<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:
    def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
        if source == target:
            return 0

        super_nodes = []
        for route in routes:
            super_nodes.append(set(route))

        graph = []
        for i in range(len(routes)):
            row = []
            for j in range(len(routes)):
                if i != j and len(super_nodes[i].intersection(super_nodes[j])) > 0:
                    row.append(1)
                else:
                    row.append(0)
            graph.append(row)
    
        def bfs(node_id, max_search):
            queue = deque([(node_id, 1)])
            visited = set()

            while queue:
                curr_node, depth = queue.pop()
                visited.add(curr_node)
                for neigh_node, is_connected in enumerate(graph[curr_node]):
                    if is_connected and neigh_node not in visited and max_search > depth:
                        if target in super_nodes[neigh_node]:
                            return depth + 1
                        queue.append((neigh_node, depth + 1))

            return 999999




        min_buses = 999999
        for node_id, super_node in enumerate(super_nodes):
            if source in super_node:
                if target in super_node:
                    return 1
                bus = bfs(node_id, min_buses)
                min_buses = min(min_buses, bus)
        return min_buses if min_buses != 999999 else -1 
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