<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 Graph {
    public:

    int n;
    vector<vector<vector<int>>> adj;

    Graph(vector<vector<vector<int>>> &adj){
        this->n = adj.size();
        this->adj = adj;
    }

    int minPathBFS(int source, int destination){
        deque<int> dq;
        
        vector<int> dist(n, INT_MAX);

        dq.push_back(source);

        dist[source] = 0;
        
        while(!dq.empty()){
            int front = dq.front();
            dq.pop_front();

            if(front == destination){
                return dist[front];
            }
            for(vector<int> &neig: adj[front]){
                if(dist[neig[0]] != INT_MAX && 
                   dist[neig[0]] <= dist[front] + (neig[1] == 1)){
                    continue;
                   }
                else if(neig[1] == 1){
                    dq.push_back(neig[0]);
                    dist[neig[0]] = dist[front] + neig[1];
                }
                else{
                    dq.push_front(neig[0]);
                    dist[neig[0]] = dist[front];
                }
            }
        }

        return dist[destination] == INT_MAX ? -1 : dist[destination];
    }
};
class Solution {
public:
    int numBusesToDestination(vector<vector<int>>& routes, int source, int target) {
        int numBusStops = 0; for(auto &v: routes) for(auto &c: v) numBusStops = max(numBusStops, c);
        if(source == target)
            return 0;
            
        if(numBusStops < max(source, target))
            return -1;
        
        numBusStops++;

        
        vector<vector<vector<int>>> adj(numBusStops);

        int currNodeNumber = numBusStops - 1;

        for(vector<int> &route: routes){
            int m = route.size();

            int firstStopNodeNum = adj.size();
            
            for(int i = 0; i < m; i++){
                adj.emplace_back();
                currNodeNumber++;
                if(i == m-1)
                    adj[currNodeNumber].push_back({firstStopNodeNum, 0});
                else{
                    adj[currNodeNumber].push_back({currNodeNumber + 1, 0});
                }

                // add edges to existing bustops
                adj[route[i]].push_back({currNodeNumber, 1});
                adj[currNodeNumber].push_back({route[i], 0});
            }
        }

        Graph g(adj);
        return g.minPathBFS(source, target);
    }
};
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