Submission #1153561

#	Time	Username	Problem	Language	Result	Execution time	Memory
1153561		elipsen	Cyberland (APIO23_cyberland)	C++20	28 / 100	3092 ms	9752 KiB

cyberland

#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 = 1000000;
    const ll tempInf = 1000000000000000;
    int countryCount; int cyberland; double minimum;
    u_m<int, v<p<int, int>>> friends; u_m<int, int> zeroFriends;
    v<ll> dspaSourceResult;
    u_m<int, ll> halvers; u_m<int, s<p<ll, int>>> customHalvers;
    u_s<int> checkedHalvers;
    v<int> powers;
    ll runthroughCount = 0;
    
    
    public:
    // Initialize the world map
    WorldMap(int countries, int destinationIndex) {
        countryCount = countries;
        cyberland = destinationIndex;
        minimum = tempInf;
        friends.clear(); zeroFriends.clear(); dspaSourceResult.clear(); halvers.clear(); customHalvers.clear(); checkedHalvers.clear(); powers.clear();
    }

    void notePowers(v<int> arr) {
        powers = arr;
    }

    void connect(int friend1, int friend2, int distance) {
        if (friend2 < friend1) {
            int temp = friend1; friend1 = friend2; friend2 = temp;
        }
        if ((friend1 == 0) || (powers[friend1] == 0)) {
            zeroFriends[friend2] = (zeroFriends[friend2] == 0) ? distance : min(zeroFriends[friend2], distance);
        } else {
            friends[friend1].push_back(make_pair(friend2, distance));
            friends[friend2].push_back(make_pair(friend1, distance));
        }
    }

    void handleZero() {
        for (p<int, int> fren : zeroFriends) {
            friends[0].push_back(make_pair(fren.first, fren.second));
            friends[fren.first].push_back(make_pair(0, fren.second));
        }
    }

    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
                    if (friendID != 0) 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) && (friendID != 0)) 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;
    }

    bool navigate(int halverInd, double currDistance, double lastDistance, int halvesUsed, int maxHalves) {
        // runthroughCount++;

        // Navigating from Cyberland back to home; first update
        double newDist = currDistance + div2(lastDistance, halvesUsed);
        
        // Then try to minimize saved path length
        if (newDist + div2(1, halvesUsed) - div2(1, maxHalves) < minimum - max(minimum / 1.0E7, 1.0E-7)) {
            minimum = min(minimum, newDist + div2(dspaSourceResult[halverInd], halvesUsed + 1));

            // If maxHalves has not been reached, go through each friend
            int friendID; ll friendDist;
            if (halvesUsed < maxHalves - 1) {
                if (checkedHalvers.find(halverInd) == checkedHalvers.end()) {
                    checkedHalvers.insert(halverInd);
                    dspaCustom(halverInd);
                    ll minDist = tempInf;
                    for (auto fren : friends[halverInd]) {
                        if (fren.first != cyberland) minDist = min(minDist, ((ll) fren.second) * 2);
                    }
                    if (minDist != tempInf) customHalvers[halverInd].insert(make_pair(minDist, halverInd));
                }
                for (auto fren : customHalvers[halverInd]) {
                    friendDist = fren.first; friendID = fren.second;
                    bool get = navigate(friendID, newDist, friendDist, halvesUsed + 1, maxHalves);
                    if (get) break;
                }
            }
            
            return false;
        } else return true;
    }

    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];
        for (auto info : halvers) 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();
            bool get = navigate(currentHalver.second, 0, currentHalver.first, 0, twoPower);
            if (get) break;
        }

        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);
    theRoadToCyberland.notePowers(arr);
    for (int road = 0; road < roadCount; road++) theRoadToCyberland.connect(x[road], y[road], c[road]);
    theRoadToCyberland.handleZero();
    return theRoadToCyberland.determinePath(bitShifter);
}

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• Subtask 2: 8 / 8
• Subtask 3: 13 / 13
• Subtask 4: 0 / 19
• Subtask 5: 7 / 7
• Subtask 6: 0 / 16
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• Subtask 8: 0 / 3