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#define PROBLEM "https://judge.yosupo.jp/problem/manhattanmst" #include "../../template/template.hpp" #include "../../graph/mst/manhattan-mst.hpp" #include "../../graph/mst/kruskal.hpp" int main() { int N; cin >> N; vector< int64_t > X(N), Y(N); for(int i = 0; i < N; i++) { cin >> X[i] >> Y[i]; } auto es = manhattan_mst(X, Y); auto ret = kruskal(es, N); cout << ret.cost << "\n"; for(auto &e : ret.edges) cout << e.from << " " << e.to << "\n"; }
#line 1 "test/verify/yosupo-manhattanmst.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/manhattanmst" #line 1 "template/template.hpp" #include<bits/stdc++.h> using namespace std; using int64 = long long; const int mod = 1e9 + 7; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 >& p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { explicit FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } #line 4 "test/verify/yosupo-manhattanmst.test.cpp" #line 2 "graph/mst/manhattan-mst.hpp" #line 2 "graph/graph-template.hpp" /** * @brief Graph Template(グラフテンプレート) */ template< typename T = int > struct Edge { int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template< typename T = int > struct Graph { vector< vector< Edge< T > > > g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const { return g.size(); } void add_directed_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false) { for(int i = 0; i < M; i++) { int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if(weighted) cin >> c; if(directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } inline vector< Edge< T > > &operator[](const int &k) { return g[k]; } inline const vector< Edge< T > > &operator[](const int &k) const { return g[k]; } }; template< typename T = int > using Edges = vector< Edge< T > >; #line 4 "graph/mst/manhattan-mst.hpp" /** * @brief Manhattan MST */ template< typename T > Edges< T > manhattan_mst(vector< T > xs, vector< T > ys) { assert(xs.size() == ys.size()); Edges< T > ret; int n = (int) xs.size(); vector< int > ord(n); iota(ord.begin(), ord.end(), 0); for(int s = 0; s < 2; s++) { for(int t = 0; t < 2; t++) { auto cmp = [&](int i, int j) -> bool { return xs[i] + ys[i] < xs[j] + ys[j]; }; sort(ord.begin(), ord.end(), cmp); map< T, int > idx; for(int i:ord) { for(auto it = idx.lower_bound(-ys[i]); it != idx.end(); it = idx.erase(it)) { int j = it->second; if(xs[i] - xs[j] < ys[i] - ys[j]) break; ret.emplace_back(i, j, abs(xs[i] - xs[j]) + abs(ys[i] - ys[j])); } idx[-ys[i]] = i; } swap(xs, ys); } for(int i = 0; i < n; i++) xs[i] *= -1; } return ret; } #line 2 "graph/mst/kruskal.hpp" #line 2 "structure/union-find/union-find.hpp" struct UnionFind { vector< int > data; UnionFind() = default; explicit UnionFind(size_t sz) : data(sz, -1) {} bool unite(int x, int y) { x = find(x), y = find(y); if(x == y) return false; if(data[x] > data[y]) swap(x, y); data[x] += data[y]; data[y] = x; return true; } int find(int k) { if(data[k] < 0) return (k); return data[k] = find(data[k]); } int size(int k) { return -data[find(k)]; } bool same(int x, int y) { return find(x) == find(y); } vector< vector< int > > groups() { int n = (int) data.size(); vector< vector< int > > ret(n); for(int i = 0; i < n; i++) { ret[find(i)].emplace_back(i); } ret.erase(remove_if(begin(ret), end(ret), [&](const vector< int > &v) { return v.empty(); }), end(ret)); return ret; } }; #line 5 "graph/mst/kruskal.hpp" /** * @brief Kruskal(最小全域木) * @docs docs/kruskal.md */ template< typename T > struct MinimumSpanningTree { T cost; Edges< T > edges; }; template< typename T > MinimumSpanningTree< T > kruskal(Edges< T > &edges, int V) { sort(begin(edges), end(edges), [](const Edge< T > &a, const Edge< T > &b) { return a.cost < b.cost; }); UnionFind tree(V); T total = T(); Edges< T > es; for(auto &e : edges) { if(tree.unite(e.from, e.to)) { es.emplace_back(e); total += e.cost; } } return {total, es}; } #line 7 "test/verify/yosupo-manhattanmst.test.cpp" int main() { int N; cin >> N; vector< int64_t > X(N), Y(N); for(int i = 0; i < N; i++) { cin >> X[i] >> Y[i]; } auto es = manhattan_mst(X, Y); auto ret = kruskal(es, N); cout << ret.cost << "\n"; for(auto &e : ret.edges) cout << e.from << " " << e.to << "\n"; }