#include "shortest-path/dual-of-shortest-path.hpp"
#pragma once #include "../graph/graph-template.hpp" template <typename T> struct Dual_of_Shortest_Path { int N; vector<vector<edge<T>>> g; T INF; vector<T> d; Dual_of_Shortest_Path(int _n) : N(_n), g(N), INF(numeric_limits<T>::max() / 2.1), d(N, INF) {} // add constraint f(j) <= f(i) + w void add_edge(int i, int j, T c) { g[i].emplace_back(i, j, c); } // solve max{f(t) - f(s)} for each t // if unsatisfiable, return empty vector vector<T> solve(int start = 0) { d[start] = 0; for (int loop = 0; loop < N; ++loop) { int upd = 0; for (int i = 0; i < N; ++i) { for (auto& e : g[i]) { if (d[i] + e.cost < d[e.to]) { d[e.to] = d[i] + e.cost; upd = 1; } } } if (!upd) break; if (loop == N - 1) return {}; } return d; } }; /** * @brief 牛ゲー(最短路問題の双対) */
#line 2 "shortest-path/dual-of-shortest-path.hpp" #line 2 "graph/graph-template.hpp" template <typename T> struct edge { int src, to; T cost; edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {} edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template <typename T> using Edges = vector<edge<T>>; template <typename T> using WeightedGraph = vector<Edges<T>>; using UnweightedGraph = vector<vector<int>>; // Input of (Unweighted) Graph UnweightedGraph graph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { UnweightedGraph g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; if (is_1origin) x--, y--; g[x].push_back(y); if (!is_directed) g[y].push_back(x); } return g; } // Input of Weighted Graph template <typename T> WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { WeightedGraph<T> g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; cin >> c; if (is_1origin) x--, y--; g[x].emplace_back(x, y, c); if (!is_directed) g[y].emplace_back(y, x, c); } return g; } // Input of Edges template <typename T> Edges<T> esgraph([[maybe_unused]] int N, int M, int is_weighted = true, bool is_1origin = true) { Edges<T> es; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; es.emplace_back(x, y, c); } return es; } // Input of Adjacency Matrix template <typename T> vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true, bool is_directed = false, bool is_1origin = true) { vector<vector<T>> d(N, vector<T>(N, INF)); for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; d[x][y] = c; if (!is_directed) d[y][x] = c; } return d; } /** * @brief グラフテンプレート * @docs docs/graph/graph-template.md */ #line 4 "shortest-path/dual-of-shortest-path.hpp" template <typename T> struct Dual_of_Shortest_Path { int N; vector<vector<edge<T>>> g; T INF; vector<T> d; Dual_of_Shortest_Path(int _n) : N(_n), g(N), INF(numeric_limits<T>::max() / 2.1), d(N, INF) {} // add constraint f(j) <= f(i) + w void add_edge(int i, int j, T c) { g[i].emplace_back(i, j, c); } // solve max{f(t) - f(s)} for each t // if unsatisfiable, return empty vector vector<T> solve(int start = 0) { d[start] = 0; for (int loop = 0; loop < N; ++loop) { int upd = 0; for (int i = 0; i < N; ++i) { for (auto& e : g[i]) { if (d[i] + e.cost < d[e.to]) { d[e.to] = d[i] + e.cost; upd = 1; } } } if (!upd) break; if (loop == N - 1) return {}; } return d; } }; /** * @brief 牛ゲー(最短路問題の双対) */