Submission #1314905

#TimeUsernameProblemLanguageResultExecution timeMemory
1314905chithanhnguyenAirplane (NOI23_airplane)C++20
100 / 100
239 ms25676 KiB
/*
Author: Nguyen Chi Thanh - High School for the Gifted - VNU.HCM (i2528)
*/
#include <bits/stdc++.h>
using namespace std;

#define int long long
#define ull unsigned long long
#define ld long double
#define pii pair<int, int>
#define fi first
#define se second
#define __builtin_popcount __builtin_popcountll
#define all(x) (x).begin(), (x).end()
#define BIT(x, i) (((x) >> (i)) & 1)
#define MASK(x) ((1ll << (x)))

#define debug(a, l, r) for (int _i = (l); _i <= (r); ++_i) cout << (a)[_i] << ' '; cout << '\n';

const int MAXN = 2e5 + 5;
const int INF  = 1e18 + 5;
int n, m, a[MAXN];
int dist1[MAXN], distn[MAXN];
vector<int> adj[MAXN];

void init() {
    cin >> n >> m;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    for (int i = 1; i <= m; ++i) {
        int u, v; cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
}

void dijkstra(int source, int dist[]) {
    for (int i = 1; i <= n; ++i) dist[i] = INF;
    dist[source] = 0;
    priority_queue<pii, vector<pii>, greater<pii>> pq;
    pq.push({dist[source], source});

    while (!pq.empty()) {
        int cost = pq.top().fi, u = pq.top().se;
        pq.pop();
        if (dist[u] > cost) continue;

        for (int v : adj[u]) {
            int cost = max(dist[u] + 1, a[v]);
            if (dist[v] > cost) {
                dist[v] = cost;
                pq.push({dist[v], v});
            }
        }
    }
}

void solve() {
    dijkstra(1, dist1);
    dijkstra(n, distn);
    
    int res = INF;
    // Relax from all nodes
    for (int i = 1; i <= n; ++i) {
        int cost = max(dist1[i], distn[i]);
        res = min(res, cost * 2);
    }

    // Relax from all edges
    for (int u = 1; u <= n; ++u) {
        for (int v : adj[u]) {
            // if (a[u] < a[v]) continue;
            // cout << u << ' ' << v << '\n';
            int cost = 2 * max(dist1[u], distn[v]) + 1;
            // cout << "Cost: " << cost << '\n';
            res = min(res, cost);
        }
    }

    // debug(dist1, 1, n);
    // debug(distn, 1, n);
    cout << res;
}

signed main() {
    #ifdef NCTHANH
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #endif
    ios_base::sync_with_stdio(0);
    cin.tie(nullptr); cout.tie(nullptr);

    init();
    solve();

    return 0;
}
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