Submission #729790

#	Time	Username	Problem	Language	Result	Execution time	Memory
729790		WonderfulWhale	Graph (BOI20_graph)	C++17	100 / 100	218 ms	38944 KiB

Graph

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

#define int int64_t
#define pb push_back
#define st first
#define nd second
#define pii pair<int, int>
#define double long double
#define pdd pair<double, double>
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()

const int MAXN = 100009;
const double eps = 1e-9;

bool f(double a, double b) {
	return abs(a-b)<eps; 
}

vector<pair<int, double>> G[MAXN];
bool vis[MAXN];
pdd val[MAXN];
double ans[MAXN];

vector<int> v;
void dfs(int x) {
	v.pb(x);
	vis[x] = true;
	for(auto [y, d]:G[x]) {
		if(vis[y]) continue;
		val[y] = {-val[x].st, d-val[x].nd};
		dfs(y);
	}
}

int32_t main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);

	cout << fixed;
	cout.precision(10);

	int n, m;
	cin >> n >> m;
	for(int i=0;i<m;i++) {
		int a, b, c;
		cin >> a >> b >> c;
		G[a].pb({b, c});
		G[b].pb({a, c});
	}
	for(int i=1;i<=n;i++) {
		if(vis[i]) continue;
		v.clear();
		val[i] = {1, 0};
		dfs(i);
		pair<bool, double> forced = {false, 0};
		for(int x:v) {
			for(auto [y, d]:G[x]) {
				if(f(val[x].st+val[y].st, 0)) {
					if(!f(val[x].nd+val[y].nd, d)) {
						cout << "NO\n";
						return 0;
					}
				} else {
					double nx = (d-val[x].nd-val[y].nd)/(val[x].st+val[y].st);
					if(forced.st) {
						if(!f(forced.nd, nx)) {
							cout << "NO\n";
							return 0;
						}
					} else {
						forced = {true, nx};
					}
	 			}
			}
		}
		if(forced.st) {
			for(int x:v) {
				ans[x] = forced.nd*val[x].st+val[x].nd;
			}
			continue;
		}
		pdd sum = {0, 0};
		vector<pair<double, pdd>> V;
		for(int x:v) {
			int root = -val[x].nd/val[x].st;
			sum.st -= 1;
			if(val[x].st>0) {
				sum.nd -= val[x].nd;
				V.pb({root, {2, val[x].nd*2}});
			} else {
				sum.nd += val[x].nd;
				V.pb({root, {2, -val[x].nd*2}});
			}
		}
		sort(all(V));
		if(sum.st>0) {
			cout << "NO\n";
			return 0;
		}
		pdd res = {sum.st*V[0].st+sum.nd, V[0].st};
		for(auto x:V) {
			sum.st += x.nd.st;
			sum.nd += x.nd.nd;
			res = min(res, {sum.st*x.st+sum.nd, x.st});
		}
		if(sum.st<0) {
			cout << "NO\n";
			return 0;
		}
		for(int x:v) {
			ans[x] = res.nd*val[x].st+val[x].nd;
		}
	}
	cout << "YES\n";
	for(int i=1;i<=n;i++) {
		cout << ans[i] << " ";
	}
	cout << "\n";
}

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