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LibreOJ/2071/2071.cpp
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78
LibreOJ/2071/2071.cpp
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#include <iostream>
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#include <algorithm>
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#include <array>
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#include <iomanip>
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#include <limits>
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#include <vector>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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const int N = 2505;
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const double eps = 1e-4;
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int k, n;
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std::array<int, N> siz;
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std::array<double, N> d;
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std::array<std::array<double, N>, N> f;
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std::array<std::vector<int>, N> g;
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std::array<std::pair<int, int>, N> a;
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void dfs(int u) {
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f[u][1] = d[u];
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siz[u] = 1;
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for (int v : g[u]) {
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dfs(v);
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siz[u] += siz[v];
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for (int i = std::min(siz[u], k + 1); i; i--) {
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for (int j = 0; j <= std::min(siz[v], i - 1); j++) {
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f[u][i] = std::max(f[u][i], f[u][i - j] + f[v][j]);
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}
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}
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}
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}
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bool check(double mid) {
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for (int i = 1; i <= n; i++) {
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d[i] = static_cast<double>(a[i].second) - mid * a[i].first;
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}
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std::for_each(f.begin(), f.end(), [&](auto &x) {
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std::fill(x.begin(), x.end(), std::numeric_limits<int>::min());
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});
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dfs(0);
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return f[0][k + 1] >= 0;
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}
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int main() {
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std::ios::sync_with_stdio(false);
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cin.tie(nullptr);
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cin >> k >> n;
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for (int i = 1, r; i <= n; i++) {
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cin >> a[i].first >> a[i].second >> r;
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g[r].emplace_back(i);
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}
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double l = 0,
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r = 10000;
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while (r - l > eps) {
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double mid = (l + r) / 2;
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if (check(mid)) l = mid;
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else r = mid;
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}
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cout << std::fixed << std::setprecision(3) << l << endl;
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return 0;
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}
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