Submission #938642

#	Time	Username	Problem	Language	Result	Execution time	Memory
938642		Gromp15	Graph (BOI20_graph)	C++17	100 / 100	116 ms	37204 KiB

Graph

#include <bits/stdc++.h>
#define ll long long
#define ar array
#define db double
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define rint(l, r) uniform_int_distribution<int>(l, r)(rng)
template<typename T> bool ckmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }
template<typename T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
void test_case() {
	int n, m;
	cin >> n >> m;
	vector<vector<ar<int, 2>>> adj(n+1);
	vector<ar<int, 3>> E;
	for (int i = 0; i < m; i++) {
		int x, y, w;
		cin >> x >> y >> w;
		E.push_back({x, y, w});
		adj[x].push_back({y, 2*w});
		adj[y].push_back({x, 2*w});
	}
	vector<int> ans(n+1);
	vector<bool> vis2(n+1);
	vector<int> depth(n+1), val(n+1);
	for (int v = 1; v <= n; v++) if (!vis2[v]) {
		ll tot_sum = 0;
		vector<ar<int, 3>> edges;
		vector<int> comp;
		auto dfs = [&](auto&& s, int v, int cur) -> void {
			vis2[v] = 1;
			comp.emplace_back(v);
			val[v] = cur;
			tot_sum += cur;
			for (auto [u, w] : adj[v]) {
				edges.push_back({v, u, w});
				if (!vis2[u]) {
					depth[u] = depth[v] + 1;
					s(s, u, w - cur);
				}
			}
		};
		dfs(dfs, v, 0);
		// val[x] + val[y] +/- 2x = 2*w
		// tot_sum + totx = final val
		int need; bool f = 1;
		for (auto [x, y, w] : edges) {
			if ((depth[x] + depth[y]) & 1) { // they must have the same val
				if (val[x] + val[y] != w) {
					cout << "NO\n"; return;
				}
			}
			else {
				// val[x] + val[y] +/- 2x = w
				int other = (w - val[x] - val[y]) * (depth[x] & 1 ? -1 : 1);
				assert(other % 2 == 0);
				other /= 2;
				if (f) {
					need = other, f = 0;
				}
				else {
					if (need != other) {
						cout << "NO\n"; return;
					}
				}
			}
		}
		if (f) {
			// choose x that minimizes tot_sum + tot*x
			int N = sz(comp);
			vector<ll> each(4 * N + 1), each2(4 * N + 1);
			auto add = [&](int L, int R, int X, int del) { // a[L...R] += x + del
				// X + 0
				// X + del
				// X + 2*del
				// X + ...
				each[L+2*N] += X;
				if (L+2*N+1 <= 4*N) {
					each2[L+2*N+1] += del;
				}
				if (R+1 <= 2*N) {
					each[R+2*N+1] -= X;
					each2[R+2*N+1] -= del;
					each[R+2*N+1] -= (R - L) * del;
				}
				/*
				for (int i = L + 2*N; i <= R + 2*N; i++) {
					each[i] += X + (i - (L + 2*N)) * del;
				}
				*/
			};
			for (int u : comp) {
				if (depth[u] & 1) {
					add(-2*N, val[u], val[u] + 2*N, -1);
					if (val[u] + 1 <= 2*N) add(val[u] + 1, 2*N, 1, 1);
				}
				else {
					add(-2*N, -val[u], -val[u] + 2*N, -1);
					if (-val[u] + 1 <= 2*N) add(-val[u] + 1, 2*N, 1, 1);
				}
			}
			for (int i = 1; i <= 4*N; i++) each[i] += each[i-1], each2[i] += each2[i-1];
			for (int i = 1; i <= 4*N; i++) each2[i] += each2[i-1];
			for (int i = 0; i <= 4*N; i++) {
				each[i] += each2[i];
			}
			int who = (min_element(each.begin(), each.end()) - each.begin()) - 2 * N;
			for (int u : comp) {
				ans[u] = val[u] + who * (depth[u] & 1 ? -1 : 1);
			}
		}
		else {
			// x is set
			for (int u : comp) {
				ans[u] = val[u] + need * (depth[u] & 1 ? -1 : 1);
			}
		}
	}
	cout << "YES\n";
	cout << fixed << setprecision(1);

	for (int i = 1; i <= n; i++) cout << (db)ans[i] / 2 << " \n"[i==n];



}
int main() {
    cin.tie(0)->sync_with_stdio(0);
    int t = 1;
//    cin >> t;
    while (t--) test_case();
}

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