<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) {
        //this is just normal bfs or dfs
        //there are multiple start nodes and multiple end nodes
        //find the min path among them
         if(source == target){
            return 0;
        }
        int busNos = routes.size();
        vector<vector<int>>adj(1e6+1);
        vector<int>startBuses;
        vector<int>endBuses;
        for(int i=0 ; i< routes.size() ; i++){
            bool startFound = false;
            bool endFound = false;
            for(auto rt : routes[i]){
                if(rt == source){
                    startBuses.push_back(i);
                    startFound = true;
                }
                if(rt == target){
                    endBuses.push_back(i);
                    endFound = true;
                }
                adj[rt].push_back(i);
                if(startFound && endFound){
                    return 1;
                }
            }
        }
        //here got the start busses and end busses
        queue<pair<int,int>>q;
        vector<bool>visited(busNos , false);
        for(auto i : startBuses){
            q.push({i,1});
            visited[i] = true;
        }
        while(!q.empty()){
            pair<int,int> bus_info = q.front();
            q.pop();
            vector<int>bus_route = routes[bus_info.first];
            for(auto rt : bus_route){
                for(auto busesThatContainRt : adj[rt]){
                    if(!visited[busesThatContainRt]){
                        //push in the queue
                        for(auto i : routes[busesThatContainRt]){
                            if(i == target){
                                return  bus_info.second+1;
                            }
                        }
                        visited[busesThatContainRt] = true;
                        q.push({busesThatContainRt , bus_info.second+1});
                    }
                }
            }
        }
        return -1;
    }
};
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