// compile: g++ -o data data.cpp -O3 -std=gnu++20 -Wall -Wextra -Wshadow -D_GLIBCXX_ASSERTIONS -ggdb3 -fmax-errors=2 -DLOCAL
// run: ./data < in/01_random_02.txt
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#ifdef LOCAL
#include <debug/codeforces.h>
#define debug(x...) _debug_print(#x, x);
#else
#define debug(x...)
#endif
template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;}
#define rep(i,a,b) for(int i=(a);i<(int)(b);++i)
#define sz(v) ((int)(v).size())
#define print(...) print_(__VA_ARGS__);
#define INTMAX (int)(9223372036854775807)
#define INF (int)(1152921504606846976)
#define double long double
#define int long long
#define MAXN 200010
int n;
struct graph {
struct node {
int u, v;
double w;
};
vector<vector<node>> e;
int n, m;
bool directed;
vector<int> vis;
graph(int V, bool D = 0) {
n = V;
e.resize(n);
vis.resize(n);
directed = D;
}
void add_edge(int u, int v, double w = 1) {
e[u].push_back(node{u, v, w});
++m;
}
void graphviz_dump(string filename = "graph.dot") {
ofstream gf;
gf.open(filename);
gf << (directed ? "digraph" : "graph") << " {\n";
gf << " "; rep(i, 0, n) gf << i << " ;"[i==n-1]; gf << endl;
string notation = directed ? " -> " : " -- ";
for (auto es: e) {
for (auto edge: es) {
gf << " " << edge.u << notation << edge.v << (directed ? " ;\n" : ";\n");
}
}
gf << "}\n";
}
int cnt = 0;
void dfs(int u, double th) {
vis[u] = 1;
++cnt;
for (auto ed: e[u]) {
if (ed.w > th) continue;
if (!vis[ed.v]) dfs(ed.v, th);
}
}
bool solve(double th) {
rep(i, 0, n) {
cnt = 0;
fill(vis.begin(), vis.end(), 0);
dfs(i, th);
if (cnt == n) return 1;
}
return 0;
}
};
int32_t main() {
ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
cin >> n;
vector<int> x(n), y(n), p(n);
rep(i, 0, n) cin >> x[i] >> y[i] >> p[i];
graph g(n);
rep(i, 0, n) rep(j, 0, n) {
if (i == j) continue;
g.add_edge(i, j, (abs(x[i] - x[j]) + abs(y[i] - y[j])) * 1.0 / p[i]);
}
double l = 0, r = 1e10, mid = (l + r) / 2;
while (r-l > 0.01) {
mid = (l + r) / 2;
if (g.solve(mid)) r = mid;
else l = mid;
}
cout << (int)ceil(mid - 0.01) << endl;
return 0;
}
No Comments