#include <bits/stdc++.h>
using namespace std;
using ll = long long;
vector<vector<ll> > adjList;
map<pair<ll, ll>, double> weightMat;
vector<bool> isReachable;
struct NodeState {
double distance;
ll currentNode;
ll numSpecialsUsed;
};
double binExp(double base, ll numTimes) {
if (numTimes == 0) return 1.0;
if (numTimes % 2 == 0) {
double res = binExp(base, numTimes / 2);
return res * res;
} else {
double res = binExp(base, numTimes - 1);
return res * base;
}
}
bool myCompFunc(NodeState ns1, NodeState ns2) {
if (ns1.distance == ns2.distance) {
if (ns1.numSpecialsUsed == ns2.numSpecialsUsed) {
return (ns1.currentNode < ns2.currentNode);
}
return ns1.numSpecialsUsed < ns2.numSpecialsUsed;
}
return ns1.distance > ns2.distance;
}
void dfs(ll node, ll H, const vector<vector<ll>>& adjList, vector<bool>& isReachable) {
if (node == H) return;
for (auto v : adjList[node]) {
if (!isReachable[v]) {
isReachable[v] = true;
dfs(v, H, adjList, isReachable);
}
}
}
double dijkstras(ll H, ll maxSpecials, vector<int> &A) {
ll N = adjList.size();
// {distance, node, number of times special is used}
priority_queue<NodeState, vector<NodeState>, function<bool(NodeState, NodeState)> > pq(myCompFunc);
pq.push({0.0, H, 0});
vector<double> distances(N, 1e16);
distances[H] = 0;
while (!pq.empty()) {
// store state of how many Ks were used here
auto [currentDistance, currentNode, currentSpecials] = pq.top();
pq.pop();
for (ll v: adjList[currentNode]) {
double newDist = currentDistance;
if (currentSpecials <= 69) {
newDist += (weightMat[{currentNode, v}]) / binExp(2.0, currentSpecials);
}
if (newDist < distances[v]) {
distances[v] = newDist;
pq.push({newDist, v, currentSpecials});
if (A[currentNode] == 2 && currentSpecials < maxSpecials) {
pq.push({newDist, v, currentSpecials + 1});
}
}
}
}
double minimumPossible = distances[0];
for (ll i = 0; i < A.size(); i++) {
if ((A[i] == 0) && isReachable[i])
minimumPossible = min(minimumPossible, distances[i]);
}
return minimumPossible;
}
double dijkstrasToOrigin(ll H, ll maxSpecials, vector<int> &A) {
ll N = adjList.size();
// {distance, node, number of times special is used}
priority_queue<NodeState, vector<NodeState>, function<bool(NodeState, NodeState)> > pq(myCompFunc);
pq.push({0.0, H, 0});
vector<double> distances(N, 1e16);
distances[H] = 0;
while (!pq.empty()) {
// store state of how many Ks were used here
auto [currentDistance, currentNode, currentSpecials] = pq.top();
pq.pop();
for (ll v: adjList[currentNode]) {
double newDist = currentDistance;
if (currentSpecials <= 69) {
newDist += (weightMat[{currentNode, v}]) / binExp(2.0, currentSpecials);
}
if (newDist < distances[v]) {
distances[v] = newDist;
pq.push({newDist, v, currentSpecials});
if (A[currentNode] == 2 && currentSpecials < maxSpecials) {
pq.push({newDist, v, currentSpecials + 1});
}
}
}
}
return distances[0];
}
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);
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];
}
isReachable.clear();
isReachable.resize(N, false);
dfs(0, H, adjList, isReachable);
isReachable[0] = true;
if (!isReachable[H]) {
return -1;
}
double response = min(dijkstras(H, K - 1, arr), dijkstrasToOrigin(H, K, arr));
return response;
}
