// 想定解1 O(NK)本の辺を張り,ベルマンフォードでポテンシャル計算 #include using namespace std; using ll = long long; template struct mcf_graph { public: std::vector dual; mcf_graph() {} mcf_graph(int n) : _n(n), g(n) { dual.resize(_n, 0); } int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); g[from].push_back(_edge{to, int(g[to].size()), cap, cost}); g[to].push_back(_edge{from, int(g[from].size()) - 1, 0, -cost}); return m; } struct edge { int from, to; Cap cap, flow; Cost cost; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{ pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost, }; } std::vector edges() { int m = int(pos.size()); std::vector result(m); for (int i = 0; i < m; i++) { result[i] = get_edge(i); } return result; } std::pair flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } std::pair flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); } std::vector> slope(int s, int t) { return slope(s, t, std::numeric_limits::max()); } std::vector> slope(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); // variants (C = maxcost): // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0 // reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge // std::vector dual(_n, 0), dist(_n); std::vector dist(_n); std::vector pv(_n), pe(_n); std::vector vis(_n); auto dual_ref_BF = [&](){ std::fill(dist.begin(), dist.end(), std::numeric_limits::max()); std::fill(pv.begin(), pv.end(), -1); std::fill(pe.begin(), pe.end(), -1); dist[s] = 0; for(int itr=0;itr<_n-1;itr++){ for(int v=0;v<_n;v++){ if(dist[v] == std::numeric_limits::max()) continue; for(int i=0;i<(int)g[v].size();i++){ auto e = g[v][i]; if(!e.cap) continue; if(dist[e.to] > dist[v] + e.cost){ dist[e.to] = dist[v] + e.cost; pv[e.to] = v; pe[e.to] = i; } } } } // detect negative cycle for(int v=0;v<_n;v++){ if(dist[v] == std::numeric_limits::max()) continue; for(auto &e: g[v]){ if(!e.cap) continue; assert(dist[v] + e.cost >= dist[e.to]); } } if(dist[t] == std::numeric_limits::max()) return false; for(int v=0;v<_n;v++){ if(dist[v] == std::numeric_limits::max()) continue; dual[v] -= dist[t] - dist[v]; } return true; }; auto dual_ref = [&]() { std::fill(dist.begin(), dist.end(), std::numeric_limits::max()); std::fill(pv.begin(), pv.end(), -1); std::fill(pe.begin(), pe.end(), -1); std::fill(vis.begin(), vis.end(), false); struct Q { Cost key; int to; bool operator<(Q r) const { return key > r.key; } }; std::priority_queue que; dist[s] = 0; que.push(Q{0, s}); while (!que.empty()) { int v = que.top().to; que.pop(); if (vis[v]) continue; vis[v] = true; if (v == t) break; // dist[v] = shortest(s, v) + dual[s] - dual[v] // dist[v] >= 0 (all reduced cost are positive) // dist[v] <= (n-1)C for (int i = 0; i < int(g[v].size()); i++) { auto e = g[v][i]; if (vis[e.to] || !e.cap) continue; // |-dual[e.to] + dual[v]| <= (n-1)C // cost <= C - -(n-1)C + 0 = nC Cost cost = e.cost - dual[e.to] + dual[v]; if (dist[e.to] - dist[v] > cost) { dist[e.to] = dist[v] + cost; pv[e.to] = v; pe[e.to] = i; que.push(Q{dist[e.to], e.to}); } } } if (!vis[t]) { return false; } for (int v = 0; v < _n; v++) { if (!vis[v]) continue; // dual[v] = dual[v] - dist[t] + dist[v] // = dual[v] - (shortest(s, t) + dual[s] - dual[t]) + (shortest(s, v) + dual[s] - dual[v]) // = - shortest(s, t) + dual[t] + shortest(s, v) // = shortest(s, v) - shortest(s, t) >= 0 - (n-1)C dual[v] -= dist[t] - dist[v]; } return true; }; Cap flow = 0; Cost cost = 0, prev_cost = -1; std::vector> result; result.push_back({flow, cost}); while (flow < flow_limit) { // 負辺がある場合 if(!flow){ if(!dual_ref_BF()) break; }else{ if(!dual_ref()) break; } // 負辺がない場合 // if(!dual_ref()) break; Cap c = flow_limit - flow; for (int v = t; v != s; v = pv[v]) { c = std::min(c, g[pv[v]][pe[v]].cap); } for (int v = t; v != s; v = pv[v]) { auto& e = g[pv[v]][pe[v]]; e.cap -= c; g[v][e.rev].cap += c; } Cost d = -dual[s]; flow += c; cost += c * d; if (prev_cost == d) { result.pop_back(); } result.push_back({flow, cost}); prev_cost = cost; } return result; } private: int _n; struct _edge { int to, rev; Cap cap; Cost cost; }; std::vector> pos; std::vector> g; }; int main(){ int N, K; cin >> N >> K; vector A(N), B(N); for(int i=0;i> A[i]; for(int i=0;i> B[i]; vector> P(N, vector(N, 0)); for(int i=0;i> P[i][j]; } } mcf_graph G(2*N+2); int s = 2*N, t = s+1; for(int i=0;i