全方位木DP (src/Graph/Rerooting.hpp)

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Last update: 2024-08-04 20:03:33+09:00
Include: #include "src/Graph/Rerooting.hpp"

image of tree dp

`Rerooting<T>` クラス

全方位木DPの値(型 : T )が入っている配列だと思って使う. (operator[](int v), begin(), end() がある. )

コンストラクタ

Rerooting<T>::Rerooting<U,F1,F2,F3>(Graph g, F1 put_edge, F2 op, U ui, F3 put_vertex) // (1)
Rerooting<T>::Rerooting<U,F1,F2,F3>(Graph g, HeavyLightDecomposition hld, F1 put_edge, F2 op, U ui, F3 put_vertex) // (2)
Rerooting<T>::Rerooting<U,F1,F2,F3>(Graph g, CSRArray<int> adje, F1 put_edge, F2 op, U ui, F3 put_vertex) // (3)
Rerooting<T>::Rerooting<U,F1,F2,F3>(Graph g, CSRArray<int> adje,  HeavyLightDecomposition hld, F1 put_edge, F2 op, U ui, F3 put_vertex) // (4)

引数	概要
`Graph g`	`Graph` クラス
`CSRArray<int> adje`	頂点 → 辺の隣接リスト(`CSRArray<int>`クラス) 省略できる (1), (2). (ただし内部で作ってる)
`HeavyLightDecomposition hld`	g を重軽分解したもの. 省略できる (1), (3). (ただし内部で作ってる)
`put_edge(int v, int e, T t) -> U`	頂点 v と v から出る辺 e の情報によってクラス `T` の値 `t` をモノイド `U` の元に変換
`op(U l, U r) -> U`	モノイド `U` の二項演算
`U ui`	モノイド `U` の単位元
`put_vertex(int v, U sum) -> T`	頂点 v でモノイド `U` の総積をクラス `T` の値に変換

その他メンバ関数

名前	概要
`operator[](int v)`	頂点 v についての全方位木DPの値を返す.
`begin()`	全方位木DPの値配列のイテレータ.
`end()`	全方位木DPの値配列のイテレータ.
`operator()(int root, int v)`	頂点 root が根である場合の頂点 v を根とする部分木のDP値を返す.

Verify

AtCoder Regular Contest 022 C - ロミオとジュリエット
AtCoder Regular Contest 028 C - 高橋王国の分割統治
AtCoder Regular Contest 097 F - Monochrome Cat
Educational DP Contest V - Subtree
Typical DP Contest N - 木
square869120Contest #4 D - Driving on a Tree
NJPC2017 E - 限界集落
第二回全国統一プログラミング王決定戦本戦 D - 木、 (根付き木ハッシュ, 二つの全方位木DP, operator()(root,v))
東京工業大学プログラミングコンテスト2019 M - Inversion Numbers of Tree
yukicoder No.1153 ねこちゃんゲーム (operator()(root,v), sp judge)
Educational Codeforces Round 46 (Div. 2) G. Two-Paths ( + LCA )

参考

https://trap.jp/post/1702/

Depends on

Verified with

Code

#pragma once
#include <valarray>
#include "src/Graph/HeavyLightDecomposition.hpp"
// put_edge(int v, int e, T t) -> U
// op(U l, U r) -> U
// ui(:U) is the identity element of op
// put_vertex(int v, U sum) -> T
template <class T> class Rerooting {
 HeavyLightDecomposition hld;
 std::valarray<T> dp, dp1, dp2;
public:
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const CSRArray<int> &adje, const HeavyLightDecomposition &hld, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex) : hld(hld){
  static_assert(std::is_invocable_r_v<U, F1, int, int, T>, "put_edge(int,int,T) is not invocable");
  static_assert(std::is_invocable_r_v<U, F2, U, U>, "op(U,U) is not invocable");
  static_assert(std::is_invocable_r_v<T, F3, int, U>, "put_vertex(int,U) is not invocable");
  const int n= g.vertex_size();
  dp.resize(n), dp1.resize(n), dp2.resize(n);
  for (int i= n, v; i--;) {
   U sum= ui;
   for (int e: adje[v= hld.to_vertex(i)])
    if (int u= g[e].to(v); u != hld.parent(v)) sum= op(sum, put_edge(v, e, dp1[u]));
   dp1[v]= put_vertex(v, sum);
  }
  for (int i= 0, v; i < n; ++i) {
   auto gv= adje[v= hld.to_vertex(i)];
   int dg= gv.size();
   std::valarray<U> f(dg + 1), b(dg + 1);
   for (int j= 0, e, u; j < dg; ++j) u= g[e= gv[j]].to(v), f[j + 1]= put_edge(v, e, u == hld.parent(v) ? dp2[v] : dp1[u]);
   f[0]= b[dg]= ui;
   for (int j= dg; j--;) b[j]= op(f[j + 1], b[j + 1]);
   for (int j= 0; j < dg; ++j) f[j + 1]= op(f[j], f[j + 1]);
   for (int j= 0; j < dg; ++j)
    if (int u= g[gv[j]].to(v); u != hld.parent(v)) dp2[u]= put_vertex(v, op(f[j], b[j + 1]));
   dp[v]= put_vertex(v, f[dg]);
  }
 }
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const CSRArray<int> &adje, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, adje, HeavyLightDecomposition(g), put_edge, op, ui, put_vertex) {}
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const HeavyLightDecomposition &hld, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, g.adjacency_edge(0), hld, put_edge, op, ui, put_vertex) {}
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, g.adjacency_edge(0), HeavyLightDecomposition(g), put_edge, op, ui, put_vertex) {}
 const T &operator[](int v) const { return dp[v]; }
 auto begin() const { return std::cbegin(dp); }
 auto end() const { return std::cend(dp); }
 const T &operator()(int root, int v) const { return root == v ? dp[v] : hld.in_subtree(root, v) ? dp2[hld.jump(v, root, 1)] : dp1[v]; }
};

#line 2 "src/Graph/Rerooting.hpp"
#include <valarray>
#line 2 "src/Graph/HeavyLightDecomposition.hpp"
#include <array>
#include <cassert>
#line 2 "src/Internal/ListRange.hpp"
#include <vector>
#include <iostream>
#include <iterator>
#include <type_traits>
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 5 "src/Graph/HeavyLightDecomposition.hpp"
class HeavyLightDecomposition {
 std::vector<int> P, PP, D, I, L, R;
public:
 HeavyLightDecomposition()= default;
 HeavyLightDecomposition(const Graph &g, int root= 0): HeavyLightDecomposition(g.adjacency_vertex(0), root) {}
 HeavyLightDecomposition(const CSRArray<int> &adj, int root= 0) {
  const int n= adj.size();
  P.assign(n, -2), PP.resize(n), D.resize(n), I.resize(n), L.resize(n), R.resize(n);
  auto f= [&, i= 0, v= 0, t= 0](int r) mutable {
   for (P[r]= -1, I[t++]= r; i < t; ++i)
    for (int u: adj[v= I[i]])
     if (P[v] != u) P[I[t++]= u]= v;
  };
  f(root);
  for (int r= 0; r < n; ++r)
   if (P[r] == -2) f(r);
  std::vector<int> Z(n, 1), nx(n, -1);
  for (int i= n, v; i--;) {
   if (P[v= I[i]] == -1) continue;
   if (Z[P[v]]+= Z[v]; nx[P[v]] == -1) nx[P[v]]= v;
   if (Z[nx[P[v]]] < Z[v]) nx[P[v]]= v;
  }
  for (int v= n; v--;) PP[v]= v;
  for (int v: I)
   if (nx[v] != -1) PP[nx[v]]= v;
  for (int v: I)
   if (P[v] != -1) PP[v]= PP[PP[v]], D[v]= D[P[v]] + 1;
  for (int i= n; i--;) L[I[i]]= i;
  for (int v: I) {
   int ir= R[v]= L[v] + Z[v];
   for (int u: adj[v])
    if (u != P[v] && u != nx[v]) L[u]= (ir-= Z[u]);
   if (nx[v] != -1) L[nx[v]]= L[v] + 1;
  }
  for (int i= n; i--;) I[L[i]]= i;
 }
 int to_seq(int v) const { return L[v]; }
 int to_vertex(int i) const { return I[i]; }
 size_t size() const { return P.size(); }
 int parent(int v) const { return P[v]; }
 int head(int v) const { return PP[v]; }
 int root(int v) const {
  for (v= PP[v];; v= PP[P[v]])
   if (P[v] == -1) return v;
 }
 bool connected(int u, int v) const { return root(u) == root(v); }
 // u is in v
 bool in_subtree(int u, int v) const { return L[v] <= L[u] && L[u] < R[v]; }
 int subtree_size(int v) const { return R[v] - L[v]; }
 int lca(int u, int v) const {
  for (;; v= P[PP[v]]) {
   if (L[u] > L[v]) std::swap(u, v);
   if (PP[u] == PP[v]) return u;
  }
 }
 int la(int v, int k) const {
  assert(k <= D[v]);
  for (int u;; k-= L[v] - L[u] + 1, v= P[u])
   if (L[v] - k >= L[u= PP[v]]) return I[L[v] - k];
 }
 int jump(int u, int v, int k) const {
  if (!k) return u;
  if (u == v) return -1;
  if (k == 1) return in_subtree(v, u) ? la(v, D[v] - D[u] - 1) : P[u];
  int w= lca(u, v), d_uw= D[u] - D[w], d_vw= D[v] - D[w];
  return k > d_uw + d_vw ? -1 : k <= d_uw ? la(u, k) : la(v, d_uw + d_vw - k);
 }
 int depth(int v) const { return D[v]; }
 int dist(int u, int v) const { return D[u] + D[v] - D[lca(u, v)] * 2; }
 // half-open interval [l,r)
 std::pair<int, int> subtree(int v) const { return {L[v], R[v]}; }
 // sequence of closed intervals [l,r]
 std::vector<std::pair<int, int>> path(int u, int v, bool edge= 0) const {
  std::vector<std::pair<int, int>> up, down;
  while (PP[u] != PP[v]) {
   if (L[u] < L[v]) down.emplace_back(L[PP[v]], L[v]), v= P[PP[v]];
   else up.emplace_back(L[u], L[PP[u]]), u= P[PP[u]];
  }
  if (L[u] < L[v]) down.emplace_back(L[u] + edge, L[v]);
  else if (L[v] + edge <= L[u]) up.emplace_back(L[u], L[v] + edge);
  return up.insert(up.end(), down.rbegin(), down.rend()), up;
 }
};
#line 4 "src/Graph/Rerooting.hpp"
// put_edge(int v, int e, T t) -> U
// op(U l, U r) -> U
// ui(:U) is the identity element of op
// put_vertex(int v, U sum) -> T
template <class T> class Rerooting {
 HeavyLightDecomposition hld;
 std::valarray<T> dp, dp1, dp2;
public:
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const CSRArray<int> &adje, const HeavyLightDecomposition &hld, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex) : hld(hld){
  static_assert(std::is_invocable_r_v<U, F1, int, int, T>, "put_edge(int,int,T) is not invocable");
  static_assert(std::is_invocable_r_v<U, F2, U, U>, "op(U,U) is not invocable");
  static_assert(std::is_invocable_r_v<T, F3, int, U>, "put_vertex(int,U) is not invocable");
  const int n= g.vertex_size();
  dp.resize(n), dp1.resize(n), dp2.resize(n);
  for (int i= n, v; i--;) {
   U sum= ui;
   for (int e: adje[v= hld.to_vertex(i)])
    if (int u= g[e].to(v); u != hld.parent(v)) sum= op(sum, put_edge(v, e, dp1[u]));
   dp1[v]= put_vertex(v, sum);
  }
  for (int i= 0, v; i < n; ++i) {
   auto gv= adje[v= hld.to_vertex(i)];
   int dg= gv.size();
   std::valarray<U> f(dg + 1), b(dg + 1);
   for (int j= 0, e, u; j < dg; ++j) u= g[e= gv[j]].to(v), f[j + 1]= put_edge(v, e, u == hld.parent(v) ? dp2[v] : dp1[u]);
   f[0]= b[dg]= ui;
   for (int j= dg; j--;) b[j]= op(f[j + 1], b[j + 1]);
   for (int j= 0; j < dg; ++j) f[j + 1]= op(f[j], f[j + 1]);
   for (int j= 0; j < dg; ++j)
    if (int u= g[gv[j]].to(v); u != hld.parent(v)) dp2[u]= put_vertex(v, op(f[j], b[j + 1]));
   dp[v]= put_vertex(v, f[dg]);
  }
 }
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const CSRArray<int> &adje, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, adje, HeavyLightDecomposition(g), put_edge, op, ui, put_vertex) {}
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const HeavyLightDecomposition &hld, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, g.adjacency_edge(0), hld, put_edge, op, ui, put_vertex) {}
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, g.adjacency_edge(0), HeavyLightDecomposition(g), put_edge, op, ui, put_vertex) {}
 const T &operator[](int v) const { return dp[v]; }
 auto begin() const { return std::cbegin(dp); }
 auto end() const { return std::cend(dp); }
 const T &operator()(int root, int v) const { return root == v ? dp[v] : hld.in_subtree(root, v) ? dp2[hld.jump(v, root, 1)] : dp1[v]; }
};

全方位木DP (src/Graph/Rerooting.hpp)

Rerooting<T> クラス

コンストラクタ

その他メンバ関数

Verify

参考

Depends on

Verified with

Code

`Rerooting<T>` クラス