Submission #642790

#	Time	Username	Problem	Language	Result	Execution time	Memory
642790		MKutayBozkurt	Graph (BOI20_graph)	C++17	0 / 100	0 ms	212 KiB

Graph

/**
*  author: kututay
*  created: 20.09.2022 13:13:02
**/
#include <bits/stdc++.h>
using namespace std;

#ifdef DEBUG
  #include "/Users/kutay/CP/templates/debug.h"
#else
  #define debug(...) void(38)
#endif

const double epsilon = 1e-6;

int32_t main() {
  ios_base::sync_with_stdio(0); cin.tie(0);
  int n, m; cin >> n >> m;
  vector<vector<pair<int, int>>> g(n);
  vector<pair<pair<int, int>, int>> edges;
  for (int i = 0; i < m; i++) {
    int x, y, z; cin >> x >> y >> z, x--, y--;
    g[x].emplace_back(y, z);
    g[y].emplace_back(x, z);
    edges.emplace_back(make_pair(x, y), z);
  }
  vector<double> ans(n);
  vector<int> components_vis(n);
  vector<pair<int, int>> n_vals(n); // (first * x + second) - node values

  auto solve = [&](int node) {
    vector<int> cycle_vis(n);
    bool cycle = false;
    vector<int> nodes;
    double x;
    bool flag = false;
    function<void(int, int, int)> find_cycle = [&](int node, int parent, int color) {
      cycle_vis[node] = 1;
      components_vis[node] = 1;
      nodes.emplace_back(node);
      for (auto next : g[node]) {
        if (parent == -1) n_vals[node] = make_pair(1, 0);
        else n_vals[node] = make_pair(-n_vals[parent].first, color - n_vals[parent].second);

        auto p = make_pair(node, next.first);
        auto col = next.second;

        auto a = n_vals[p.first];
        auto b = n_vals[p.second];
        pair<int, int> should = make_pair(-a.first, col - a.second);
        if (b == should) continue;
        pair<int, int> sum = make_pair(b.first + a.first, col - (b.second + a.second));
        if (sum.first == 0) {
          cout << "NO\n";
          exit(0);
        }
        if (flag == false) x = (double) sum.second / sum.first;
        flag = true;

        if (cycle_vis[next.first]) {
          cycle = true;
          continue;
        }
        if (next.first != parent) find_cycle(next.first, node, next.second);
      }
      ans[node] = n_vals[node].first * x + n_vals[node].second;
    };
    find_cycle(node, -1, -1);
    if ((int) nodes.size() == 0) return;
    if (flag == false or cycle == false) {
      int N = 101;
      vector<double> s(2 * N + 1);
      for (int i : nodes) {
        for (int j = -N; j < N; j++) {
          s[j + N] += abs(n_vals[i].first * j + n_vals[i].second);
        }
      }
      int mn = 1e9;
      for (int j = -N; j < N; j++) {
        if (s[j + N] < mn) {
          x = j;
          mn = s[j + N];
        }
      }
      debug(x);
      for (int i : nodes) {
        ans[i] = n_vals[i].first * x + n_vals[i].second;
      }
      return;
    }
  };

  for (int i = 0; i < n; i++) {
    if (components_vis[i]) continue;
    solve(i);
  }
  for (auto [p, color] : edges) {
    double sum = ans[p.first] + ans[p.second];
    if (abs(sum - color) > epsilon) {
      cout << "NO\n";
      exit(0);
    }
  }
  cout << "YES\n";
  for (auto x : ans) cout << fixed << setprecision(6) << x << " ";
  cout << '\n';
  double top = 0;
  for (auto x : ans) top += abs(x);
  debug(ans.size(), top);
}

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