Submission #917370

#	Time	Username	Problem	Language	Result	Execution time	Memory
917370		NK_	Graph (BOI20_graph)	C++17	34 / 100	72 ms	3164 KiB

Graph

// Success consists of going from failure to failure without loss of enthusiasm
#include <bits/stdc++.h>

using namespace std;

#define nl '\n'
#define pb push_back
#define f first
#define s second
#define mp make_pair
#define sz(x) int(x.size())

template<class T> using V = vector<T>;
using pi = pair<int, int>;
using vi = V<int>;
using vpi = V<pi>;
using db = long double;

const int INF = 1e9;
const int B = 1e8;
const db EPS = 1e-11;
const db BEPS = 1e-8;

int main() {
	cin.tie(0)->sync_with_stdio(0);
	
	int N, M; cin >> N >> M;

	V<vpi> adj(N); for(int i = 0; i < M; i++) {
		int u, v, w; cin >> u >> v >> w; --u, --v;
		adj[u].pb(mp(v, w));
		adj[v].pb(mp(u, w));
	}


	auto C = [&](pi p, int w) {
		// cout << p.f << " " << p.s << " " << w << endl;
		return mp(w - p.f, -p.s);
	};

	cout << fixed << setprecision(10);

	vi vis(N), COMP; V<set<pi>> S(N);
	function<void(int)> dfs = [&](int u) {
		vis[u] = 1; COMP.pb(u);
		pi p = *begin(S[u]);
		// cout << u << " => " << p.f << " " << p.s << endl;
		for(auto& e : adj[u]) {
			int v, w; tie(v, w) = e;
			// cout << v << " " << w << endl;

			S[v].insert(C(p, w));
			if (!vis[v]) dfs(v);
		}
	};

	V<db> ans(N, INF); 
	function<void(int)> get = [&](int u) {
		// cout << u << endl;
		for(auto& e : adj[u]) {
			int v, w; tie(v, w) = e;
			// cout << u << " => " << v << endl;
			// cout << ans[u] << " -> " << ans[v] << endl;
			db x = w - ans[u];
			if (ans[v] > B) {
				ans[v] = x; get(v);
			} else {
				if (abs(ans[v] - x) > EPS) {
					cout << "NO" << nl;
					exit(0-0);
				}
			}	
		}
	};

	for(int r = 0; r < N; r++) if (!vis[r]) {
		COMP = {}; S[r].insert(mp(0, 1)); dfs(r);
		// cout << endl << endl;

		db x = INF; int R = -1;
		for(auto& i : COMP) if (sz(S[i]) >= 2) {
			// cout << i << endl;
			vi pos, neg; for(auto& p : S[i]) {
				// cout << p.f << " " << p.s << endl;
				if (p.s == -1) neg.pb(p.f);
				else pos.pb(p.f);
			}

			if (max(sz(pos), sz(neg)) > 1) {
				cout << "NO" << nl;
				exit(0-0);
			}

			x = db(pos.back() + neg.back()) / db(2);
			// cout << x << endl;
			R = i;
			// cout << "DONE" << endl;
			break;
		}

		if (R == -1) {
			// cout << "R: " << r << endl;
			db bst = -INF, val = INF;
			auto check = [&](db x) {
				ans[r] = x; get(r);
				db cost = 0; for(auto& i : COMP) cost += abs(ans[i]), ans[i] = INF;
				// cout << x << " => " << cost << endl;
				if (cost + EPS < val) bst = x, val = cost;
				return cost;
			};

			db lo = -INF, hi = INF;
			for(int t = 0; t < 100; t++) {
				db mid = (lo + hi) / 2;
				if (check(mid) < check(mid + BEPS)) hi = mid;
				else lo = mid;
			}

			// cout << bst << endl;
			ans[r] = bst; get(r);
		} else {
			ans[R] = x; get(R);
		}
	}

	cout << "YES" << nl;
	for(auto& x : ans) cout << x << " ";
	cout << nl;
	
	exit(0-0);
}

• Subtask 1: 5 / 5
• Subtask 2: 12 / 12
• Subtask 3: 17 / 17
• Subtask 4: 0 / 24
• Subtask 5: 0 / 42