#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct disj {
int pa[100005];
void init(int n) { iota(pa, pa + n + 1, 0); }
int find(int x) { return pa[x] = (pa[x] == x ? x : find(pa[x])); }
bool uni(int p, int q) {
p = find(p);
q = find(q);
if (p == q)
return 0;
pa[q] = p;
return 1;
}
} disj;
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);
for (int i = 0; i < M; ++i) {
if (x[i] != H && y[i] != H) disj.uni(x[i], y[i]);
adj[x[i]].emplace_back(y[i],c[i]);
adj[y[i]].emplace_back(x[i], c[i]);
}
K = min(K, 60);
vector<vector<double>> dist(N + 10, vector<double>(K + 10, 1e18));
priority_queue<tuple<double, ll, ll>, vector<tuple<double, ll, ll>>, greater<>> q;
vector<double> divideBy(K + 1, 1);
for (int i = 1; i <= K; ++i) {
divideBy[i] = divideBy[i - 1]/2;
}
q.emplace(0, H, 0);
dist[H][0] = 0;
while(!q.empty()) {
double curDistance = get<0>(q.top());
ll curNode = get<1>(q.top());
ll curK = get<2>(q.top());
q.pop();
if(dist[curNode][curK] < curDistance) continue;
if((arr[curNode] == 0 || curNode == 0)) return curDistance;
for(auto [newNode, distance] : adj[curNode]) {
if (disj.find(newNode) != disj.find(0)) continue;
double newDistance = curDistance + double(distance) * divideBy[curK];
if(newDistance < dist[newNode][curK]) {
dist[newNode][curK] = newDistance;
q.emplace(newDistance, newNode, curK);
}
if(arr[curNode] == 2) {
if(curK < K) {
double betterDistance = curDistance + double(distance) * divideBy[curK + 1];
if(betterDistance < dist[newNode][curK + 1]) {
dist[newNode][curK + 1] = betterDistance;
q.emplace(betterDistance, newNode, curK + 1);
}
}
}
}
}
return -1;
}
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