<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;
        }

        std::unordered_set<int> all_stops;
        for (const auto& route : routes) {
            for (int stop : route) {
                all_stops.insert(stop);
            }
        }

        int N = all_stops.size();
        int M = routes.size();

        std::cout << N << " " << M << std::endl;

        std::unordered_map<int, std::unordered_set<int>> station2lines;
        for (int i = 0; i < M; ++i) {

            int stations_on_line = routes[i].size();

            int station;
            for (int j = 0; j < stations_on_line; ++j) {
                station = routes[i][j];
                station2lines[station].insert(i);
            }        
        }

        int start = source;
        int finish = target;

        // ### END INPUT ###

        // ### BUILD LINE GRAPH ###
        std::vector<std::unordered_set<int>> adj_lines(M);
        for (const auto& kv : station2lines) {
            std::vector<int> neighbour_lines(kv.second.begin(), kv.second.end());
            for (int i = 0; i < neighbour_lines.size(); ++i) {
                for (int j = i + 1; j < neighbour_lines.size(); ++j) {
                    adj_lines[neighbour_lines[i]].insert(neighbour_lines[j]);
                    adj_lines[neighbour_lines[j]].insert(neighbour_lines[i]);
                }
            }
        }

        // ### END BUILD LINE GRAPH ###

        const auto& finish_lines = station2lines[finish];
        
        int min_change = INT_MAX;
        for (int start_line : station2lines[start]) {
            
            std::vector<int> dists(M, INT_MAX);
            dists[start_line] = 1;
            
            std::queue<int> bfs_queue;
            bfs_queue.push(start_line);

            while (!bfs_queue.empty()) {

                int line = bfs_queue.front();
                bfs_queue.pop();

                if (finish_lines.find(line) != finish_lines.end()) {
                    min_change = std::min(min_change, dists[line]);
                    break;
                }

                for (int next_line : adj_lines[line]) {
                    if (dists[next_line] == INT_MAX) {
                        dists[next_line] = dists[line] + 1;
                        bfs_queue.push(next_line);
                    }
                }
            }
        }

        return min_change == INT_MAX ? -1 : min_change;
    }
};
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