Wide delivery

#include <iostream>
#include <vector>
#include <queue>
#include <limits>

using namespace std;

const int MAX_N = 100000 + 5;
vector<pair<int, int>> adj[MAX_N]; 
vector<int> max_width;

void max_width_from_factory(int n) {
    max_width.resize(n + 1, 0);
    vector<bool> visited(n + 1, false);
    priority_queue<pair<int, int>> pq;

    max_width[1] = numeric_limits<int>::max();
    pq.push({max_width[1], 1});

    while (!pq.empty()) {
        int width = pq.top().first;
        int node = pq.top().second;
        pq.pop();

        if (visited[node]) continue;
        visited[node] = true;


        for (auto& edge : adj[node]) {
            int next_node = edge.first;
            int next_width = edge.second;
            int new_width = min(width, next_width);
            
            if (new_width > max_width[next_node]) {
                max_width[next_node] = new_width;
                pq.push({max_width[next_node], next_node});
            }
        }
    }
}

int main() {
    int n, m;
    cin >> n >> m;

    for (int i = 0; i < m; i++) {
        int a, b, w;
        cin >> a >> b >> w;
        adj[a].push_back({b, w});
        adj[b].push_back({a, w}); 
    }

    max_width_from_factory(n);

    for (int i = 2; i <= n; i++) {
        cout << max_width[i] << (i < n ? " " : "");
    }
    cout << endl;

    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

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Test 4

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Test 5

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Test 6

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 37

Verdict: ACCEPTED

Test 38

Verdict: ACCEPTED

Test 39

Verdict: ACCEPTED

Test 40

Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 42

Verdict: ACCEPTED

Test 43

Verdict: ACCEPTED

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: ACCEPTED

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 64

Verdict: ACCEPTED

Test 65

Verdict: ACCEPTED

Test 66

Verdict: ACCEPTED

Test 67

Verdict: ACCEPTED

Test 68

Verdict: ACCEPTED

Test 69

Verdict: ACCEPTED