#include #include #include #include #include #include #include #include namespace atcoder { namespace internal { template struct simple_queue { std::vector payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder #include #include #include #include namespace atcoder { template struct mf_graph { public: mf_graph() : _n(0) {} mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); g[from].push_back(_edge{to, int(g[to].size()), cap}); g[to].push_back(_edge{from, int(g[from].size()) - 1, 0}); return m; } struct edge { int from, to; Cap cap, flow; }; 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}; } std::vector edges() { int m = int(pos.size()); std::vector result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); std::vector level(_n), iter(_n); internal::simple_queue que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(g[v].size()); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) break; } return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); while (flow < flow_limit) { Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } } return flow; } std::vector min_cut(int s) { std::vector visited(_n); internal::simple_queue que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector> pos; std::vector> g; }; } // namespace atcoder #define rep(i, n) for(i = 0; i < n; i++) using namespace std; using namespace atcoder; void printMat(vector> &a) { int i, j; rep(i, a.size()) { rep(j, a[i].size()) { cout << a[i][j]; if (j + 1 < a[i].size()) cout << " "; } cout << endl; } cout << endl; } bool isAllZero(vector> &a) { int i, j; rep(i, a.size()) rep(j, a[i].size()) if (a[i][j] != 0) return false; return true; } map>, int> dp; int dfs(vector> &a) { if (isAllZero(a)) return 0; if (dp.find(a) != dp.end()) return dp[a]; int i, j; int ret = 114514; rep(i, a.size()) { vector backup = a[i]; int mmax = a[i][0]; rep(j, a[i].size()) mmax = max(mmax, a[i][j]); if (mmax == 0) continue; rep(j, a[i].size()) if (a[i][j] == mmax) a[i][j] = 0; int res = dfs(a) + 1; ret = min(ret, res); a[i] = backup; } rep(j, a[0].size()) { vector backup(a.size()); rep(i, a.size()) backup[i] = a[i][j]; int mmax = a[0][j]; rep(i, a.size()) mmax = max(mmax, a[i][j]); if (mmax == 0) continue; rep(i, a.size()) if (a[i][j] == mmax) a[i][j] = 0; int res = dfs(a) + 1; ret = min(ret, res); rep(i, a.size()) a[i][j] = backup[i]; } return dp[a] = ret; } int allSearch(vector> a) { dp.clear(); return dfs(a); } void to_unique(vector &v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); } int greedy(vector> a) { int i, j; int maxA = 0; rep(i, a.size()) rep(j, a[i].size()) maxA = max(maxA, a[i][j]); typedef pair P; vector> poses(maxA + 1); vector> rows(maxA + 1); vector> cols(maxA + 1); rep(i, a.size()) { rep(j, a[i].size()) { poses[a[i][j]].push_back(P(i, j)); rows[a[i][j]].push_back(i); cols[a[i][j]].push_back(j); } } rep(i, maxA + 1) { to_unique(rows[i]); to_unique(cols[i]); } int ret = 0; rep(i, maxA + 1) { if (i == 0) continue; int n = rows[i].size(); int m = cols[i].size(); mf_graph g(n + m + 2); int s = n + m; int t = n + m + 1; rep(j, poses[i].size()) { int row = poses[i][j].first; int col = poses[i][j].second; row = lower_bound(rows[i].begin(), rows[i].end(), row) - rows[i].begin(); col = lower_bound(cols[i].begin(), cols[i].end(), col) - cols[i].begin(); g.add_edge(row, n + col, 1); } rep(j, n) g.add_edge(s, j, 1); rep(j, m) g.add_edge(n + j, t, 1); ret += g.flow(s, t); } return ret; } void test() { int h = 4, w = 4, K = 4, T = 1000; mt19937 mt(252521); for (int t = 0; t < T; t++) { vector> a(h, vector(w)); int i, j; rep(i, h) rep(j, w) a[i][j] = mt() % K; int res1 = allSearch(a); int res2 = greedy(a); if (res1 != res2) { cout << "Wrong Answer[" << t << "]" << endl; printMat(a); cout << "all = " << res1 << endl; cout << "greedy = " << res2 << endl; return; } } cout << "Accepted !" << endl; } signed main() { int h, w; cin >> h >> w; vector> a(h, vector(w)); int i, j; rep(i, h) rep(j, w) cin >> a[i][j]; cout << greedy(a) << endl; return 0; }