Submission #973789

#	Time	Username	Problem	Language	Result	Execution time	Memory
973789		duckindog	Harbingers (CEOI09_harbingers)	C++17	70 / 100	1054 ms	24920 KiB

harbingers

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
 
using namespace std;

#define in ({int x = 0; int c = getchar(), n = 0; for(; !isdigit(c); c = getchar()) n = (c == '-'); for(; isdigit(c); c = getchar()) x = x * 10 + c - '0'; n ? -x : x;})
 
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 { 
  int top;
  array<Line, N> hull;
  array<pair<int, Line>, N> save;

  void add(Line line, int u) { 
    int preTop = top;
    while (top > 1 && hull[top].x(hull[top - 1]) >= hull[top].x(line)) top--;
    save[u] = {preTop, hull[top + 1]};
    hull[++top] = 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 = 1, r = top - 1, it = 1;
    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}, u);

  for (const auto& [v, w] : ad[u]) { 
    if (v == p) continue;
    d[v] = d[u] + w;
    dfs(v, u);
  }
  
  auto[top, line] = convex.save[u];
  convex.hull[convex.top] = line;
  convex.top = top;
}
 
int32_t main() { 
  cin.tie(0)->sync_with_stdio(0);
 
  n = in;
  for (int i = 2; i <= n; ++i) { 
    int u = in, v = in, w = in;
    ad[u].push_back({v, w});
    ad[v].push_back({u, w});
  }
  for (int i = 2; i <= n; ++i) s[i] = in, velocity[i] = in;
 
  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:17:18: warning: use of 'auto' in parameter declaration only available with '-fconcepts-ts'
   17 |   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:37:19: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   37 |       int mid = l + r >> 1;
      |                 ~~^~~

• Subtask 1: 70 / 100