<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:
        n = len(routes)
        # 1->2->7//->6->3
        # 1:2,7
        # 2:1,7
        # 7:1,2,3,6
        #... j in tbl[i], means src i dest j returns 1
        # if not 2 ->7 ->3 2 buses
        # if two nodes are not connected, return -1
        # make sure that 1->2 is 1 but 1->3 is 2
        # nodes are routes not stops
        if source == target:
            return 0
        adjList={s:[] for route in routes for s in route}
        for i in range(0,n):
            route=routes[i]
            for s1 in route:
                adjList[s1].append(i)
        if source not in adjList or target not in adjList:
            return -1
        visited=set() # routes not stops
        q=deque()
        for route in adjList[source]:
            q.append((route, 1))
            visited.add(route)
        while q:
            route, numRoutes = q.popleft()
            for stop in routes[route]:
                if stop == target:
                    return numRoutes
                for connecting_routes in adjList[stop]:
                    if connecting_routes not in visited:
                        visited.add(connecting_routes)
                        q.append((connecting_routes,numRoutes+1))

        # visitied is stops nto routes
        # while q:
        #     stop, numRoutes = q.popleft()
        #     if stop == target:
        #         return numRoutes
        #     for route_idx in adjList[stop]:
        #         for stop in routes[route_idx]:
        #             if stop in visited:
        #                 continue
        #             visited.add(stop)
        #             q.append((stop,numRoutes+1))
        return -1
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