#644320 (C++17) No.1473 おでぶなおばけさん

• 問題: No.1473 おでぶなおばけさん
• ユーザー: nok0
• 提出日時: 2021-04-04 10:06:52
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: TLE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 18,169 bytes
• コンパイル時間: 2,561 ms
• コンパイル使用メモリ: 219,804 KB
• 最終ジャッジ日時: 2025-01-20 11:01:17
• ジャッジサーバーID （参考情報）: judge5 / judge5

ファイルパターン	結果
sample	AC * 2
other	AC * 44 TLE * 3

ソースコード

#include <bits/stdc++.h>
using namespace std;

#pragma region Graph Graph
#include <algorithm>
#include <cassert>
#include <deque>
#include <iostream>
#include <queue>
#include <vector>

struct Edge {
	int to;
	long long cost;
	Edge() = default;
	Edge(int to_, long long cost_) : to(to_), cost(cost_) {}
	bool operator<(const Edge &a) const { return cost < a.cost; }
	bool operator>(const Edge &a) const { return cost > a.cost; }
	friend std::ostream &operator<<(std::ostream &s, Edge &a) {
		s << "to: " << a.to << ", cost: " << a.cost;
		return s;
	}
};

class Graph {
	std::vector<std::vector<Edge>> edges;

public:
	inline const std::vector<Edge> &operator[](int k) const { return edges[k]; }
	inline std::vector<Edge> &operator[](int k) { return edges[k]; }

	int size() const { return edges.size(); }
	void resize(const int n) { edges.resize(n); }

	Graph() = default;
	Graph(int n) : edges(n) {}
	Graph(int n, int e, bool weight = 0, bool directed = 0, int idx = 1) : edges(n) { input(e, weight, directed, idx); }
	const long long INF = 3e18;

	void input(int e = -1, bool weight = 0, bool directed = false, int idx = 1) {
		if(e == -1) e = size() - 1;
		while(e--) {
			int u, v;
			long long cost = 1;
			std::cin >> u >> v;
			if(weight) std::cin >> cost;
			u -= idx, v -= idx;
			edges[u].emplace_back(v, cost);
			if(!directed) edges[v].emplace_back(u, cost);
		}
	}

	void add_edge(int u, int v, long long cost = 1, bool directed = false, int idx = 0) {
		u -= idx, v -= idx;
		edges[u].emplace_back(v, cost);
		if(!directed) edges[v].emplace_back(u, cost);
	}

	// Ο(V+E)
	std::vector<long long> bfs(int s) {
		std::vector<long long> dist(size(), INF);
		std::queue<int> que;
		dist[s] = 0;
		que.push(s);
		while(!que.empty()) {
			int v = que.front();
			que.pop();
			for(auto &e : edges[v]) {
				if(dist[e.to] != INF) continue;
				dist[e.to] = dist[v] + e.cost;
				que.push(e.to);
			}
		}
		return dist;
	}

	// Ο(V+E)
	// constraint: cost of each edge is zero or one
	std::vector<long long> zero_one_bfs(int s) {
		std::vector<long long> dist(size(), INF);
		std::deque<int> deq;
		dist[s] = 0;
		deq.push_back(s);
		while(!deq.empty()) {
			int v = deq.front();
			deq.pop_front();
			for(auto &e : edges[v]) {
				assert(0LL <= e.cost and e.cost < 2LL);
				if(e.cost and dist[e.to] > dist[v] + 1) {
					dist[e.to] = dist[v] + 1;
					deq.push_back(e.to);
				} else if(!e.cost and dist[e.to] > dist[v]) {
					dist[e.to] = dist[v];
					deq.push_front(e.to);
				}
			}
		}
		return dist;
	}

	// Ο((E+V)logV)
	// cannot reach: INF
	std::vector<long long> dijkstra(int s) {  // verified
		std::vector<long long> dist(size(), INF);
		const auto compare = [](const std::pair<long long, int> &a, const std::pair<long long, int> &b) { return a.first > b.first; };
		std::priority_queue<std::pair<long long, int>, std::vector<std::pair<long long, int>>, decltype(compare)> que{compare};
		dist[s] = 0;
		que.emplace(0, s);
		while(!que.empty()) {
			std::pair<long long, int> p = que.top();
			que.pop();
			int v = p.second;
			if(dist[v] < p.first) continue;
			for(auto &e : edges[v]) {
				if(dist[e.to] > dist[v] + e.cost) {
					dist[e.to] = dist[v] + e.cost;
					que.emplace(dist[e.to], e.to);
				}
			}
		}
		return dist;
	}

	// Ο(VE)
	// cannot reach: INF
	// negative cycle: -INF
	std::vector<long long> bellman_ford(int s) {  // verified
		int n = size();
		std::vector<long long> res(n, INF);
		res[s] = 0;
		for(int loop = 0; loop < n - 1; loop++) {
			for(int v = 0; v < n; v++) {
				if(res[v] == INF) continue;
				for(auto &e : edges[v]) {
					res[e.to] = std::min(res[e.to], res[v] + e.cost);
				}
			}
		}
		std::queue<int> que;
		std::vector<int> chk(n);
		for(int v = 0; v < n; v++) {
			if(res[v] == INF) continue;
			for(auto &e : edges[v]) {
				if(res[e.to] > res[v] + e.cost and !chk[e.to]) {
					que.push(e.to);
					chk[e.to] = 1;
				}
			}
		}
		while(!que.empty()) {
			int now = que.front();
			que.pop();
			for(auto &e : edges[now]) {
				if(!chk[e.to]) {
					chk[e.to] = 1;
					que.push(e.to);
				}
			}
		}
		for(int i = 0; i < n; i++)
			if(chk[i]) res[i] = -INF;
		return res;
	}

	// Ο(V^3)
	std::vector<std::vector<long long>> warshall_floyd() {  // verified
		int n = size();
		std::vector<std::vector<long long>> dist(n, std::vector<long long>(n, INF));
		for(int i = 0; i < n; i++) dist[i][i] = 0;
		for(int i = 0; i < n; i++)
			for(auto &e : edges[i]) dist[i][e.to] = std::min(dist[i][e.to], e.cost);
		for(int k = 0; k < n; k++)
			for(int i = 0; i < n; i++) {
				if(dist[i][k] == INF) continue;
				for(int j = 0; j < n; j++) {
					if(dist[k][j] == INF) continue;
					dist[i][j] = std::min(dist[i][j], dist[i][k] + dist[k][j]);
				}
			}
		return dist;
	}

	// Ο(V) (using DFS)
	// if a directed cycle exists, return {}
	std::vector<int> topological_sort() {  // verified
		std::vector<int> res;
		int n = size();
		std::vector<int> used(n, 0);
		bool not_DAG = false;
		auto dfs = [&](auto self, int k) -> void {
			if(not_DAG) return;
			if(used[k]) {
				if(used[k] == 1) not_DAG = true;
				return;
			}
			used[k] = 1;
			for(auto &e : edges[k]) self(self, e.to);
			used[k] = 2;
			res.push_back(k);
		};
		for(int i = 0; i < n; i++) dfs(dfs, i);
		if(not_DAG) return std::vector<int>{};
		std::reverse(res.begin(), res.end());
		return res;
	}

	bool is_DAG() { return !topological_sort().empty(); }  // verified

	// Ο(V)
	// array of the distance from each vertex to the most distant vertex
	std::vector<long long> height() {  // verified
		auto vec1 = bfs(0);
		int v1 = -1, v2 = -1;
		long long dia = -1;
		for(int i = 0; i < int(size()); i++)
			if(dia < vec1[i]) dia = vec1[i], v1 = i;
		vec1 = bfs(v1);
		dia = -1;
		for(int i = 0; i < int(size()); i++)
			if(dia < vec1[i]) dia = vec1[i], v2 = i;
		auto vec2 = bfs(v2);
		for(int i = 0; i < int(size()); i++) {
			if(vec1[i] < vec2[i]) vec1[i] = vec2[i];
		}
		return vec1;
	}

	// O(V+E)
	// vector<(int)(0 or 1)>
	// if it is not bipartite, return {}
	std::vector<int> bipartite_grouping() {
		std::vector<int> colors(size(), -1);
		auto dfs = [&](auto self, int now, int col) -> bool {
			colors[now] = col;
			for(auto &e : edges[now]) {
				if(col == colors[e.to]) return false;
				if(colors[e.to] == -1 and !self(self, e.to, !col)) return false;
			}
			return true;
		};
		for(int i = 0; i < int(size()); i++)
			if(!colors[i] and !dfs(dfs, i, 0)) return std::vector<int>{};
		return colors;
	}

	bool is_bipartite() { return !bipartite_grouping().empty(); }

	// Ο(V+E)
	// ((v1, v2), diameter)
	std::pair<std::pair<int, int>, long long> diameter() {  // verified
		auto vec = bfs(0);
		int v1 = -1, v2 = -1;
		long long dia = -1;
		for(int i = 0; i < int(size()); i++)
			if(dia < vec[i]) dia = vec[i], v1 = i;
		vec = bfs(v1);
		dia = -1;
		for(int i = 0; i < int(size()); i++)
			if(dia < vec[i]) dia = vec[i], v2 = i;
		std::pair<std::pair<int, int>, long long> res = {{v1, v2}, dia};
		return res;
	}

	// Ο(ElogV)
	long long prim() {  // verified
		long long res = 0;
		std::priority_queue<Edge, std::vector<Edge>, std::greater<Edge>> que;
		for(auto &e : edges[0]) que.push(e);
		std::vector<int> chk(size());
		chk[0] = 1;
		int cnt = 1;
		while(cnt < size()) {
			auto e = que.top();
			que.pop();
			if(chk[e.to]) continue;
			cnt++;
			res += e.cost;
			chk[e.to] = 1;
			for(auto &e2 : edges[e.to]) que.push(e2);
		}
		return res;
	}

	// Ο(ElogE)
	long long kruskal() {  // verified
		std::vector<std::tuple<int, int, long long>> Edges;
		for(int i = 0; i < int(size()); i++)
			for(auto &e : edges[i]) Edges.emplace_back(i, e.to, e.cost);
		std::sort(Edges.begin(), Edges.end(), [](const std::tuple<int, int, long long> &a, const std::tuple<int, int, long long> &b) {
			return std::get<2>(a) < std::get<2>(b);
		});
		std::vector<int> uf_data(size(), -1);
		auto root = [&uf_data](auto self, int x) -> int {
			if(uf_data[x] < 0) return x;
			return uf_data[x] = self(self, uf_data[x]);
		};
		auto unite = [&uf_data, &root](int u, int v) -> bool {
			u = root(root, u), v = root(root, v);
			if(u == v) return false;
			if(uf_data[u] > uf_data[v]) std::swap(u, v);
			uf_data[u] += uf_data[v];
			uf_data[v] = u;
			return true;
		};
		long long ret = 0;
		for(auto &e : Edges)
			if(unite(std::get<0>(e), std::get<1>(e))) ret += std::get<2>(e);
		return ret;
	}

	// O(V)
	std::vector<int> centroid() {
		int n = size();
		std::vector<int> centroid, sz(n);
		auto dfs = [&](auto self, int now, int per) -> void {
			sz[now] = 1;
			bool is_centroid = true;
			for(auto &e : edges[now]) {
				if(e.to != per) {
					self(self, e.to, now);
					sz[now] += sz[e.to];
					if(sz[e.to] > n / 2) is_centroid = false;
				}
			}
			if(n - sz[now] > n / 2) is_centroid = false;
			if(is_centroid) centroid.push_back(now);
		};
		dfs(dfs, 0, -1);
		return centroid;
	}

	// Ο(V+E)
	// directed graph from root to leaf
	Graph root_to_leaf(int root = 0) {
		Graph res(size());
		std::vector<int> chk(size(), 0);
		chk[root] = 1;
		auto dfs = [&](auto self, int now) -> void {
			for(auto &e : edges[now]) {
				if(chk[e.to] == 1) continue;
				chk[e.to] = 1;
				res.add_edge(now, e.to, e.cost, 1, 0);
				self(self, e.to);
			}
		};
		dfs(dfs, root);
		return res;
	}

	// Ο(V+E)
	// directed graph from leaf to root
	Graph leaf_to_root(int root = 0) {
		Graph res(size());
		std::vector<int> chk(size(), 0);
		chk[root] = 1;
		auto dfs = [&](auto self, int now) -> void {
			for(auto &e : edges[now]) {
				if(chk[e.to] == 1) continue;
				chk[e.to] = 1;
				res.add_edge(e.to, now, e.cost, 1, 0);
				self(self, e.to);
			}
		};
		dfs(dfs, root);
		return res;
	}

	// long long Chu_Liu_Edmonds(int root = 0) {}
};

struct tree_doubling {
private:
	std::vector<std::vector<int>> parent;
	std::vector<int> depth;
	std::vector<long long> dist;
	int max_jump = 1;

	void build() {
		for(int i = 0; i < max_jump - 1; i++) {
			for(int v = 0; v < (int)dist.size(); v++) {
				if(parent[i][v] == -1)
					parent[i + 1][v] = -1;
				else
					parent[i + 1][v] = parent[i][parent[i][v]];
			}
		}
	}

public:
	tree_doubling() = default;
	tree_doubling(const Graph &g, const int root = 0) : dist(g.size()), depth(g.size()) {
		int n = g.size();
		while((1 << max_jump) < n) max_jump++;
		parent.assign(max_jump, std::vector<int>(n, -1));
		auto dfs = [&](auto self, int now, int per, int d, long long cost) -> void {
			parent[0][now] = per;
			depth[now] = d;
			dist[now] = cost;
			for(auto &e : g[now])
				if(e.to != per) self(self, e.to, now, d + 1, cost + e.cost);
		};
		dfs(dfs, root, -1, 0, 0LL);
		build();
	}

	int lowest_common_ancestor(int u, int v) {
		if(depth[u] < depth[v]) std::swap(u, v);
		int k = parent.size();
		for(int i = 0; i < k; i++)
			if((depth[u] - depth[v]) >> i & 1) u = parent[i][u];
		if(u == v) return u;
		for(int i = k - 1; i >= 0; i--)
			if(parent[i][u] != parent[i][v]) u = parent[i][u], v = parent[i][v];
		return parent[0][u];
	}

	long long length_of_path(const int u, const int v) { return dist[u] + dist[v] - dist[lowest_common_ancestor(u, v)] * 2; }

	int level_ancestor(int v, int level) {
		assert(level >= 0);
		for(int jump = 0; jump < max_jump and level; jump++) {
			if(level & 1) v = parent[jump][v];
			level >>= 1;
		}
		return v;
	}
};

struct strongly_connected_components {
private:
	enum { CHECKED = -1,
		   UNCHECKED = -2 };
	const Graph &graph_given;
	Graph graph_reversed;
	std::vector<int> order, group_number; /* at the beginning of the building, 'group_number' is used as 'checked' */

	void dfs(int now) {
		if(group_number[now] != UNCHECKED) return;
		group_number[now] = CHECKED;
		for(auto &e : graph_given[now]) dfs(e.to);
		order.push_back(now);
	}

	void rdfs(int now, int group_count) {
		if(group_number[now] != UNCHECKED) return;
		group_number[now] = group_count;
		for(auto &e : graph_reversed[now]) rdfs(e.to, group_count);
	}

	void build(bool create_compressed_graph) {
		for(int i = 0; i < (int)graph_given.size(); i++) dfs(i);
		reverse(order.begin(), order.end());
		group_number.assign(graph_given.size(), UNCHECKED);
		int group = 0;
		for(auto &i : order)
			if(group_number[i] == UNCHECKED) rdfs(i, group), group++;
		graph_compressed.resize(group);
		groups.resize(group);
		for(int i = 0; i < (int)graph_given.size(); i++) groups[group_number[i]].push_back(i);
		if(create_compressed_graph) {
			std::vector<int> edges(group, -1);
			for(int i = 0; i < group; i++)
				for(auto &vertex : groups[i])
					for(auto &e : graph_given[vertex])
						if(group_number[e.to] != i and edges[group_number[e.to]] != i) {
							edges[group_number[e.to]] = i;
							graph_compressed[i].emplace_back(group_number[e.to], 1);
						}
		}
		return;
	}

public:
	std::vector<std::vector<int>> groups;
	Graph graph_compressed;

	strongly_connected_components(const Graph &g_, bool create_compressed_graph = false)
	  : graph_given(g_), graph_reversed(g_.size()), group_number(g_.size(), UNCHECKED) {
		for(size_t i = 0; i < g_.size(); i++)
			for(auto &e : graph_given[i]) graph_reversed[e.to].emplace_back(i, 1);
		build(create_compressed_graph);
	}

	const int &operator[](const int k) { return group_number[k]; }
};

struct low_link {
private:
	const Graph &graph_given;
	int order_next;

	void build() {
		int n = graph_given.size();
		order.resize(n, -1);
		low.resize(n);
		order_next = 0;
		for(int i = 0; i < n; i++)
			if(order[i] == -1) dfs(i);
	}

	void dfs(int now, int par = -1) {
		low[now] = order[now] = order_next++;
		bool is_articulation = false;
		int cnt = 0, cnt_par = 0;
		for(const auto &ed : graph_given[now]) {
			const int &nxt = ed.to;
			if(order[nxt] == -1) {
				cnt++;
				dfs(nxt, now);
				if(order[now] < low[nxt]) bridge.push_back(std::minmax(now, nxt));
				if(order[now] <= low[nxt]) is_articulation = true;
				low[now] = std::min(low[now], low[nxt]);
			} else if(nxt != par or cnt_par++ == 1) {
				low[now] = std::min(low[now], order[nxt]);
			}
		}
		if(par == -1 and cnt < 2) is_articulation = false;
		if(is_articulation) articulation.push_back(now);
		return;
	}

public:
	std::vector<int> order, low, articulation;
	std::vector<std::pair<int, int>> bridge;
	low_link() = default;
	low_link(const Graph &g_) : graph_given(g_) { build(); }
};

struct two_edge_connected_components {
private:
	const Graph &graph_given;
	int group_next;
	low_link li;
	std::vector<int> group_number;

	void build(bool create_compressed_graph) {
		int n = graph_given.size();
		group_number.resize(n, -1);
		group_next = 0;
		for(int i = 0; i < n; i++)
			if(group_number[i] == -1) dfs(i);
		groups.resize(group_next);
		for(int i = 0; i < graph_given.size(); i++) groups[group_number[i]].push_back(i);

		if(create_compressed_graph) {
			graph_compressed.resize(group_next);
			for(const auto &[u, v] : li.bridge) {
				int x = group_number[u], y = group_number[v];
				graph_compressed.add_edge(x, y);
			}
		}
	}

	void dfs(int now, int par = -1) {
		if(par != -1 and li.order[par] >= li.low[now])
			group_number[now] = group_number[par];
		else
			group_number[now] = group_next++;
		for(const auto &e : graph_given[now])
			if(group_number[e.to] == -1) dfs(e.to, now);
	}

public:
	Graph graph_compressed;
	std::vector<std::vector<int>> groups;
	two_edge_connected_components(const Graph &g_, bool create_compressed_graph = false)
	  : graph_given(g_), li(g_) {
		build(create_compressed_graph);
	}

	const int &operator[](const int k) { return group_number[k]; }
};

struct heavy_light_decomposition {
public:
	std::vector<int> sz, in, out, head, rev, par;

private:
	Graph &g;

	void dfs_sz(int v, int p = -1) {
		par[v] = p;
		if(!g[v].empty() and g[v].front().to == p) std::swap(g[v].front(), g[v].back());
		for(auto &e : g[v]) {
			if(e.to == p) continue;
			dfs_sz(e.to, v);
			sz[v] += sz[e.to];
			if(sz[g[v].front().to] < sz[e.to]) std::swap(g[v].front(), e);
		}
	}

	void dfs_hld(int v, int &t, int p = -1) {
		in[v] = t++;
		rev[in[v]] = v;
		for(auto &e : g[v]) {
			if(e.to == p) continue;
			head[e.to] = (g[v].front().to == e.to ? head[v] : e.to);
			dfs_hld(e.to, t, v);
		}
		out[v] = t;
	}

	void build(int root = 0) {
		dfs_sz(root);
		int t = 0;
		head[root] = root;
		dfs_hld(root, t);
	}

public:
	heavy_light_decomposition(Graph &g_, int root = 0) : g(g_) {
		int n = g.size();
		sz.resize(n, 1);
		in.resize(n);
		out.resize(n);
		head.resize(n);
		rev.resize(n);
		par.resize(n);
		build(root);
	}

	int level_ancestor(int v, int level) {
		while(true) {
			int u = head[v];
			if(in[v] - level >= in[u]) return rev[in[v] - level];
			level -= in[v] - in[u] + 1;
			v = par[u];
		}
	}

	int lowest_common_ancestor(int u, int v) {
		for(;; v = par[head[v]]) {
			if(in[u] > in[v]) std::swap(u, v);
			if(head[u] == head[v]) return u;
		}
	}

	// u, v: vertex, unit: unit, q: query on a path, f: binary operation ((T, T) -> T)
	template <typename T, typename Q, typename F>
	T query(int u, int v, const T &unit, const Q &q, const F &f, bool edge = false) {
		T l = unit, r = unit;
		for(;; v = par[head[v]]) {
			if(in[u] > in[v]) std::swap(u, v), std::swap(l, r);
			if(head[u] == head[v]) break;
			l = f(q(in[head[v]], in[v] + 1), l);
		}
		return f(f(q(in[u] + edge, in[v] + 1), l), r);
	}

	// u, v: vertex, q: update query
	template <typename Q>
	void add(int u, int v, const Q &q, bool edge = false) {
		for(;; v = par[head[v]]) {
			if(in[u] > in[v]) std::swap(u, v);
			if(head[u] == head[v]) break;
			q(in[head[v]], in[v] + 1);
		}
		q(in[u] + edge, in[v] + 1);
	}

	std::pair<int, int> subtree(int v, bool edge = false) { return std::pair<int, int>(in[v] + edge, out[v]); }
};
#pragma endregion

int min_cost;
int main() {
	int n, m;
	cin >> n >> m;
	vector<int> s(m), t(m), d(m);
	for(int i = 0; i < m; i++)
		cin >> s[i] >> t[i] >> d[i], --s[i], --t[i];

	auto judge = [&](int mid) {
		Graph G(n);
		for(int i = 0; i < m; i++)
			if(d[i] >= mid) G.add_edge(s[i], t[i]);
		auto dist = G.bfs(0)[n - 1];
		if(dist < G.INF) {
			min_cost = dist;
			return true;
		} else
			return false;
	};

	int ok = 0, ng = 2000000000, mid;
	while(mid = (ok + ng) / 2, abs(ok - ng) > 1) (judge(mid) ? ok : ng) = mid;

	cout << ok << " " << min_cost << endl;

	return 0;
}