<p>You are given a positive integer <code>n</code> representing <code>n</code> cities numbered from <code>1</code> to <code>n</code>. You are also given a <strong>2D</strong> array <code>roads</code> where <code>roads[i] = [a<sub>i</sub>, b<sub>i</sub>, distance<sub>i</sub>]</code> indicates that there is a <strong>bidirectional </strong>road between cities <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> with a distance equal to <code>distance<sub>i</sub></code>. The cities graph is not necessarily connected.</p>

<p>The <strong>score</strong> of a path between two cities is defined as the <strong>minimum </strong>distance of a road in this path.</p>

<p>Return <em>the <strong>minimum </strong>possible score of a path between cities </em><code>1</code><em> and </em><code>n</code>.</p>

<p><strong>Note</strong>:</p>

<ul>
	<li>A path is a sequence of roads between two cities.</li>
	<li>It is allowed for a path to contain the same road <strong>multiple</strong> times, and you can visit cities <code>1</code> and <code>n</code> multiple times along the path.</li>
	<li>The test cases are generated such that there is <strong>at least</strong> one path between <code>1</code> and <code>n</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/12/graph11.png" style="width: 190px; height: 231px;" />
<pre>
<strong>Input:</strong> n = 4, roads = [[1,2,9],[2,3,6],[2,4,5],[1,4,7]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> The path from city 1 to 4 with the minimum score is: 1 -&gt; 2 -&gt; 4. The score of this path is min(9,5) = 5.
It can be shown that no other path has less score.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/12/graph22.png" style="width: 190px; height: 231px;" />
<pre>
<strong>Input:</strong> n = 4, roads = [[1,2,2],[1,3,4],[3,4,7]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The path from city 1 to 4 with the minimum score is: 1 -&gt; 2 -&gt; 1 -&gt; 3 -&gt; 4. The score of this path is min(2,2,4,7) = 2.
</pre>

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

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= roads.length &lt;= 10<sup>5</sup></code></li>
	<li><code>roads[i].length == 3</code></li>
	<li><code>1 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li><code>1 &lt;= distance<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
	<li>There are no repeated edges.</li>
	<li>There is at least one path between <code>1</code> and <code>n</code>.</li>
</ul>

class Solution
{
public:
    int my_n;
    int minDist;
    vector<unordered_map<int, int>> nodesConnect; // i node와 연결된 다른 node 목록
    vector<bool> visit;
    bool DFS(int v)
    {
        int res = false;
        if (v == 1 || v == my_n)
            res = true;

        visit[v] = true;
        for (auto it = nodesConnect[v].begin(); it != nodesConnect[v].end(); ++it)
        {
            //다음노드가 이전에 방문한 노드여도, 이번 노드와 연결된 dist를 확인하지 않았을 수 있기 때문에 체크하고 감.
            minDist = min(minDist, it->second);

            if (!visit[it->first])
            {
                if (DFS(it->first))
                    res = true;
            }
        }
        return res;
    }
    int minScore(int n, vector<vector<int>> &roads)
    {
        nodesConnect = vector<unordered_map<int, int>>(n + 1); // i node와 연결된 다른 node 목록
        visit = vector<bool>(n + 1, false);
        my_n = n;
        minDist = INT_MAX;

        // 최소값 추적
        for (int i = 0; i < roads.size(); ++i)
        {
            nodesConnect[roads[i][0]].emplace(roads[i][1], roads[i][2]);
            nodesConnect[roads[i][1]].emplace(roads[i][0], roads[i][2]);
        }

        for (int i = 1; i <= n; ++i)
        {
            minDist = INT_MAX;
            if (DFS(i))
                return minDist;
        }
        return minDist;
    }
};
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