Code : Dijkstra?

#include <bits/stdc++.h>
using namespace std;

const long long inf = (long long)1e12;

class Graph {
  public:
    int n;
    vector<vector<pair<int, long long>>> adj;
    Graph(int n) {
        this->n = n;
        adj.resize(n);
    }

  public:
    void dijkstra();
};

void Graph ::dijkstra() {
    int src = 0;
    vector<long long> d(n, inf);
    vector<int> parent(n);

    set<pair<long long, int>> heap;

    parent[src] = -1;
    d[src] = 0;

    for (int i = 0; i < n; i++) {
        heap.insert({d[i], i});
    }

    for (int i = 0; i < n; i++) {
        int v = heap.begin()->second;
        heap.erase(heap.begin());

        for (auto [c, w] : adj[v]) {
            auto nxt = d[v] + w;
            if (d[c] > nxt) {
                heap.erase({d[c], c});
                d[c] = nxt;
                parent[c] = v;
                heap.insert({d[c], c});
            }
        }
    }

    int dest = n - 1;
    if (d[dest] >= inf) {
        cout << -1 << endl;
        return;
    }

    vector<int> res;
    int now = dest;
    while (now != -1) {
        res.push_back(now);
        now = parent[now];
    }
    reverse(res.begin(), res.end());

    for (auto &ele : res) {
        cout << ele + 1 << " ";
    }
    cout << endl;
}

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

    Graph g(n);
    for (int i = 0; i < m; i++) {
        int x, y, w;
        cin >> x >> y >> w;
        x--;
        y--;
        g.adj[x].push_back({y, w});
        g.adj[y].push_back({x, w});
    }

    g.dijkstra();
}

int main() {
    solve();
    return 0;
}

#include <bits/stdc++.h>
using namespace std;

const long long inf = (long long)1e12;

class Graph {
  public:
    int n;
    vector<vector<pair<int, long long>>> adj;
    Graph(int n) {
        this->n = n;
        adj.resize(n);
    }

  public:
    void dijkstra() {
        int src = 0;
        vector<long long> wave_arrival_time(n, inf);
        vector<bool> visited(n);
        vector<int> parent(n);

        parent[src] = -1;
        wave_arrival_time[src] = 0;

        // At every minute, a wave reaches a vertex for the first time, and
        // that timestamp is the shortest path of that node from src.
        // Hence, we only need to run this algorithm for n times.
        for (int i = 0; i < n; i++) {
            int vertex;
            long long current_time = inf;
            for (int v = 0; v < n; v++) {
                if (!visited[v] && wave_arrival_time[v] < current_time) {
                    current_time = wave_arrival_time[v];
                    vertex = v;
                }
            }

            visited[vertex] = true;
            // Emit waves for all the neighbors.
            for (auto [child, weight] : adj[vertex]) {
                auto arrival_time_of_this_wave = current_time + weight;
                // Ignore the wave if there's a faster wave that would arrive
                // at the children.
                if (wave_arrival_time[child] > arrival_time_of_this_wave) {
                    wave_arrival_time[child] = arrival_time_of_this_wave;
                    parent[child] = vertex;
                }
            }
        }

        int dest = n - 1;
        if (wave_arrival_time[dest] >= inf) {
            cout << -1 << endl;
            return;
        }

        vector<int> res;
        int now = dest;
        while (now != -1) {
            res.push_back(now);
            now = parent[now];
        }
        reverse(res.begin(), res.end());

        for (auto &ele : res) {
            cout << ele + 1 << " ";
        }
        cout << endl;
    }
};

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

    Graph g(n);
    for (int i = 0; i < m; i++) {
        int x, y, w;
        cin >> x >> y >> w;
        x--;
        y--;
        g.adj[x].push_back({y, w});
        g.adj[y].push_back({x, w});
    }

    g.dijkstra();
}

int main() {
    solve();
    return 0;
}