#line 1 "combinatorial_opt/test/maxflow.pushrelabel.yuki957.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/957" #line 2 "combinatorial_opt/maxflow_pushrelabel.hpp" #include #include #include #include // Maxflow (push-relabel, highest-label) // Complexity: O(N^2 M^(1/2)) template ::max() / 2, bool UseGlobalRelabeling = true, bool UseGapRelabeling = true> struct mf_pushrelabel { struct pque_ { std::vector> even_, odd_; int se, so; void init(int n) { even_.resize(n), odd_.resize(n), se = so = 0; }; void clear() { se = so = 0; } bool empty() const { return se + so == 0; } void push(int i, int h) { (h & 1 ? odd_[so++] : even_[se++]) = {i, h}; } int highest() const { int a = se ? even_[se - 1].second : -1, b = so ? odd_[so - 1].second : -1; return a > b ? a : b; } int pop() { if (!se or (so and odd_[so - 1].second > even_[se - 1].second)) { return odd_[--so].first; } else { return even_[--se].first; } } } pque; int _n; struct _edge { int to, rev; Cap cap; }; std::vector> g; std::vector> pos; mf_pushrelabel(int n) : _n(n), g(n) { static_assert(INF > 0, "INF must be positive."); } int add_edge(int from, int to, Cap cap) { assert(0 <= from and from < _n); assert(0 <= to and to < _n); assert(0 <= cap); int m = int(pos.size()); pos.emplace_back(from, int(g[from].size())); int from_id = g[from].size(), to_id = g[to].size() + (from == to); g[from].push_back({to, to_id, cap}); g[to].push_back({from, from_id, Cap(0)}); return m; } std::vector dist; std::vector dcnt; std::vector excess; int gap; void global_relabeling(int t) { dist.assign(_n, _n), dist[t] = 0; static std::vector q; if (q.empty()) q.resize(_n); q[0] = t; int qb = 0, qe = 1; pque.clear(); if (UseGapRelabeling) gap = 1, dcnt.assign(_n * 2, 0); while (qb < qe) { int now = q[qb++]; if (UseGapRelabeling) gap = dist[now] + 1, dcnt[dist[now]]++; if (excess[now] > 0) pque.push(now, dist[now]); for (const auto &e : g[now]) { if (g[e.to][e.rev].cap and dist[e.to] == _n) { dist[e.to] = dist[now] + 1; q[qe++] = e.to; } } } } Cap flow(const int &s, const int &t) { assert(0 <= s and s < _n); assert(0 <= t and t < _n); assert(s != t); excess.assign(_n, 0); excess[s] = INF, excess[t] = -INF; dist.assign(_n, 0); dist[s] = _n; pque.init(_n); for (auto &e : g[s]) push(s, e); if (UseGapRelabeling) gap = 1, dcnt.assign(_n * 2, 0), dcnt[0] = _n - 1; if (UseGlobalRelabeling) global_relabeling(t); int tick = _n; while (!pque.empty()) { int i = pque.pop(); if (UseGapRelabeling and dist[i] > gap) continue; int dnxt = _n * 2 - 1; for (auto &e : g[i]) { if (!e.cap) continue; if (dist[e.to] == dist[i] - 1) { push(i, e); if (excess[i] == 0) break; } else { if (dist[e.to] + 1 < dnxt) dnxt = dist[e.to] + 1; } } if (excess[i] > 0) { if (UseGapRelabeling) { if (dnxt != dist[i]) { dcnt[dist[i]]--, dcnt[dnxt]++; if (!dcnt[dist[i]] and dist[i] < gap) gap = dist[i]; } if (dnxt == gap) gap++; while (pque.highest() > gap) pque.pop(); if (dnxt > gap) dnxt = _n; } pque.push(i, dist[i] = dnxt); } if (UseGlobalRelabeling and --tick == 0) tick = _n, global_relabeling(t); } return excess[t] + INF; } void push(int i, _edge &e) { Cap delta = e.cap < excess[i] ? e.cap : excess[i]; excess[i] -= delta, e.cap -= delta; excess[e.to] += delta, g[e.to][e.rev].cap += delta; if (excess[e.to] > 0 and excess[e.to] <= delta) pque.push(e.to, dist[e.to]); } }; #line 3 "combinatorial_opt/test/maxflow.pushrelabel.yuki957.test.cpp" #include #include #include using namespace std; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); int H, W; cin >> H >> W; vector> G(H, vector(W)); for (auto &v : G) { for (auto &x : v) cin >> x; } vector R(H), C(W); for (auto &x : R) cin >> x; for (auto &x : C) cin >> x; long long tot = accumulate(R.begin(), R.end(), 0LL) + accumulate(C.begin(), C.end(), 0LL); long long f1 = 0; int Z = 1 + H + W; mf_pushrelabel g(Z + 1); for (int i = 0; i < H; i++) { auto gtot = accumulate(G[i].begin(), G[i].end(), 0LL); auto f0 = min(gtot, R[i]); f1 += f0; g.add_edge(0, i + 1, gtot - f0); for (int j = 0; j < W; j++) g.add_edge(i + 1, H + 1 + j, G[i][j]); } for (int j = 0; j < W; j++) g.add_edge(H + 1 + j, Z, C[j]); cout << tot - f1 - g.flow(0, Z) << '\n'; }