Submission #367409

#	Time	Username	Problem	Language	Result	Execution time	Memory
367409		arujbansal	Relay Marathon (NOI20_relaymarathon)	C++17	100 / 100	2382 ms	164300 KiB

RelayMarathon

#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
#include <array>
#include <stack>
#include <queue>
#include <random>
#include <numeric>
#include <functional>
#include <chrono>
#include <utility>
#include <iomanip>
#include <assert.h>

using namespace std;

void dbg_out() { cerr << endl; }
template<typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); }
#define dbg(...) cerr << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)

#define rng_init mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#define rng_seed(x) mt19937 rng(x)
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
// #define int long long

const int MXN = 1e5 + 5, INF = 1e9 + 5;
int N, M, K;
int par[MXN];
vector<pair<int, int>> g[MXN];
vector<array<int, 3>> edges;

vector<int> dijkstra(const vector<int> &src) {
    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<>> pq;
    vector<int> dist(N, INF);

    for (int i = 0; i < N; i++)
        par[i] = i;

    for (const auto &x : src) {
        dist[x] = 0;
        pq.emplace(0, x);
    }

    while (!pq.empty()) {
        auto cur = pq.top();
        pq.pop();

        int u = cur.second, cur_dist = cur.first;
        if (cur_dist != dist[u]) continue;

        for (const auto &[v, wt] : g[u]) {
            int new_dist = cur_dist + wt;

            if (new_dist < dist[v]) {
                dist[v] = new_dist;
                pq.emplace(new_dist, v);

                par[v] = par[u];
            }
        }
    }

    return dist;
}

array<int, 3> best_pair(const vector<int> &dist) {
    pair<int, int> points = {-1, -1};
    int points_dist = INF;

    for (const auto &[u, v, w] : edges) {
        if (par[u] == par[v]) continue;

        int cur_dist = dist[u] + dist[v] + w;

        if (cur_dist < points_dist) {
            points.first = par[u];
            points.second = par[v];

            points_dist = cur_dist;
        }
    }

    return array<int, 3>{points.first, points.second, points_dist};
}

void solve() {
    cin >> N >> M >> K;

    for (int i = 0; i < M; i++) {
        int u, v, w;
        cin >> u >> v >> w;
        u--, v--;

        edges.push_back({u, v, w});

        g[u].emplace_back(v, w);
        g[v].emplace_back(u, w);
    }

    vector<int> special(K);
    for (auto &x : special) {
        cin >> x;
        x--;
    }

    vector<int> dist_special = dijkstra(special);

    array<int, 3> points1 = best_pair(dist_special);

    vector<int> special_new;
    for (const auto &x : special) {
        if (x == points1[0] || x == points1[1]) continue;

        special_new.push_back(x);
    }

    vector<int> dist_special_new = dijkstra(special_new);

    array<int, 3> points2 = best_pair(dist_special_new);

    int ans = points1[2] + points2[2];

    vector<int> dist1 = dijkstra(vector<int>{points1[0]});
    vector<int> dist2 = dijkstra(vector<int>{points1[1]});

    set<pair<int, int>> dist2_set;
    for (const auto &i : special) {
        if (i == points1[0] || i == points1[1]) continue;

        dist2_set.insert({dist2[i], i});
    }

    for (const auto &i : special) {
        if (i == points1[0] || i == points1[1]) continue;

        dist2_set.erase({dist2[i], i});
        pair<int, int> dist2_best = *dist2_set.begin();
        dist2_set.insert({dist2[i], i});

        ans = min(ans, dist1[i] + dist2_best.first);
    }

    cout << ans;
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int TC = 1;
    // cin >> TC;
    while (TC--) solve();
}

• Subtask 1: 5 / 5
• Subtask 2: 12 / 12
• Subtask 3: 25 / 25
• Subtask 4: 58 / 58