<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 {
public:
    vector<vector<int>> graph;
    void showGraph(int n){
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++)cout<<graph[i][j]<<" ";
            cout<<"\n";
        }
        cout<<"\n";
        return;
    }
    void showDist(int* costs,int n){
        for(int i=0;i<n;i++)cout<<costs[i]<<" ";
        cout<<"\n";
        return;
    }
    int getVertex(int* costs, int n, int* isvisited){
        int min = INT_MAX;
        int cand = -1;
        for(int i=0;i<n;i++){
            if(!isvisited[i] && min>costs[i]){
                min = costs[i];
                cand = i;
            }
        }
        //cout<<cand<<" ";
        return cand;
    }
    void dijstra(int s, int n, int costs[], vector<vector<int>>& edges){
        int cnt = 0;
        int isvisited[n];
        for(int i=0;i<n;i++)isvisited[i]=0;
        while(cnt<n){
            //find next vertex with min cost
            int cand = getVertex(costs,n,isvisited);
            if(cand==-1)break;
            isvisited[cand]=1;
            if(edges.size()<n){
                for(int i=0;i<edges.size();i++){
                    int s = edges[i][0]-1;
                    int e = edges[i][1]-1;
                    int val = edges[i][2];
                    if(!isvisited[e] && cand==s)costs[e] = min(costs[e],costs[s]+val);
                }
            }
            else{
                for(int i=0;i<n;i++){
                    if(graph[cand][i]!=-1 && !isvisited[i] && costs[cand]!=INT_MAX){
                        costs[i] = min(costs[i],costs[cand]+graph[cand][i]);
                    }
                }
            }
            cnt++;
        }
        //showDist(costs,n);
        return;
    }
    int networkDelayTime(vector<vector<int>>& times, int n, int k) {
        ///initial
        for(int i=0;i<n;i++){
            vector<int>path;
            for(int j=0;j<n;j++){
                if(i==j)path.push_back(0);
                else path.push_back(-1);
            }
            graph.push_back(path);
        }
        for(int i=0;i<times.size();i++){
            int s = times[i][0]-1;
            int e = times[i][1]-1;
            int val = times[i][2];
            graph[s][e] = val;
        }
        //showGraph(n);
        ///dijstra
        int costs[n];
        for(int i=0;i<n;i++)costs[i] = INT_MAX;
        int start = k-1;
        costs[start] = 0;
        dijstra(start,n,costs,times);
        ///find max cost
        int max = -1;
        for(int i=0;i<n;i++)max = max<costs[i]? costs[i]:max;
        if(max == INT_MAX)return -1;
        return max;
    }
};
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