<p>You are given a network of <code>n</code> nodes, labeled from <code>1</code> to <code>n</code>. You are also given <code>times</code>, a list of travel times as directed edges <code>times[i] = (u<sub>i</sub>, v<sub>i</sub>, w<sub>i</sub>)</code>, where <code>u<sub>i</sub></code> is the source node, <code>v<sub>i</sub></code> is the target node, and <code>w<sub>i</sub></code> is the time it takes for a signal to travel from source to target.</p>

<p>We will send a signal from a given node <code>k</code>. Return <em>the <strong>minimum</strong> time it takes for all the</em> <code>n</code> <em>nodes to receive the signal</em>. If it is impossible for all the <code>n</code> nodes to receive the signal, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/05/23/931_example_1.png" style="width: 217px; height: 239px;" />
<pre>
<strong>Input:</strong> times = [[2,1,1],[2,3,1],[3,4,1]], n = 4, k = 2
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> times = [[1,2,1]], n = 2, k = 1
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> times = [[1,2,1]], n = 2, k = 2
<strong>Output:</strong> -1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= n &lt;= 100</code></li>
	<li><code>1 &lt;= times.length &lt;= 6000</code></li>
	<li><code>times[i].length == 3</code></li>
	<li><code>1 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt;= n</code></li>
	<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>
	<li><code>0 &lt;= w<sub>i</sub> &lt;= 100</code></li>
	<li>All the pairs <code>(u<sub>i</sub>, v<sub>i</sub>)</code> are <strong>unique</strong>. (i.e., no multiple edges.)</li>
</ul>

class Solution {

class NetworkWeight {
public:
    int delay;
    int node;

    NetworkWeight(int user_delay, int user_node){
        delay = user_delay;
        node = user_node;
    }

    bool operator>(const NetworkWeight& other) const {
        return delay > other.delay;
    }
};

public:
    int networkDelayTime(vector<vector<int>>& times, int n, int k) {
        unordered_map<int, vector<NetworkWeight>> adjList;
        for (const vector<int>& time : times){
            adjList[time[0]].emplace_back(time[2], time[1]);
        }

        priority_queue<NetworkWeight, vector<NetworkWeight>, greater<NetworkWeight>> pq;
        NetworkWeight nw(0, k);
        pq.push(nw);

        int visited_nodes = 0;
        int max_time = 0;
        unordered_set<int> visitedNodes;

        while (pq.size()){
            NetworkWeight nw = pq.top();
            pq.pop();
            if (visitedNodes.count(nw.node) != 0){
                continue;
            }

            visitedNodes.insert(nw.node);
            visited_nodes++;
            max_time = max(max_time, nw.delay);

            for (NetworkWeight& neighbor : adjList[nw.node]){
                pq.emplace(nw.delay + neighbor.delay, neighbor.node);
            }
        }

        if (visited_nodes != n){
            return -1;
        }

        return max_time;
    }
};
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