<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;
        unordered_map<int, vector<int>> stop2buses;
        for (int bus = 0; bus < routes.size(); bus++) {
            for (int j = 0; j < routes[bus].size(); j++) {
                int stop = routes[bus][j];
                stop2buses[stop].push_back(bus);
            }
        }
        vector<unordered_set<int>> bus2buses(routes.size());
        for (int bus = 0; bus < routes.size(); bus++) {
            unordered_set<int> buses;
            vector<int> &stops = routes[bus];
            for (auto stop: stops) {
                vector<int> &next_buses = stop2buses[stop];
                for (auto next_bus: next_buses) {
                    buses.insert(next_bus);
                    // cout << "bus from " << bus << " to " << next_bus << endl;
                }
            }
            bus2buses[bus] = buses;
        }
        vector<int> visited_buses(routes.size());
        unordered_set<int> target_buses;
        for (auto t: stop2buses[target]) {
            target_buses.insert(t);
        }
        queue<int> q;
        int level = 1;
        for (auto s: stop2buses[source]) {
            q.push(s);
            visited_buses[s] = 1;
        }
        while (!q.empty()) {
            int len = q.size();
            for (int i = 0; i < len; i++) {
                int cur = q.front();
                // cout << "level: " << level << " cur bus: " << cur << endl;
                q.pop();
                if (target_buses.count(cur))
                    return level;
                unordered_set<int> &trans_buses = bus2buses[cur];
                for (const auto &bus: trans_buses) {
                    // cout << "bus from " << cur << " to " << bus << endl;
                    if (!visited_buses[bus]) {
                        visited_buses[bus] = 1;
                        q.push(bus);
                    }
                }
            }
            level++;
        }
        return -1;
        
    }
};
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