#include "cyberland.h"
#include <vector>
#include <queue>
#include <iostream>
using namespace std;
typedef long long ll;
typedef long double ld;
const ld INF = 9e18;
// hmm okay this looks like it works
struct T {
ld cdist;
ll k;
ll node;
bool operator>(const T &other) const {
if (cdist != other.cdist) return cdist > other.cdist;
if (k != other.k) return k > other.k;
return node > other.node;
}
};
// this should work for k <= 30
ld divByPow2(ll x, ll k) {
if (k > 30) return (ld)0;
return (ld)(x / (1LL << k));
}
// pretty sure this works too
void checkReal(int start, int H, vector<vector<pair<ll, ll>>> &adj, vector<bool> &real) {
real[start] = true;
if (start == H) return;
for (const pair<ll, ll> &i : adj[start]) {
if (!real[i.first]) {
checkReal(i.first, H, adj, real);
}
}
}
double solve(int N, int M, int K, int H, std::vector<int> x, std::vector<int> y, std::vector<int> c, std::vector<int> arr) {
vector<vector<pair<ll, ll>>> adj(N+5);
for (int i = 0; i < M; i++) {
adj[x[i]].push_back({y[i], c[i]});
adj[y[i]].push_back({x[i], c[i]});
}
vector<bool> real(N+5, false);
checkReal(0, H, adj, real);
if (!real[H]) return -1;
vector<vector<ld>> dist(N+5, vector<ld>(K + 1 + 5, INF));
dist[H][0] = 0;
priority_queue<T, vector<T>, greater<T>> pq;
pq.push({0, 0, H});
while (!pq.empty()) {
const auto [cdist, k, node] = pq.top();
pq.pop();
if (arr[node] == 0 || node == 0) {
return cdist;
}
if (cdist != dist[node][k]) continue;
for (const pair<ll, ll> &i : adj[node]) {
if (i.first == H) continue;
if (!real[i.first]) continue;
if ((cdist + divByPow2(i.second, k)) < dist[i.first][k]) {
dist[i.first][k] = cdist + divByPow2(i.second, k);
pq.push({dist[i.first][k], k, i.first});
}
if (arr[node] == 2 && i.first != H && k < K && (cdist + divByPow2(i.second, k + 1)) < dist[i.first][k+1]) {
dist[i.first][k+1] = cdist + divByPow2(i.second, k + 1);
pq.push({dist[i.first][k+1], k + 1, i.first});
}
}
}
return -1;
}
