Submission #821696

#	Time	Username	Problem	Language	Result	Execution time	Memory
821696		tch1cherin	Graph (BOI20_graph)	C++17	100 / 100	603 ms	21636 KiB

Graph

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

const int MAX_N = 1e5 + 5;
vector<pair<int, int>> G[MAX_N];
int color[MAX_N];
vector<int> comp, path, path_edges, cycle, cycle_edges;
bool visited[MAX_N] = {};
long double A[MAX_N];

void DFS(int u) {
  comp.push_back(u);
  for (auto [v, c] : G[u]) {
    if (color[v] == -1) {
      color[v] = !color[u];
      DFS(v);
    }
  }
}

bool find_cycle(int u) {
  visited[u] = true;
  path.push_back(u);
  for (auto [v, c] : G[u]) {
    if (!visited[v]) {
      path_edges.push_back(c);
      if (find_cycle(v)) {
        return true;
      }
      path_edges.pop_back();
    } else if (color[u] == color[v]) {
      path_edges.push_back(c);
      while (path.back() != v) {
        cycle.push_back(path.back());
        cycle_edges.push_back(path_edges.back());
        path.pop_back();
        path_edges.pop_back();
      }
      cycle.push_back(path.back());
      cycle_edges.push_back(path_edges.back());
      return true;
    }
  }
  path.pop_back();
  return false;
}

long double check(int s, long double value) {
  for (int v : comp) {
    visited[v] = false;
  }
  A[s] = value;
  queue<int> Q;
  Q.push(s);
  visited[s] = true;
  while (!Q.empty()) {
    int u = Q.front();
    Q.pop();
    for (auto [v, c] : G[u]) {
      if (!visited[v]) {
        A[v] = c - A[u];
        visited[v] = true;
        Q.push(v);
      } else if (abs(A[u] + A[v] - c) > 1e-15l) {
        cout << "NO\n";
        exit(0);
      }
    }
  }
  long double ans = 0;
  for (int v : comp) {
    ans += abs(A[v]);
  }
  return ans;
}

void solve(int u) {
  cycle = cycle_edges = path = path_edges = vector<int>();
  if (find_cycle(u)) {
    long double sum = 0;
    rotate(cycle_edges.begin(), cycle_edges.begin() + 1, cycle_edges.end());
    for (int i = 0; i < (int)cycle_edges.size(); i++) {
      sum += cycle_edges[i] * (i % 2 ? -1 : +1);
    }
    check(cycle[0], sum /= 2);
  } else {
    long double l = -1e6, r = 1e6;
    for (int i = 0; i < 60; i++) {
      long double m1 = l + (r - l) / 2.1;
      long double m2 = r - (r - l) / 2.1;
      if (check(u, m1) < check(u, m2)) {
        r = m2;
      } else {
        l = m1;
      }
    }
    check(u, (l + r) / 2);
  }
}

int main() {
  cout << fixed << setprecision(9);
  cin.tie(nullptr)->sync_with_stdio(false);
  int N, M;
  cin >> N >> M;
  for (int i = 0; i < M; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    a--, b--;
    G[a].push_back(pair {b, c});
    G[b].push_back(pair {a, c});
  }
  memset(color, -1, sizeof color);
  for (int i = 0; i < N; i++) {
    if (color[i] == -1) {
      comp = vector<int>();
      color[i] = 0;
      DFS(i);
      solve(i);
    }
  }
  cout << "YES\n";
  for (int i = 0; i < N; i++) {
    cout << A[i] << " \n"[i + 1 == N];
  }
}

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