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:heavy_check_mark: 区間に辺を張るテク (src/Graph/RangeToRangeGraph.hpp)

RangeToRangeGraph<cost_t=int> クラス

メンバ変数 概要
graph 区間に辺を張るテクによって構築された有向グラフ．
Graph クラス
weight 区間に辺を張るテクによって構築された有向グラフの辺の重み．
vector<cost_t>
メンバ関数 概要 計算量
RangeToRangeGraph(n) コンストラクタ．区間の長さ $n$ を渡す．  
add(s,t,w=0) 点 $s$ から 点 $t$ へ重み $w$ の有向辺を張る． $O(1)$
add_from_range(s_l,s_r,t,w=0) 区間 $\lbrack s_l, s_r)$ から点 $t$ へ重み $w$ の有向辺を張る． $O(\log n)$
add_to_range(s,t_l,t_r,w=0) 点 $s$ から区間 $\lbrack t_l, t_r)$ へ重み $w$ の有向辺を張る． $O(\log n)$
add_from_range_to_range(s_l,s_r,t_l,t_r,w=0) 区間 $\lbrack s_l, s_r)$ から区間 $\lbrack t_l, t_r)$ へ重み $w$ の有向辺を張る． $O(\log n)$

Verify

参考

https://lorent-kyopro.hatenablog.com/entry/2020/07/24/170656

Depends on

Verified with

Code

#pragma once
#include "src/Graph/Graph.hpp"
template <typename cost_t= int> class RangeToRangeGraph {
 int n;
 inline int to_upper_idx(int i) const { return i >= n ? i - n : n + i; }
 inline int to_lower_idx(int i) const { return i >= n ? i - n : n + n + i; }
public:
 Graph graph;
 std::vector<cost_t> weight;
 RangeToRangeGraph(int n): n(n), graph(n * 3) {
  for (int i= 2; i < n + n; ++i) add(to_upper_idx(i / 2), to_upper_idx(i));
  for (int i= 2; i < n + n; ++i) add(to_lower_idx(i), to_lower_idx(i / 2));
 }
 void add(int s, int t, cost_t w= 0) { graph.add_edge(s, t), weight.emplace_back(w); }
 // [s_l, s_r) -> t
 void add_from_range(int s_l, int s_r, int t, cost_t w= 0) {
  for (int l= s_l + n, r= s_r + n; l < r; l>>= 1, r>>= 1) {
   if (l & 1) add(to_lower_idx(l++), t, w);
   if (r & 1) add(to_lower_idx(--r), t, w);
  }
 }
 // s -> [t_l, t_r)
 void add_to_range(int s, int t_l, int t_r, cost_t w= 0) {
  for (int l= t_l + n, r= t_r + n; l < r; l>>= 1, r>>= 1) {
   if (l & 1) add(s, to_upper_idx(l++), w);
   if (r & 1) add(s, to_upper_idx(--r), w);
  }
 }
 // [s_l, s_r) -> [t_l, t_r)
 void add_from_range_to_range(int s_l, int s_r, int t_l, int t_r, cost_t w= 0) { add_from_range(s_l, s_r, graph.n, w), add_to_range(graph.n, t_l, t_r, 0), ++graph.n; }
};
#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 3 "src/Graph/RangeToRangeGraph.hpp"
template <typename cost_t= int> class RangeToRangeGraph {
 int n;
 inline int to_upper_idx(int i) const { return i >= n ? i - n : n + i; }
 inline int to_lower_idx(int i) const { return i >= n ? i - n : n + n + i; }
public:
 Graph graph;
 std::vector<cost_t> weight;
 RangeToRangeGraph(int n): n(n), graph(n * 3) {
  for (int i= 2; i < n + n; ++i) add(to_upper_idx(i / 2), to_upper_idx(i));
  for (int i= 2; i < n + n; ++i) add(to_lower_idx(i), to_lower_idx(i / 2));
 }
 void add(int s, int t, cost_t w= 0) { graph.add_edge(s, t), weight.emplace_back(w); }
 // [s_l, s_r) -> t
 void add_from_range(int s_l, int s_r, int t, cost_t w= 0) {
  for (int l= s_l + n, r= s_r + n; l < r; l>>= 1, r>>= 1) {
   if (l & 1) add(to_lower_idx(l++), t, w);
   if (r & 1) add(to_lower_idx(--r), t, w);
  }
 }
 // s -> [t_l, t_r)
 void add_to_range(int s, int t_l, int t_r, cost_t w= 0) {
  for (int l= t_l + n, r= t_r + n; l < r; l>>= 1, r>>= 1) {
   if (l & 1) add(s, to_upper_idx(l++), w);
   if (r & 1) add(s, to_upper_idx(--r), w);
  }
 }
 // [s_l, s_r) -> [t_l, t_r)
 void add_from_range_to_range(int s_l, int s_r, int t_l, int t_r, cost_t w= 0) { add_from_range(s_l, s_r, graph.n, w), add_to_range(graph.n, t_l, t_r, 0), ++graph.n; }
};
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