<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:
    from collections import deque

    def bfs(self, routes, stops, src, dst):
        visited_stops = set()
        visited_routes = set()
        queue = deque()
        next_queue = deque()
        queue.append(src)
        level = 0
        while len(queue) != 0:
            node = queue.popleft()
            if node == dst:
                return level
            visited_stops.add(node)
            next_routes = []
            for route in stops[node]:
                if route in visited_routes:
                    continue
                next_routes.append(route)
            for route in next_routes:
                visited_routes.add(route)
                for nbr in routes[route]:
                    if nbr in visited_stops:
                        continue
                    next_queue.append(nbr)
            if len(queue) == 0:
                next_queue, queue = deque(), next_queue
                level += 1
        return -1

        
    def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
        stops = {}
        for i in range(len(routes)):
            routes[i] = set(routes[i])
            for stop in routes[i]:
                if stop not in stops:
                    stops[stop] = set()
                stops[stop].add(i)

        if source == target:
            return 0
        elif source not in stops:
            return -1
        return self.bfs(routes, stops, source, target)
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