz[u] = 1;
          if constexpr (state & td_fa) fa[u] = f;
          if constexpr (state & td_go) {
            go[u][0] = f;
            for (u32 i = 1; i <= 20u && go[u][i - 1] < n; i++) go[u][i] = go[go[u][i - 1]][i - 1];
          }
        },
        [&](u32 to, u32 u, weight_type const& w = 1) {
          if constexpr (state & td_dep) dep[to] = dep[u] + 1;
          if constexpr (state & td_dis) dis[to] = dis[u] + w;
        },
        [&](u32 to, u32 u, weight_type const& = 1) {
          if constexpr (state & (td_sz | td_maxson)) sz[u] += sz[to];
          if constexpr (state & td_maxson)
            if (maxson[u] == n || sz[to] > sz[maxson[u]]) maxson[u] = to;
        },
        [&](u32 u, u32) {
          if constexpr (state & td_maxdfn) maxdfn[u] = cnt - 1;
        });
    return *this;
  }
};

}  // namespace tifa_libs::graph


#line 1 "src/code/tree/tree.hpp"



#line 5 "src/code/tree/tree.hpp"

namespace tifa_libs::graph {

struct tree : alist<false> {
  u32 root;

  explicit constexpr tree(u32 n, u32 root = 0) : alist(n), root(root) {}
};

}  // namespace tifa_libs::graph


#line 1 "src/code/tree/tree_top.hpp"



#line 5 "src/code/tree/tree_top.hpp"

namespace tifa_libs::graph {

template <class G, bool need_dfn = false>
constexpr vecu tree_top(G const &tr, tree_dfs_info<G> &info) {
  u32 n = (u32)tr.g.size();
  if (info.maxson.empty()) info.template reset_dfs_info<td_maxson>(tr);
  if constexpr (need_dfn) info.dfn = vecu(n);

  vecu top(n, n);
  u32 cnt = 0;
  auto dfs = [&](auto &&dfs, u32 u, u32 top_) -> void {
    if constexpr (need_dfn) info.dfn[u] = cnt++;
    top[u] = top_;
    if (info.maxson[u] == tr.g.size()) return;
    dfs(dfs, info.maxson[u], top_);
    for (auto v : tr.g[u])
      if constexpr (is_alist<G>) {
        if (top[v] == tr.g.size()) dfs(dfs, v, v);
      } else {
        if (top[v.first] == tr.g.size()) dfs(dfs, v.first, v.first);
      }
  };

  dfs(dfs, tr.root, tr.root);
  return top;
}

}  // namespace tifa_libs::graph


#line 7 "src/code/tree/lca_hld.hpp"

namespace tifa_libs::graph {

struct lca_hld {
  tree_dfs_info<tree> info;
  vecu top;

  constexpr lca_hld(tree& tr) {
    info.template reset_dfs_info<td_dep | td_fa>(tr);
    top = tree_top(tr, info);
  }

  constexpr u32 operator()(u32 u, u32 v) const {
    while (top[u] != top[v]) info.dep[top[u]] < info.dep[top[v]] ? v = info.fa[top[v]] : u = info.fa[top[u]];
    return info.dep[u] > info.dep[v] ? v : u;
  }
  constexpr ptt<vecpt<u32>> getchain(u32 u, u32 v) {
    u32 lca = (*this)(u, v);
    vecpt<u32> retu, retv;
    while (top[u] != top[lca]) {
      retu.emplace_back(u, top[u]), u = info.fa[top[u]];
    }
    retu.emplace_back(u, lca);
    while (top[v] != top[lca]) {
      retv.emplace_back(top[v], v), v = info.fa[top[v]];
    }
    if (v != lca) retv.emplace_back(info.maxson[lca], v);
    std::ranges::reverse(retv);
    return {retu, retv};
  }
};

}  // namespace tifa_libs::graph


#line 6 "src/code/tree/virtual_tree.hpp"

namespace tifa_libs::graph {

class virtual_tree {
  tree& tr;
  lca_hld lca_;
  vecu st;

  constexpr void insert(u32 x) {
    u32 lca = lca_(x, st.back());
    if (lca == st.back()) {
      st.push_back(x);
      return;
    }
    while (st.size() > 1 && lca_.info.dep[st[st.size() - 2]] >= lca_.info.dep[lca]) vt.add_arc(st[st.size() - 2], st.back()), st.pop_back();
    if (lca_.info.dep[st.back()] > lca_.info.dep[lca]) vt.add_arc(lca, st.back()), st.pop_back();
    if (st.back() != lca) st.push_back(lca);
    st.push_back(x);
  }

 public:
  tree vt;

  explicit constexpr virtual_tree(tree& tr) : tr(tr), lca_(tr), vt((u32)tr.g.size()) {}

  constexpr void build(vecu& a) {
    std::ranges::sort(a, [&](u32 a, u32 b) { return lca_.info.dfn[a] < lca_.info.dfn[b]; });
    vt.g.clear();
    st.push_back(tr.root);
    for (u32 x : a) insert(x);
    while (st.size() > 1) vt.add_arc(st[st.size() - 2], st.back()), st.pop_back();
    st.pop_back();
  }
};

}  // namespace tifa_libs::graph


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