Submission #1094714

#	Time	Username	Problem	Language	Result	Execution time	Memory
1094714		buzdi	Graph (BOI20_graph)	C++17	100 / 100	251 ms	24008 KiB

Graph

#include <iostream>
#include <algorithm>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <vector>
#include <set>
#define ll long long

using namespace std;

const int NMAX = 1e5;
const int INF = 1e9;
const long double EPS = 1e-6;

struct Value {
    int a, b;
}values[NMAX + 1];

int n, m, components;
vector<pair<int, int>> G[NMAX + 1];
bool visited[NMAX + 1];
bool ok;
long double unique_solution;
vector<int> component[NMAX + 1];
long double answer[NMAX + 1];

int GCD(int a, int b) {
    while (b) {
        int r = a % b;
        a = b;
        b = r;
    }
    return a;
}

Value make_value(int a, int b) {
    Value answer;
    answer.a = a;
    answer.b = b;
    return answer;
}

void Simplify(pair<int, int> &a) {
    int gcd = GCD(abs(a.first), abs(a.second));
    a.first /= gcd;
    a.second /= gcd;
}

bool GetSolution(Value x, Value y, int which) {
    if (x.a + y.a == 0) {
        return x.b + y.b == which;
    }

    pair<int, int> solution_x = { which - x.b - y.b, x.a + y.a };
    if ((solution_x.first <= 0 && solution_x.second <= 0) || (solution_x.first >= 0 && solution_x.second <= 0)) {
        solution_x.first = -solution_x.first;
        solution_x.second = -solution_x.second;
    }
    Simplify(solution_x);
    long double real_solution_x = (long double) solution_x.first / (long double) solution_x.second;
    if(unique_solution == INF) {
        unique_solution = real_solution_x;
        return true;
    }
    return abs(unique_solution - real_solution_x) <= EPS;
}

void DFS(int node, Value curent_value) {
    values[node] = curent_value;
    visited[node] = 1;
    component[components].push_back(node);
    for (auto [next_node, which] : G[node]) {
        if (!visited[next_node]) {
            DFS(next_node, make_value(-curent_value.a, which - curent_value.b));
        }
        else {
            if(!GetSolution(values[node], values[next_node], which)) {
                ok = false;
            }
        }
    }
}

long double GetValue(long double x, vector<int> &a) {
    long double answer = 0;
    for (int node : a) {
        answer += abs(values[node].a * x + values[node].b);
    }
    return answer;
}

void GetAnswer(vector<int> &a) {
    if (unique_solution != INF) {
        for(int node : a) {
            answer[node] = values[node].a * unique_solution + values[node].b;
        }
    }
    else {
        long double left = -INF, right = INF;
        int iterations = 400;
        while (iterations--) {
            long double mid1 = left + (right - left) / 3.0;
            long double mid2 = right - (right - left) / 3.0;

            long double value1 = GetValue(mid1, a);
            long double value2 = GetValue(mid2, a);
            if (value1 > value2) {
                left = mid1;
            }
            else {
                right = mid2;
            }
        }

        for(int node : a) {
            answer[node] = values[node].a * left + values[node].b;
        }
    }
}

signed main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    cin >> n >> m;
    for (int i = 1; i <= m; i++) {
        int a, b, c;
        cin >> a >> b >> c;
        G[a].push_back({ b, c });
        G[b].push_back({ a, c });
    }

    for (int i = 1; i <= n; i++) {
        if (!visited[i]) {
            components++;
            ok = true;
            unique_solution = INF;
            DFS(i, make_value(1, 0));
            if(!ok) {
                cout << "NO" << '\n';
                return 0;
            }
            GetAnswer(component[components]);
        }
    }
    cout << "YES" << '\n';
    for(int i = 1; i <= n; i++) {
        cout << fixed << setprecision(6) << answer[i] << ' ';
    }

    return 0;
}

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