Submission #973724

#	Time	Username	Problem	Language	Result	Execution time	Memory
973724		duckindog	Harbingers (CEOI09_harbingers)	C++17	70 / 100	1049 ms	26560 KiB

harbingers

#include <bits/stdc++.h>
 
using namespace std;
 
const int N = 100'000 + 1;
int n;
vector<pair<int, int>> ad[N];
int s[N], velocity[N];
int d[N];
 
struct Line { 
  long long a, b;
  double x(const auto& rhs) { return 1.0 * (rhs.b - b) / (a - rhs.a); }
};
struct CHT { 
  vector<Line> hull;
  vector<pair<int, Line>> save;
 
  CHT() { hull.push_back({0, 0}); }
 
  void add(Line line) { 
    while (hull.size() > 1 && hull.end()[-2].x(hull.end()[-1]) >= hull.end()[-2].x(line)) { 
      save.push_back({1, hull.end()[-1]});
      hull.pop_back();
    }
    save.push_back({-1, line});
    hull.push_back(line);
  }
  long long query(int u) { 
    auto cal = [&](int it) { 
      return hull[it].a * velocity[u] + hull[it].b + 1ll * d[u] * velocity[u] + s[u];
    };
    int l = 0, r = hull.size() - 2, it = 0;
    while (l <= r) { 
      int mid = l + r >> 1;
      if (cal(mid) >= cal(mid + 1)) l = it = mid + 1;
      else r = mid - 1;
    }
    return cal(it);
  }
} convex;
 
long long dp[N];
void dfs(int u, int p = 0) {  
  auto& ret = dp[u];
  ret = min(ret, convex.query(u));
  convex.add({-d[u], ret});
  
  for (const auto& [v, w] : ad[u]) { 
    if (v == p) continue;
    d[v] = d[u] + w;
    dfs(v, u);
  }

  vector<Line> toBeAdded;
 
  bool pass = false;
  while (convex.save.size()) { 
    auto [t, line] = convex.save.end()[-1];
    if (t == -1) { 
      if (pass) break;
      convex.hull.pop_back();
      pass = true;
    } else toBeAdded.push_back(line);
    // convex.hull.push_back(line);
    convex.save.pop_back();
  }

  for (const auto& line : toBeAdded) convex.hull.push_back(line);
}
 
int32_t main() { 
  cin.tie(0)->sync_with_stdio(0);
 
  cin >> n;
  for (int i = 2; i <= n; ++i) { 
    int u, v, w; cin >> u >> v >> w;
    ad[u].push_back({v, w});
    ad[v].push_back({u, w});
  }
  for (int i = 2; i <= n; ++i) cin >> s[i] >> velocity[i];
 
  memset(dp, 40, sizeof dp);
  dfs(1);
 
  for (int i = 2; i <= n; ++i) cout << dp[i] << " \n"[i == n];
}

Compilation message (stderr)

harbingers.cpp:13:18: warning: use of 'auto' in parameter declaration only available with '-fconcepts-ts'
   13 |   double x(const auto& rhs) { return 1.0 * (rhs.b - b) / (a - rhs.a); }
      |                  ^~~~
harbingers.cpp: In member function 'long long int CHT::query(int)':
harbingers.cpp:35:19: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   35 |       int mid = l + r >> 1;
      |                 ~~^~~

• Subtask 1: 70 / 100