#include "cyberland.h"
#include <vector>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <utility>
#define v vector
#define s set
#define u_s unordered_set
#define u_m unordered_map
#define q queue
#define p_q priority_queue
#define p pair
#define ll long long
using namespace std;
class WorldMap {
const int maxShift = 50;
const ll tempInf = 1000000000000000;
int countryCount; int cyberland; double minimum;
u_m<int, v<p<int, int>>> friends;
v<ll> dspaSourceResult;
u_m<int, ll> halvers; u_m<int, s<p<ll, int>>> customHalvers;
v<int> powers;
public:
// Initialize the world map
WorldMap(int countries, int destinationIndex) {
countryCount = countries;
cyberland = destinationIndex;
minimum = tempInf;
friends.clear(); dspaSourceResult.clear(); halvers.clear(); customHalvers.clear(); powers.clear();
}
void connect(int friend1, int friend2, int distance) {
friends[friend1].push_back(make_pair(friend2, distance));
friends[friend2].push_back(make_pair(friend1, distance));
}
void notePowers(v<int> arr) {
powers = arr;
}
void dspaSource() {
// Initialize stuff
dspaSourceResult.clear(); dspaSourceResult.resize(countryCount, tempInf);
p_q<p<ll, int>, v<p<ll, int>>, greater<p<ll, int>>> dspaQueue;
dspaQueue.push(make_pair(0, 0));
dspaSourceResult[0] = 0;
int selected; int friendID; int friendDist;
// Go through the queue
while (!(dspaQueue.empty())) {
selected = dspaQueue.top().second; dspaQueue.pop();
// Go through the first-in-line's friends
for (p<int, int> fren : friends[selected]) {
friendID = fren.first; friendDist = fren.second;
// If the friend has 0-powers
if (powers[friendID] == 0) {
// Propagate only if it hasn't been hit before
if (dspaSourceResult[friendID] > 0) {
dspaSourceResult[friendID] = 0;
// Note that we cannot leave Cyberland
if (friendID != cyberland) dspaQueue.push(make_pair(0, friendID));
}
} else {
// Propagate only if the value changes
if (dspaSourceResult[selected] + friendDist < dspaSourceResult[friendID]) {
dspaSourceResult[friendID] = dspaSourceResult[selected] + friendDist;
// Note that we cannot leave Cyberland
if (friendID != cyberland) dspaQueue.push(make_pair(dspaSourceResult[friendID], friendID));
}
}
}
}
}
void dspaDestination() {
// Initialize stuff
v<ll> dspaDestinationResult(countryCount, tempInf);
p_q<p<ll, int>, v<p<ll, int>>, greater<p<ll, int>>> dspaQueue;
u_s<int> halverSet;
dspaQueue.push(make_pair(0, cyberland));
dspaDestinationResult[cyberland] = 0;
int selected; int friendID; int friendDist;
// Go through the queue
while (!(dspaQueue.empty())) {
selected = dspaQueue.top().second; dspaQueue.pop();
// Go through the first-in-line's friends
for (p<int, int> fren : friends[selected]) {
friendID = fren.first; friendDist = fren.second;
// Propagate only if the value changes
if (dspaDestinationResult[selected] + friendDist < dspaDestinationResult[friendID]) {
dspaDestinationResult[friendID] = dspaDestinationResult[selected] + friendDist;
// Log if friend's power is 2
dspaQueue.push(make_pair(dspaDestinationResult[friendID], friendID));
if (powers[friendID] == 2) halverSet.insert(friendID);
}
}
}
// Deal with the queue for 2-powers
for (auto selected: halverSet) halvers[selected] = dspaDestinationResult[selected];
}
void dspaCustom(int halverInd) {
// Initialize stuff
v<ll> dspaCustomResult(countryCount, tempInf);
p_q<p<ll, int>, v<p<ll, int>>, greater<p<ll, int>>> dspaQueue;
dspaQueue.push(make_pair(0, halverInd));
dspaCustomResult[halverInd] = 0;
int selected; int friendID; int friendDist;
// Go through the queue
while (!(dspaQueue.empty())) {
selected = dspaQueue.top().second; dspaQueue.pop();
// Go through the first-in-line's friends
for (p<int, int> fren : friends[selected]) {
friendID = fren.first; friendDist = fren.second;
// Propagate only if the value changes
if (dspaCustomResult[selected] + friendDist < dspaCustomResult[friendID]) {
dspaCustomResult[friendID] = dspaCustomResult[selected] + friendDist;
// Note that we cannot leave Cyberland, & it's sub-optimal to pass by a 2-power for the path
if (friendID != cyberland) dspaQueue.push(make_pair(dspaCustomResult[friendID], friendID));
// return if friend's power is 2 - this shall be the closest friend
if (powers[friendID] == 2) customHalvers[halverInd].insert(make_pair(dspaCustomResult[friendID], friendID));
}
}
}
}
double div2(double ans, int expo) {
double k = 2;
while (expo != 0) {
if (expo & 1) ans = ans / k;
expo = expo >> 1; k = k * k;
}
return ans;
}
void navigate(int halverInd, double currDistance, double lastDistance, int halvesUsed, int maxHalves) {
// Navigating from Cyberland back to home; first update
double newDist = currDistance + div2(lastDistance, halvesUsed);
// Then try to minimize saved path length
double distToZero = newDist + div2(dspaSourceResult[halverInd], halvesUsed + 1);
if (distToZero > minimum) return;
minimum = min(minimum, distToZero);
// If maxHalves has not been reached, go through each friend
int friendID; ll friendDist;
if (halvesUsed < maxHalves - 1) {
for (auto fren : customHalvers[halverInd]) {
friendDist = fren.first; friendID = fren.second;
navigate(friendID, newDist, friendDist, halvesUsed + 1, maxHalves);
}
}
}
double determinePath(int twoPower) {
// Perform DijkstraSPA once from source, apply 0 and 1 rules
dspaSource();
// Perform DijkstraSPA once from destination, record 2s
dspaDestination();
// Then consolidate hereon
if (dspaSourceResult[cyberland] == tempInf) return -1;
// If Cyberland is reachable
p_q<p<ll, int>, v<p<ll, int>>, greater<p<ll, int>>> dfsFromDestinationQueue;
minimum = dspaSourceResult[cyberland];
ll minDist;
for (auto info : halvers) {
minDist = tempInf;
for (auto fren : friends[info.first]) {
if (fren.first != cyberland) minDist = min(minDist, ((ll) fren.second) * 2);
}
if (minDist != tempInf) customHalvers[info.first].insert(make_pair(minDist, info.first));
dspaCustom(info.first);
dfsFromDestinationQueue.push(make_pair(info.second, info.first));
}
twoPower = min(twoPower, maxShift);
// Go through each 2-power starting from destination, dfs-style
p<ll, int> currentHalver;
while (!(dfsFromDestinationQueue.empty())) {
currentHalver = dfsFromDestinationQueue.top(); dfsFromDestinationQueue.pop();
navigate(currentHalver.second, 0, currentHalver.first, 0, twoPower);
}
return minimum;
}
};
double solve(int N, int M, int K, int H, v<int> x, v<int> y, v<int> c, v<int> arr) {
// Rename every int to something more descriptive
int countryCount = N; int roadCount = M; int bitShifter = K; int cyberLocation = H;
WorldMap theRoadToCyberland(countryCount, cyberLocation);
for (int road = 0; road < roadCount; road++)
theRoadToCyberland.connect(x[road], y[road], c[road]);
theRoadToCyberland.notePowers(arr);
return theRoadToCyberland.determinePath(bitShifter);
}
