<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) {
        vector<vector<int>> stationToBus(1e6);
        for (int bus = 0; bus < routes.size(); bus++) {
            for (int j = 0; j < routes[bus].size(); j++) {
                stationToBus[routes[bus][j]].push_back(bus);
            }
        }

        vector<int> dis(1e6, 1e9);
        vector<bool> visited(6e2);
        dis[source] = 0;
        queue<int> qq;
        qq.push(source);
        while (!qq.empty()) {
            int u = qq.front();
    
            qq.pop();
            if (u == target) {
                return dis[u];
            }
          
            for (auto& u_bus : stationToBus[u]) {
              
                if (visited[u_bus]) {
                    continue;
                }
                
                for (auto& v : routes[u_bus]) {
                    if (dis[v] > dis[u] + 1) {
                        dis[v] = dis[u] + 1;
                        qq.push(v);
                    }
                }
                visited[u_bus] = true;
            }
        }
        return -1;
    }
};
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