Submission #722728

#	Time	Username	Problem	Language	Result	Execution time	Memory
722728		gagik_2007	Graph (BOI20_graph)	C++17	0 / 100	3 ms	5032 KiB

Graph

#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <chrono>
#include <ctime>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <deque>
#include <limits>
#include <iomanip>
#include <unordered_set>
#include <unordered_map>
#include <fstream>
#include <functional>
#include <random>
#include <cassert>
using namespace std;

typedef long long ll;
typedef long double ld;

#define ff first
#define ss second

ll ttt;
const ll INF = 1e18;
const ll MOD = 1e9 + 7;
const ll N = 200007;
const ll LG = 31;
ll n, m, k;
vector<pair<int, int>>g[N];
bool used[N];
bool neg[N]; // if the x in the value formula has the negative sign
ll val[N]; // if neg[v]: value = val[v] - x, else: value = x + val[v]
bool defined_value = false;
ll vlx2 = 0;

void dfs(int v, int par) {
	for (auto e : g[v]) {
		int to = e.ff;
		int c = e.ss;
		if (to != par) {
			if (!used[to]) {
				if (neg[v]) {
					val[to] = c - val[v];
				}
				else {
					neg[to] = true;
					val[to] = c - val[v];
				}
				used[to] = true;
				dfs(to, v);
			}
			else {
				if (neg[v] == neg[to]) {
					if (neg[v]) {
						if (!defined_value) {
							vlx2 = val[v] + val[to] - c;
							defined_value = true;
						}
						else if (vlx2 != val[v] + val[to] - c) {
							cout << "NO\n";
							exit(0);
						}
					}
					else {
						if (!defined_value) {
							vlx2 = c - val[v] - val[to];
							defined_value = true;
						}
						else if (vlx2 != c - val[v] - val[to]) {
							cout << "NO\n";
							exit(0);
						}
					}
				}
				else {
					if (val[v] + val[to] != c) {
						cout << "NO\n";
						exit(0);
					}
				}
			}
		}
	}
}

ll get_sum(ll curvlx2) {
	//cout << "PROCESSING: " << curvlx2 << endl;
	ll sum = 0;
	for (int v = 1; v <= n; v++) {
		ll vl = 0;
		if (neg[v]) {
			vl = val[v] * 2 - curvlx2;
		}
		else {
			vl = val[v] * 2 + curvlx2;
		}
		//cout << vl << " ";
		sum += abs(vl);
	}
	//cout << endl;
	return sum;
}

int main() {
	//freopen("in.txt", "r", stdin);
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	cin >> n >> m;
	for (int i = 0; i < m; i++) {
		int x, y;
		int tp;
		cin >> x >> y >> tp;
		g[x].push_back({ y,tp });
		g[y].push_back({ x,tp });
	}
	for (int v = 1; v <= n; v++) {
		if (!used[v]) {
			dfs(v, -1);
		}
	}
	cout << setprecision(12) << fixed;
	cout << "YES\n";
	if (defined_value) {
		for (int v = 1; v <= n; v++) {
			ld vl = 0;
			if (neg[v]) {
				vl = val[v] - ld(vlx2) / 2.0;
			}
			else {
				vl = val[v] + ld(vlx2) / 2.0;
			}
			cout << vl << " ";
		}
		cout << endl;
	}
	else {
		pair<ll, ll>mn = { INF,INF };
		for (int v = 1; v <= n; v++) {
			ll cur = 0;
			if (neg[v]) {
				cur = val[v];
			}
			else {
				cur = -val[v];
			}
			//cout << cur << " " << get_sum(cur) << endl;
			mn = min(mn, { get_sum(cur),cur });
		}
		vlx2 = mn.ss;
		for (int v = 1; v <= n; v++) {
			ld vl = 0;
			if (neg[v]) {
				vl = val[v] - ld(vlx2) / 2.0;
			}
			else {
				vl = val[v] + ld(vlx2) / 2.0;
			}
			cout << vl << " ";
		}
		cout << endl;
	}
}

/// ---- - --------  ------ -------- -- - - -
/// Just a reminder. Ubuntu password is I O I
/// ---- - --------  ------ -------- -- - - -

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