<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 collections import deque

class Solution:
    def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
        if source == target:
            return 0
        
        adj_list = self.build_adjacency_list(routes)
        source = self.find_source_buses(routes, source)

        bfs = deque([[s, 1] for s in source])
        seen = set()
        while bfs:
            curr, bus_no = bfs.popleft()
            if target in routes[curr]:
                return bus_no
            if curr in seen:
                continue
            seen.add(curr)

            for neighbor in adj_list[curr]:
                bfs.append([neighbor, bus_no + 1])
        
        return -1

    def build_adjacency_list(self, routes):
        adj_list = defaultdict(list)
        for i in range(len(routes)):
            first = set(routes[i])
            for j in range(i + 1, len(routes)):
                second = set(routes[j])
                if len(first.intersection(second)) != 0:
                    adj_list[i].append(j)
                    adj_list[j].append(i)
        
        return adj_list
    
    def find_source_buses(self, routes, source):
        res = []
        for i in range(len(routes)):
            st = set(routes[i])
            if source in st:
                res.append(i)
        return res
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