<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>

# https://leetcode.com/problems/bus-routes/
from typing import DefaultDict, List, Set, Deque, Tuple
from collections import defaultdict, deque


class Solution:
    def numBusesToDestination(
        self, routes: List[List[int]], source: int, target: int
    ) -> int:
        # given a station, return a set of buses going thru this station
        station_to_buses: DefaultDict[int, Set[int]] = defaultdict(set)

        for i, stations in enumerate(routes):
            for station in stations:
                station_to_buses[station].add(i)

        # Create a queue with initial source and bus count of 0.
        queue: Deque[Tuple[int, int]] = deque([(source, 0)])
        # Create a set to contain visited routes of bus.
        visited_buses: Set[int] = set()

        # Iterate till queue is empty
        while queue:
            # Pop station and number of buses taken and store in variables.
            station, buses_taken = queue.popleft()
            # If we have reached the destination station, return the number of buses taken.
            if station == target:
                return buses_taken

            # If station is in graph, then iterate over the stations in graph.
            # and if it is not already visited, enqueue all the stations in that bus route
            # along with an incremented bus count and mark the bus visited.
            if station in station_to_buses:
                for bus in station_to_buses[station]:
                    if bus not in visited_buses:
                        for s in routes[bus]:
                            queue.append([s, buses_taken + 1])
                        visited_buses.add(bus)

        # If the route is not found, return -1
        return -1

51051