Wide delivery

#include <iostream>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long ll;


void dijkstra(const vector<vector<pair<long long,long long>>> &adj, long long start, vector<long long> &dist) {
    long long n = adj.size();
    vector<bool> processed(n, false);
    dist.assign(n, 0);
    priority_queue<pair<long long,long long>> pq;
    dist[start] = 9223372036854775807;
    pq.push({0, start});

    while (!pq.empty()) {
        long long a = pq.top().second;
        pq.pop();
        if (processed[a]) continue;
        processed[a] = true;

        for (auto [b, w] : adj[a]) {
            if(dist[b] < min(dist[a],w)) {
            dist[b] = min(w,dist[a]);
            pq.push({dist[b], b});
            }
        }
    }
}

void topological_sort(const vector<vector<long long>> &adj, vector<long long> &order) {
    int n = adj.size();
    vector<long long> indegree(n, 0);

    for (int u = 0; u < n; u++) {
        for (int v : adj[u]) {
            indegree[v]++;
        }
    }

    queue<int> q;

    for (int i = 0; i < n; i++) {
        if (indegree[i] == 0) q.push(i);
    }

    order.reserve(n);

    while (!q.empty()) {
        int u = q.front();
        q.pop();
        order.push_back(u);


        for (int v : adj[u]) {
            indegree[v]--;
            if (indegree[v] == 0) q.push(v);
        }
    }


    if ((int)order.size() != n) {
        cout << "IMPOSSIBLE" << endl;
        return ;

    }


}

void task1(){
int n, q;
    cin >> n >> q;
    vector<ll> cells(n);
    for(int i = 0; i < n; i++){
        cin >> cells[i];
    }

    vector<ll> queries(n);
    for(int i = 0; i < q; i++){
        cin >> queries[i];
    }


}

void task2(){
    int n, m;
    cin >> n >> m;

   vector<vector<pair<long long,long long>>> adj(n);
    vector<long long> dist;
    for (long long i = 0; i < m; i++) {
        long long a, b, w;
        cin >> a >> b >> w;
        a--; b--;  
        adj[a].push_back({b, w});
        adj[b].push_back({a, w});

        
    }

    
   
    dijkstra(adj, 0, dist);

    for (long long i = 0; i < n; i++) {
       
        cout << dist[i] << " ";
    }

}

int main() {
    task2();
    return 0;

}

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