<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>

def min_bus(routes, source, target):
    if source==target:
        return 0
    bus_to_buses=defaultdict(list)
    bus_to_stops=defaultdict(set)
    start_buses=[]
    for bus, stops in enumerate(routes):
        if source in stops:
            start_buses.append(bus)
        bus_to_stops[bus]=set(stops)
        for bus2 in range(bus+1, len(routes)):
            if len(set(stops).intersection(set(routes[bus2])))!=0:
                bus_to_buses[bus].append(bus2)
                bus_to_buses[bus2].append(bus)

    min_res=[float("inf")]
    for start_b in start_buses:
        queue=[(start_b, 1)]
        visited=set([start_b])
        if target in bus_to_stops[start_b]:
            return 1

        while len(queue)!=0:
            curr_bus, curr_number=queue.pop(0)

            for next_bus in bus_to_buses[curr_bus]:
                if not next_bus in visited:
                    visited.add(next_bus)
                    queue.append((next_bus, curr_number+1))
                    if target in bus_to_stops[next_bus]:
                        min_res.append(curr_number+1)

    return min(min_res)

class Solution:
    def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
        res=min_bus(routes, source, target)
        if res<float("inf"):
            return int(res)
        else:
            return -1
         
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