<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:
    vector<vector<int>>bus_stop{1000007};

    void attach_nodes(vector<set<int>>& adj_list, int stoppage){
        for(int i = 0 ; i < bus_stop[stoppage].size(); i++){
            int bus1 = bus_stop[stoppage][i];
            for(int j = i+1 ; j < bus_stop[stoppage].size(); j++){
                int bus2 = bus_stop[stoppage][j];
                if(adj_list[bus1].find(bus2) != adj_list[bus1].end()){
                    continue;
                }
                else{
                    adj_list[bus1].insert(bus2);
                    adj_list[bus2].insert(bus1);
                }
            }
        }
    }

    int traverse(vector<vector<int>>& routes, vector<set<int>>& adj_list, int source, int target, vector<bool>& visited){
        queue<pair<int,int>> node ; // bus , count of bus taken
        set<int>target_bus;

        for(int i = 0 ; i < routes.size(); i++){
            for(int stoppage : routes[i]){
                if(stoppage == source)
                    node.push(pair<int,int>{i,1});
                if(stoppage == target)
                    target_bus.insert(i);
            }
        }

        while(!node.empty()){
            int cur_node = node.front().first;
            int bus_count = node.front().second;

            if(target_bus.find(cur_node) != target_bus.end())
                return bus_count;
            node.pop();
            visited[cur_node] = true;

            for(auto itr : adj_list[cur_node]){
                if(!visited[itr]){
                    node.push(pair<int,int>{itr, bus_count+1});
                }
            }
        }

        return -1 ;
        
    }

    int numBusesToDestination(vector<vector<int>>& routes, int source, int target) {
        if(source == target)
            return 0;
        int n = routes.size();
        for(int i = 0 ; i < routes.size(); i++){
            for(int stoppage : routes[i]){
                bus_stop[stoppage].push_back(i);
            }
        }

        vector<set<int>> adj_list(n);
        vector<bool>visited(n,false);
        for(int i = 0 ; i < bus_stop.size(); i++){
            if(bus_stop[i].size() > 1)
                attach_nodes(adj_list,i);
        }

        return traverse(routes, adj_list,source,target, visited);
    }
};
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