#952858 (C++23) No.2642 Don't cut line!

提出ソース

結果

問題	No.2642 Don't cut line!
ユーザー	Aeren
提出日時	2024-02-19 22:28:14
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	167 ms / 4,000 ms
コード長	11,873 bytes
コンパイル時間	3,967 ms
コンパイル使用メモリ	292,844 KB
実行使用メモリ	39,992 KB
最終ジャッジ日時	2024-02-20 12:47:28
合計ジャッジ時間	8,359 ms
ジャッジサーバーID （参考情報）	judge14 / judge13

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,548 KB
testcase_01	AC	159 ms 39,352 KB
testcase_02	AC	157 ms 39,992 KB
testcase_03	AC	152 ms 36,152 KB
testcase_04	AC	155 ms 35,896 KB
testcase_05	AC	156 ms 37,560 KB
testcase_06	AC	54 ms 6,548 KB
testcase_07	AC	56 ms 6,548 KB
testcase_08	AC	55 ms 6,548 KB
testcase_09	AC	54 ms 6,548 KB
testcase_10	AC	55 ms 6,548 KB
testcase_11	AC	54 ms 6,548 KB
testcase_12	AC	56 ms 6,548 KB
testcase_13	AC	54 ms 6,548 KB
testcase_14	AC	55 ms 6,548 KB
testcase_15	AC	57 ms 6,548 KB
testcase_16	AC	91 ms 12,728 KB
testcase_17	AC	122 ms 32,680 KB
testcase_18	AC	133 ms 32,768 KB
testcase_19	AC	95 ms 26,024 KB
testcase_20	AC	57 ms 13,096 KB
testcase_21	AC	47 ms 6,548 KB
testcase_22	AC	65 ms 10,780 KB
testcase_23	AC	167 ms 36,724 KB
testcase_24	AC	71 ms 15,384 KB
testcase_25	AC	68 ms 14,100 KB
testcase_26	AC	61 ms 8,640 KB
testcase_27	AC	99 ms 25,768 KB
testcase_28	AC	150 ms 33,904 KB
testcase_29	AC	62 ms 10,244 KB
testcase_30	AC	66 ms 12,836 KB
testcase_31	AC	122 ms 28,468 KB
testcase_32	AC	65 ms 11,984 KB
testcase_33	AC	2 ms 6,548 KB
testcase_34	AC	2 ms 6,548 KB
testcase_35	AC	2 ms 6,548 KB

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ソースコード

raw source code

// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif

template<bool Enable_small_to_large = true>
struct disjoint_set{
	int n, _group_count;
	vector<int> p;
	vector<list<int>> group;
	disjoint_set(){ }
	disjoint_set(int n): n(n), _group_count(n), p(n, -1), group(n){ assert(n >= 0);
		for(auto i = 0; i < n; ++ i) group[i] = {i};
	}
	int make_set(){
		p.push_back(-1);
		group.push_back(list<int>{p});
		++ _group_count;
		return n ++;
	}
	int root(int u){
		return p[u] < 0 ? u : p[u] = root(p[u]);
	}
	bool share(int a, int b){
		return root(a) == root(b);
	}
	int size(int u){
		return -p[root(u)];
	}
	bool merge(int u, int v){
		u = root(u), v = root(v);
		if(u == v) return false;
		-- _group_count;
		if constexpr(Enable_small_to_large) if(p[u] > p[v]) swap(u, v);
		p[u] += p[v], p[v] = u;
		group[u].splice(group[u].end(), group[v]);
		return true;
	}
	bool merge(int u, int v, auto act){
		u = root(u), v = root(v);
		if(u == v) return false;
		-- _group_count;
		bool swapped = false;
		if constexpr(Enable_small_to_large) if(p[u] > p[v]) swap(u, v), swapped = true;
		p[u] += p[v], p[v] = u;
		group[u].splice(group[u].end(), group[v]);
		act(u, v, swapped);
		return true;
	}
	int group_count() const{
		return _group_count;
	}
	const list<int> &group_of(int u){
		return group[root(u)];
	}
	vector<vector<int>> group_up(){
		vector<vector<int>> g(n);
		for(auto i = 0; i < n; ++ i) g[root(i)].push_back(i);
		g.erase(remove_if(g.begin(), g.end(), [&](auto &s){ return s.empty(); }), g.end());
		return g;
	}
	void clear(){
		_group_count = n;
		fill(p.begin(), p.end(), -1);
		for(auto i = 0; i < n; ++ i) group[i] = {i};
	}
	friend ostream &operator<<(ostream &out, disjoint_set dsu){
		auto gs = dsu.group_up();
		out << "{";
		if(!gs.empty()) for(auto i = 0; i < (int)gs.size(); ++ i){
			out << "{";
			for(auto j = 0; j < (int)gs[i].size(); ++ j){
				out << gs[i][j];
				if(j + 1 < (int)gs[i].size()) out << ", ";
			}
			out << "}";
			if(i + 1 < (int)gs.size()) out << ", ";
		}
		return out << "}";
	}
};

// Requires disjoint_set
template<class G>
vector<int> minimum_spanning_forest(const G &g){
	vector<int> order(g.edge.size());
	iota(order.begin(), order.end(), 0);
	if(g.ignore) order.erase(remove_if(order.begin(), order.end(), [&](int id){ return g.ignore(id); }), order.end());
	sort(order.begin(), order.end(), [&](int i, int j){ return g.edge[i].cost < g.edge[j].cost; });
	disjoint_set dsu(g.n);
	vector<int> res;
	for(auto id: order){
		auto &e = g.edge[id];
		if(dsu.merge(e.from, e.to)) res.push_back(id);
	}
	return res;
}
template<class T>
vector<int> minimum_spanning_forest(int n, const vector<tuple<int, int, T>> &edge){
	vector<int> order(edge.size());
	iota(order.begin(), order.end(), 0);
	sort(order.begin(), order.end(), [&](int i, int j){ return get<2>(edge[i]) < get<2>(edge[j]); });
	disjoint_set dsu(n);
	vector<int> res;
	for(auto id: order){
		auto &e = edge[id];
		if(dsu.merge(get<0>(e), get<1>(e))) res.push_back(id);
	}
	return res;
}

template<class T>
struct graph{
	using Weight_t = T;
	struct Edge_t{
		int from, to;
		T cost;
	};
	int n;
	vector<Edge_t> edge;
	vector<vector<int>> adj;
	function<bool(int)> ignore;
	graph(int n = 1): n(n), adj(n){
		assert(n >= 1);
	}
	graph(const vector<vector<int>> &adj, bool undirected = true): n((int)adj.size()), adj(n){
		assert(n >= 1);
		if(undirected){
			for(auto u = 0; u < n; ++ u) for(auto v: adj[u]) if(u < v) link(u, v);
		}
		else for(auto u = 0; u < n; ++ u) for(auto v: adj[u]) orient(u, v);
	}
	graph(const vector<vector<pair<int, T>>> &adj, bool undirected = true): n((int)adj.size()), adj(n){
		assert(n >= 1);
		if(undirected){
			for(auto u = 0; u < n; ++ u) for(auto [v, w]: adj[u]) if(u < v) link(u, v, w);
		}
		else for(auto u = 0; u < n; ++ u) for(auto [v, w]: adj[u]) orient(u, v, w);
	}
	graph(int n, vector<array<int, 2>> &edge, bool undirected = true): n(n), adj(n){
		assert(n >= 1);
		for(auto [u, v]: edge) undirected ? link(u, v) : orient(u, v);
	}
	graph(int n, vector<tuple<int, int, T>> &edge, bool undirected = true): n(n), adj(n){
		assert(n >= 1);
		for(auto [u, v, w]: edge) undirected ? link(u, v, w) : orient(u, v, w);
	}
	int operator()(int u, int id) const{
		#ifdef LOCAL
		assert(0 <= id && id < (int)edge.size());
		assert(edge[id].from == u || edge[id].to == u);
		#endif
		return u ^ edge[id].from ^ edge[id].to;
	}
	int link(int u, int v, T w = {}){ // insert an undirected edge
		int id = (int)edge.size();
		adj[u].push_back(id), adj[v].push_back(id), edge.push_back({u, v, w});
		return id;
	}
	int orient(int u, int v, T w = {}){ // insert a directed edge
		int id = (int)edge.size();
		adj[u].push_back(id), edge.push_back({u, v, w});
		return id;
	}
	void clear(){
		for(auto [u, v, w]: edge){
			adj[u].clear();
			adj[v].clear();
		}
		edge.clear();
		ignore = {};
	}
	graph transposed() const{ // the transpose of the directed graph
		graph res(n);
		for(auto &e: edge) res.orient(e.to, e.from, e.cost);
		res.ignore = ignore;
		return res;
	}
	int degree(int u) const{ // the degree (outdegree if directed) of u (without the ignoration rule)
		return (int)adj[u].size();
	}
	// The adjacency list is sorted for each vertex.
	vector<vector<int>> get_adjacency_list() const{
		vector<vector<int>> res(n);
		for(auto u = 0; u < n; ++ u) for(auto id: adj[u]){
			if(ignore && ignore(id)) continue;
			res[(*this)(u, id)].push_back(u);
		}
		return res;
	}
	void set_ignoration_rule(const function<bool(int)> &f){
		ignore = f;
	}
	void reset_ignoration_rule(){
		ignore = nullptr;
	}
	friend ostream &operator<<(ostream &out, const graph &g){
		for(auto id = 0; id < (int)g.edge.size(); ++ id){
			if(g.ignore && g.ignore(id)) continue;
			auto &e = g.edge[id];
			out << "{" << e.from << ", " << e.to << ", " << e.cost << "}\n";
		}
		return out;
	}
};

// Requires graph
struct heavy_light_decomposition{
	int n;
	vector<vector<int>> adj; // stores edge ids
	vector<int> pv;
	vector<int> pe;
	vector<int> size;
	vector<int> root_of;
	vector<int> root;
	vector<int> depth;
	vector<int> next; // highest point of the heavy path
	vector<int> prev; // lowest point of the heavy path
	vector<int> pos;
	vector<int> end;
	vector<int> order;
	vector<int> was;
	void init(int n){
		assert(n >= 1);
		this->n = n;
		adj.assign(n, {});
		pv.assign(n, -1);
		pe.assign(n, -1);
		order.clear();
		pos.assign(n, -1);
		end.assign(n, -1);
		size.assign(n, 1);
		root_of.assign(n, -1);
		root.clear();
		depth.assign(n, -1);
		next.assign(n, -1);
		prev.assign(n, -1);
		was.assign(n, -2);
		attempt = -1;
	}
	int attempt;
	template<class T>
	void build(const graph<T> &g, const vector<int> &src){
		assert(g.n <= n);
		++ attempt;
		root.clear(), order.clear();
		for(auto id = 0; id < (int)g.edge.size(); ++ id){
			if(g.ignore && g.ignore(id)) continue;
			auto &e = g.edge[id];
			adj[e.from].push_back(id), adj[e.to].push_back(id);
		}
		auto dfs_init = [&](auto self, int u)->void{
			assert(was[u] != attempt); // CYCLE FOUND
			was[u] = attempt;
			prev[u] = u;
			size[u] = 1;
			if(root_of[u] != u){
				adj[u].erase(find(adj[u].begin(), adj[u].end(), pe[u]));
			}
			for(auto &id: adj[u]){
				int v = g(u, id);
				pv[v] = u;
				pe[v] = id;
				depth[v] = depth[u] + 1;
				root_of[v] = root_of[u];
				next[v] = u;
				self(self, v);
				size[u] += size[v];
				if(size[v] > size[g(u, adj[u][0])]) swap(id, adj[u][0]);
			}
			if(!adj[u].empty()) prev[u] = prev[g(u, adj[u][0])];
		};
		auto dfs_hld = [&](auto self, int u)->void{
			pos[u] = (int)order.size();
			order.push_back(u);
			if(!adj[u].empty()){
				int hv = g(u, adj[u][0]);
				for(auto id: adj[u]){
					int v = g(u, id);
					next[v] = (v == hv ? next[u] : v);
					self(self, v);
				}
			}
			end[u] = (int)order.size();
		};
		for(auto r: src){
			if(was[r] == attempt) continue;
			pv[r] = pe[r] = -1;
			depth[r] = 0;
			root_of[r] = r;
			root.push_back(r);
			next[r] = r;
			dfs_init(dfs_init, r);
			dfs_hld(dfs_hld, r);
		}
	}
	// Check if u is visited during the last build call
	bool visited(int u) const{
		assert(0 <= u && u < n);
		return was[u] == attempt;
	}
	// O(1)
	bool ancestor_of(int u, int v) const{
		return pos[u] <= pos[v] && end[v] <= end[u];
	}
	int lca(int u, int v) const{
		for(; next[u] != next[v]; v = pv[next[v]]) if(depth[next[u]] > depth[next[v]]) swap(u, v);
		return depth[u] < depth[v] ? u : v;
	}
	int steps(int u, int v, int w = -1) const{
		return depth[u] + depth[v] - 2 * depth[~w ? w : lca(u, v)];
	}
	// f reads the position in the data structure
	// One application of f
	void access_node(int u, auto f) const{
		f(pos[u]);
	}
	// One application of f
	template<int VALS_IN_EDGES = 0>
	void access_subtree(int u, auto f) const{
		f(pos[u] + VALS_IN_EDGES, end[u]);
	}
	// f(left, right, (left->right ?))
	// O(log(n)) applications of f
	template<int VALS_IN_EDGES = 0>
	void access_path(int u, int v, auto f) const{
		bool dir = true;
		for(; next[u] != next[v]; v = pv[next[v]]){
			if(depth[next[u]] > depth[next[v]]) swap(u, v), dir = !dir;
			f(pos[next[v]], pos[v] + 1, dir);
		}
		if(depth[u] > depth[v]) swap(u, v), dir = !dir;
		f(pos[u] + VALS_IN_EDGES, pos[v] + 1, dir);
	}
	// Pair of indices {l, r} in the data structure. resr is reversed(v->next[v], pv[next[v]]-> ...)
	// O(log(n))
	auto get_path(int u, int v) const{
		vector<pair<int, int>> resl, resr;
		access_path(u, v, [&](int l, int r, bool dir){ (dir ? resl : resr).push_back({l, r}); });
		return pair{resl, resr};
	}
};

// Specialization of sparse_table
// Range min query by default. Set cmp = greater for max query
template<class T, class Compare = less<>>
struct range_minmax_query_solver{
	int n;
	vector<vector<T>> data;
	Compare cmp;
	T T_id;
	range_minmax_query_solver(){ }
	// O(n * log(n))
	range_minmax_query_solver(const vector<T> &a, Compare cmp = less<>(), T T_id = numeric_limits<T>::max()): n((int)a.size()), cmp(cmp), T_id(T_id), data({a}){
		for(auto p = 1, i = 1; p << 1 <= n; p <<= 1, ++ i){
			data.emplace_back(n - (p << 1) + 1);
			for(auto j = 0; j < (int)data[i].size(); ++ j) data[i][j] = cmp(data[i - 1][j], data[i - 1][j + p]) ? data[i - 1][j] : data[i - 1][j + p];
		}
	}
	// O(1)
	T query(int l, int r) const{
		assert(0 <= l && l <= r && r <= n);
		if(l == r) return T_id;
		int d = __lg(r - l);
		return cmp(data[d][l], data[d][r - (1 << d)]) ? data[d][l] : data[d][r - (1 << d)];
	}
};

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	int n, m;
	long long th;
	cin >> n >> m >> th;
	vector<tuple<int, int, int>> edge(m);
	vector<int> profit(m);
	for(auto i = 0; i < m; ++ i){
		auto &[u, v, w] = edge[i];
		cin >> u >> v >> w >> profit[i], -- u, -- v;
	}
	auto mst = minimum_spanning_forest(n, edge);
	long long mst_cost = 0;
	vector<int> on_mst(m);
	int res = 0;
	graph<int> g(n);
	for(auto id: mst){
		mst_cost += get<2>(edge[id]);
		on_mst[id] = true;
		res = max(res, profit[id]);
		auto [u, v, w] = edge[id];
		g.link(u, v, w);
	}
	if(mst_cost > th){
		cout << "-1\n";
		return 0;
	}
	heavy_light_decomposition hld;
	hld.init(n);
	hld.build(g, {0});
	vector<int> init(n);
	for(auto i = 1; i < n; ++ i){
		init[i] = g.edge[hld.pe[hld.order[i]]].cost;
	}
	range_minmax_query_solver rmaxq(init, greater<>(), numeric_limits<int>::min());
	vector<int> order(m);
	iota(order.begin(), order.end(), 0);
	ranges::sort(order, [&](int i, int j){ return profit[i] > profit[j]; });
	for(auto i: order){
		if(on_mst[i] || profit[i] < res){
			continue;
		}
		auto [u, v, w] = edge[i];
		int maxv = 0;
		hld.access_path<true>(u, v, [&](int l, int r, bool){ maxv = max(maxv, rmaxq.query(l, r)); });
		if(mst_cost + get<2>(edge[i]) - maxv <= th){
			cout << profit[i] << "\n";
			return 0;
		}
	}
	cout << res << "\n";
	return 0;
}

/*

*/

yukicoder

結果

テストケース

ソースコード