#include #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") using namespace std; using std::cout; using std::cin; using std::endl; using ll=long long; using ld=long double; const ll ILL=2167167167167167167; const int INF=2100000000; const int mod=998244353; #define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++) #define all(p) p.begin(),p.end() template using _pq = priority_queue, greater>; template ll LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template ll UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;} template bool chmax(T &a,const T &b){if(a void So(vector &v) {sort(v.begin(),v.end());} template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} void yneos(bool a,bool upp=0){if(a) cout<<(upp?"YES\n":"Yes\n"); else cout<<(upp?"NO\n":"No\n");} template void vec_out(vector &p,int ty=0){ if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'< T vec_min(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;} template T vec_max(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;} template T vec_sum(vector &a){assert(!a.empty());T ans=a[0]-a[0];for(auto &x:a) ans+=x;return ans;} int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;} namespace atcoder { namespace internal { template struct csr { std::vector start; std::vector elist; explicit csr(int n, const std::vector>& edges) : start(n + 1), elist(edges.size()) { for (auto e : edges) { start[e.first + 1]++; } for (int i = 1; i <= n; i++) { start[i] += start[i - 1]; } auto counter = start; for (auto e : edges) { elist[counter[e.first]++] = e.second; } } }; } // namespace internal 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 template struct mcf_graph { public: mcf_graph() {} explicit mcf_graph(int n) : _n(n) {} int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); assert(0 <= cost); int m = int(_edges.size()); _edges.push_back({from, to, cap, 0, cost}); return m; } struct edge { int from, to; Cap cap, flow; Cost cost; }; edge get_edge(int i) { int m = int(_edges.size()); assert(0 <= i && i < m); return _edges[i]; } std::vector edges() { return _edges; } 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); int m = int(_edges.size()); std::vector edge_idx(m); auto g = [&]() { std::vector degree(_n), redge_idx(m); std::vector> elist; elist.reserve(2 * m); for (int i = 0; i < m; i++) { auto e = _edges[i]; edge_idx[i] = degree[e.from]++; redge_idx[i] = degree[e.to]++; elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}}); elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}}); } auto _g = internal::csr<_edge>(_n, elist); for (int i = 0; i < m; i++) { auto e = _edges[i]; edge_idx[i] += _g.start[e.from]; redge_idx[i] += _g.start[e.to]; _g.elist[edge_idx[i]].rev = redge_idx[i]; _g.elist[redge_idx[i]].rev = edge_idx[i]; } return _g; }(); auto result = slope(g, s, t, flow_limit); for (int i = 0; i < m; i++) { auto e = g.elist[edge_idx[i]]; _edges[i].flow = _edges[i].cap - e.cap; } return result; } std::vector slope_all(int s, int t,Cap flow_limit) { std::vector> tmp=slope(s, t, flow_limit); std::vector ans((*tmp.rbegin()).first+1); ans[0]=0; for(int i=0;i<(int)(tmp.size())-1;i++){ Cost diff=(tmp[i+1].second-tmp[i].second)/(tmp[i+1].first-tmp[i].first); for(int j=1+tmp[i].first;j<=tmp[i+1].first;j++){ ans[j]=ans[j-1]+diff; } } return ans; } std::vector slope_all(int s, int t){ return slope_all(s,t,std::numeric_limits::max()); } private: int _n; std::vector _edges; // inside edge struct _edge { int to, rev; Cap cap; Cost cost; }; std::vector> slope(internal::csr<_edge>& g, int s, int t, Cap flow_limit) { // 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 // dual_dist[i] = (dual[i], dist[i]) std::vector> dual_dist(_n); std::vector prev_e(_n); std::vector vis(_n); struct Q { Cost key; int to; bool operator<(Q r) const { return key > r.key; } }; std::vector que_min; std::vector que; auto dual_ref = [&]() { for (int i = 0; i < _n; i++) { dual_dist[i].second = std::numeric_limits::max(); } std::fill(vis.begin(), vis.end(), false); que_min.clear(); que.clear(); // que[0..heap_r) was heapified size_t heap_r = 0; dual_dist[s].second = 0; que_min.push_back(s); while (!que_min.empty() || !que.empty()) { int v; if (!que_min.empty()) { v = que_min.back(); que_min.pop_back(); } else { while (heap_r < que.size()) { heap_r++; std::push_heap(que.begin(), que.begin() + heap_r); } v = que.front().to; std::pop_heap(que.begin(), que.end()); que.pop_back(); heap_r--; } 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 Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second; for (int i = g.start[v]; i < g.start[v + 1]; i++) { auto e = g.elist[i]; if (!e.cap) continue; // |-dual[e.to] + dual[v]| <= (n-1)C // cost <= C - -(n-1)C + 0 = nC Cost cost = e.cost - dual_dist[e.to].first + dual_v; if (dual_dist[e.to].second - dist_v > cost) { Cost dist_to = dist_v + cost; dual_dist[e.to].second = dist_to; prev_e[e.to] = e.rev; if (dist_to == dist_v) { que_min.push_back(e.to); } else { que.push_back(Q{dist_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_dist[v].first -= dual_dist[t].second - dual_dist[v].second; } return true; }; Cap flow = 0; Cost cost = 0, prev_cost_per_flow = -1; std::vector> result = {{Cap(0), Cost(0)}}; while (flow < flow_limit) { if (!dual_ref()) break; Cap c = flow_limit - flow; for (int v = t; v != s; v = g.elist[prev_e[v]].to) { c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap); } for (int v = t; v != s; v = g.elist[prev_e[v]].to) { auto& e = g.elist[prev_e[v]]; e.cap += c; g.elist[e.rev].cap -= c; } Cost d = -dual_dist[s].first; flow += c; cost += c * d; if (prev_cost_per_flow == d) { result.pop_back(); } result.push_back({flow, cost}); prev_cost_per_flow = d; } return result; } }; } // namespace atcoder using namespace atcoder; void solve(); // oddloop int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t=1; //cin>>t; rep(i,0,t) solve(); } void solve(){ int H,W; cin>>H>>W; vector L(W),R(W); int tmp=0; rep(i,0,W){ int x,y; cin>>x>>y; tmp+=x-1; L[i]=y-x; R[i]=y-1; } mcf_graph G(2*W+2); int S=W*2,T=W*2+1; rep(i,0,W){ G.add_edge(S,i,1,0); G.add_edge(i+W,T,1,0); } rep(i,0,W) rep(j,0,W){ if(j