<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>

from queue import Queue
class Solution:
    def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
        if source==target: return 0
        
        bus_routes_at_stops = {}
        for idx, route in enumerate(routes):
            for stop in route: 
                if stop in bus_routes_at_stops:
                    bus_routes_at_stops[stop].add(idx)
                else:
                    bus_routes_at_stops[stop] = set([idx])
        
        # base case when source or target are not a part of any routes
        if source not in bus_routes_at_stops: return -1
        if target not in bus_routes_at_stops: return -1

        source_routes = bus_routes_at_stops[source]
        target_routes = bus_routes_at_stops[target]
        
        bus_route_graph = {}
        for route_num, route in enumerate(routes):
            route_connections = set()
            for stop in route:
                for r in bus_routes_at_stops[stop]:
                    if r!=route_num:
                        route_connections.add(r)
            bus_route_graph[route_num] = route_connections
            
        q = Queue()
        for r in source_routes:
            q.put([r,1])
        
        visited_routes = set()
        while q.qsize()>0:
            curr, d = q.get()
            visited_routes.add(curr)
            if curr in target_routes: return d
            else:
                for connections in bus_route_graph[curr]:
                    if connections not in visited_routes:
                        q.put([connections, d+1])

        return -1
                    



        # base case when no route is found
        return -1
            
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