<p>You are given an array <code>routes</code> representing bus routes where <code>routes[i]</code> is a bus route that the <code>i<sup>th</sup></code> bus repeats forever.</p>

<ul>
	<li>For example, if <code>routes[0] = [1, 5, 7]</code>, this means that the <code>0<sup>th</sup></code> bus travels in the sequence <code>1 -&gt; 5 -&gt; 7 -&gt; 1 -&gt; 5 -&gt; 7 -&gt; 1 -&gt; ...</code> forever.</li>
</ul>

<p>You will start at the bus stop <code>source</code> (You are not on any bus initially), and you want to go to the bus stop <code>target</code>. You can travel between bus stops by buses only.</p>

<p>Return <em>the least number of buses you must take to travel from </em><code>source</code><em> to </em><code>target</code>. Return <code>-1</code> if it is not possible.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> routes = [[1,2,7],[3,6,7]], source = 1, target = 6
<strong>Output:</strong> 2
<strong>Explanation:</strong> The best strategy is take the first bus to the bus stop 7, then take the second bus to the bus stop 6.
</pre>

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

<pre>
<strong>Input:</strong> routes = [[7,12],[4,5,15],[6],[15,19],[9,12,13]], source = 15, target = 12
<strong>Output:</strong> -1
</pre>

<p>&nbsp;</p>

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

<ul>
	<li><code>1 &lt;= routes.length &lt;= 500</code>.</li>
	<li><code>1 &lt;= routes[i].length &lt;= 10<sup>5</sup></code></li>
	<li>All the values of <code>routes[i]</code> are <strong>unique</strong>.</li>
	<li><code>sum(routes[i].length) &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= routes[i][j] &lt; 10<sup>6</sup></code></li>
	<li><code>0 &lt;= source, target &lt; 10<sup>6</sup></code></li>
</ul>

class Solution {
public:
  int numBusesToDestination(vector<vector<int>>& routes, int source, int target) {
    if (source == target) return 0;
    int n = (int) routes.size();
    const int N = (int) 1e6 + 1;
    vector<set<int>> g(N);
    for (int i = 0; i < n; i++) {
      for (int x : routes[i]) {
        g[x].insert(i);
      }
    }
    vector<int> que;
    const int inf = (int) 1e9;
    vector<int> dist(n, inf);
    vector<int> vis(n, 0);
    for (int x : g[source]) {
      que.push_back(x);
      dist[x] = 1;
      vis[x] = 1;
    }
    for (int b = 0; b < (int) que.size(); b++) {
      int cur = que[b]; // group
      for (int u : routes[cur]) {
        for (int v : g[u]) {
          if (!vis[v]) {
            vis[v] = true;
            que.push_back(v);
            dist[v] = dist[cur] + 1;
          }
        }
      }
    }
    int mn = (int) 1e9;
    for (int x : g[target]) {
      mn = min(mn, dist[x]);
    }
    return (mn == inf ? -1 : mn);
  }
};
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