<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:
        from collections import defaultdict, deque
        
        graph = defaultdict(list)

        for bus_number, route in enumerate(routes):  # i.e. for idx, routes[idx]
            for bus_stop_idx in range(len(route)):
                bus_stop = route[bus_stop_idx]
                graph[bus_stop].append((route[(bus_stop_idx+1)% len(route)], bus_number))
        
        # If the source and target are the same stop, no buses are needed
        if source == target:
            return 0

        if source not in graph or target not in graph:
            return -1

        qu = deque()
        bus_boarded = set()
        stops_visited = set()
        
        for bus_stop, bus_number in graph.get(source, []):
            qu.append((bus_stop, bus_number, 1))  # this is bus stop, bus number, current bus count
            bus_boarded.add(bus_number)
            stops_visited.add(bus_stop)

        best_bus_count = -1
        while len(qu) > 0:
            bus_stop, bus_number, bus_count = qu.popleft()

            if bus_stop == target or target in routes[bus_number]:
                best_bus_count = bus_count if best_bus_count == -1 else min(bus_count, best_bus_count)
                continue
            
            for nbus_stop, nbus_number in graph.get(bus_stop, []):
                if not nbus_stop in stops_visited or nbus_number not in bus_boarded:
                    stops_visited.add(nbus_stop)
                    bus_boarded.add(nbus_number)
                    new_bus_count = bus_count + 1 if bus_number != nbus_number else bus_count
                    qu.append((nbus_stop, nbus_number, new_bus_count))
        return best_bus_count

45486