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Tifa · 2023-12-01 · via Tifa's Blog
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#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
template <class Tp>
using vec = vector<Tp>;
template <class Tp>
using vvec = vector<vector<Tp>>;
#define for_(i, l, r, v...) for (i64 i = (l), i##e = (r), ##v; i <= i##e; ++i)
vec<int> dijkstra(vvec<pair<int, int>> const &g, int s) {
vec<int> dis(g.size(), 0x3f3f3f3f);
vec<bool> vis(g.size());
priority_queue<pair<int, int>,
vector<pair<int, int>>,
greater<pair<int, int>>>
q;
q.emplace(dis[s] = 0, s);
while (!q.empty()) {
auto [dis_now, now] = q.top();
q.pop();
if (vis[now]) continue;
vis[now] = 1;
for (auto [to, w] : g[now])
if (dis[now] + w < dis[to]) {
dis[to] = dis[now] + w;
if (!vis[to]) q.emplace(dis[to], to);
}
}
return dis;
}
void solve(int t_ = 0) {
int t, r;
cin >> t >> r;
int n, m;
cin >> n >> m;
vvec<pair<int, int>> g(n + 1);
for_(i, 1, m, u, v, w) {
cin >> u >> v >> w;
g[u].emplace_back(v, w);
g[v].emplace_back(u, w);
}
int k;
cin >> k;
vec<int> a(k);
vec<double> p(k);
for_(i, 0, k - 1) cin >> a[i] >> p[i], p[i] /= 100;
auto dis0 = dijkstra(g, 1);
if (dis0[n] == 0x3f3f3f3f) {
cout << "-1\n";
return;
}
vvec<int> dis;
for_(i, 0, k - 1) dis.push_back(dijkstra(g, a[i]));
int state = 1 << k;
vec<vec<double>> ans(state, vec<double>(k, 1e50)),
pi(state, vec<double>(k, 0));
for (int i = 0; i < k; ++i) {
ans[1 << i][i] = 1.0 * dis0[a[i]] / t;
pi[1 << i][i] = 1;
}
double mn = 1. * dis0[n] / t;
for (int sta = 1; sta < state; ++sta) {
for (int i = 0; i < k; ++i) {
if ((sta >> i) & 1) {
for (int j = 0; j < k; ++j) {
if (!((sta >> j) & 1)) {
if (p[i] < 1e-6) {
mn = min(mn,
ans[sta][i] + pi[sta][i] * dis[i][n] *
((1.0 - p[i]) / r + p[i] / t));
} else {
ans[sta | (1 << j)][j] =
min(ans[sta | (1 << j)][j],
ans[sta][i] + pi[sta][i] * (1. - p[i]) * dis[i][n] / r +
pi[sta][i] * p[i] * dis[i][a[j]] / t);
pi[sta | (1 << j)][j] = pi[sta][i] * p[i];
}
}
}
}
}
}
for (int sta = 1; sta < state; ++sta) {
for (int i = 0; i < k; ++i) {
if ((sta >> i) & 1) {
mn = min(mn,
ans[sta][i] +
pi[sta][i] * dis[i][n] * ((1.0 - p[i]) / r + p[i] / t));
}
}
}
cout << fixed << setprecision(8) << mn << '\n';
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cerr << fixed << setprecision(6);
int i_ = 0;
solve(i_);
return 0;
}