#include <bits/stdc++.h>
#include "cyberland.h"
#include <vector>
using namespace std;
using ll = long long;
const ll INF = 1e15;
vector<vector<ll> > adjList;
map<pair<ll, ll>, ll> weightMat;
class UnionFind {
private:
ll N;
vector<ll> p, sz;
public:
UnionFind() {}
UnionFind(ll _N) {
N = _N;
p.resize(N); sz.resize(N);
for (ll i = 0; i < N; i++) {
p[i] = i; sz[i] = 1;
}
}
ll root(ll x) {
if (p[x] != x) return p[x] = root(p[x]);
return p[x];
}
void unify(ll x, ll y) {
x = root(x), y = root(y);
if (x == y) return;
if (sz[x] > sz[y]) swap(x, y);
sz[y] += sz[x];
p[x] = p[y];
}
};
UnionFind uf;
double dijkstras(ll startingNode, vector<int> &A) {
ll N = adjList.size();
priority_queue<pair<ll, ll>, vector<pair<ll, ll> >, greater<pair<ll, ll> > > pq;
pq.push({0, startingNode});
// check if H is actually reachable to 0
vector<ll> distances(N, INF);
distances[startingNode] = 0;
while (!pq.empty()) {
auto [currentDistance, currentNode] = pq.top();
pq.pop();
if (currentDistance > distances[currentNode]) {
continue;
}
for (ll v: adjList[currentNode]) {
if (currentDistance + weightMat[{currentNode, v}] < distances[v]) {
distances[v] = currentDistance + weightMat[{currentNode, v}];
pq.push({distances[v], v});
}
}
}
ll minimumPossible = INF;
for (ll i = 0; i < N; i++) {
if ((A[i] == 0 || i == 0) && (uf.root(i) == uf.root(0) && uf.root(i) == uf.root(startingNode)))
minimumPossible = min(minimumPossible, distances[i]);
}
return (double)(minimumPossible);
}
double solve(int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr) {
adjList.clear();
weightMat.clear();
adjList.resize(N);
uf = UnionFind(N);
for (ll i = 0; i < M; i++) {
adjList[x[i]].push_back(y[i]);
adjList[y[i]].push_back(x[i]);
weightMat[{x[i], y[i]}] = (double)c[i];
weightMat[{y[i], x[i]}] = (double)c[i];
uf.unify(x[i], y[i]);
}
if (uf.root(0) != uf.root(H)) return -1.0;
double response = dijkstras(H, arr);
if (response >= INF) {
return -1.0;
} else {
return response;
}
}
