Jack goes to Rapture

• Time : O(v + e)
• Space : O(v + e)

void getCost(int n, vector<int> f, vector<int> t, vector<int> w) {
    vector<int> vis(n + 1, INT_MAX);
    vis[1] = 0;
    vector<pair<int, int>> adj[n + 1];
    for(int i = 0; i < w.size(); i++) {
        int u = f[i], v = t[i], c = w[i];
        adj[u].push_back({v, c});
        adj[v].push_back({u, c});
    }
    queue<int> q;
    vector<int> inc(n + 1, 0);
    q.push(1);
    while(!q.empty()) {
        auto u = q.front(); q.pop();
        inc[u] = false;
        for(auto& [v, c] : adj[u]) {
            if(vis[v] > max(vis[u], c)) {
                vis[v] = max(vis[u], c);
                if(!inc[v]) {
                    inc[v] = true;
                    q.push(v);
                }
            }
        }
    }
    
    if(vis[n] != INT_MAX)
        cout<< vis[n] << '\n';
    else
        cout<< "NO PATH EXISTS" << '\n';
}