<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 __init__(self):
        self.adj_list = []
    
    def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:

        if source == target:
                return 0

        self.adj_list = [[] for _ in range(len(routes))]
        for route in routes:
            route.sort()

        self.create_graph(routes)

        q = deque()
        self.add_starting_nodes(q, routes, source)

        vis = set()
        bus_count = 1

        while q:
            sz = len(q)
            for _ in range(sz):
                node = q.popleft()
                if self.is_stop_exist(routes[node], target):
                    return bus_count
                for adj in self.adj_list[node]:
                    if adj not in vis:
                        vis.add(adj)
                        q.append(adj)
            bus_count += 1

        return -1

    def create_graph(self, routes):
        for i in range(len(routes)):
            for j in range(i + 1, len(routes)):
                if self.have_common_node(routes[i], routes[j]):
                    self.adj_list[i].append(j)
                    self.adj_list[j].append(i)

    def have_common_node(self, route1, route2):
        i, j = 0, 0
        while i < len(route1) and j < len(route2):
            if route1[i] == route2[j]:
                return True
            if route1[i] < route2[j]:
                i += 1
            else:
                j += 1
        return False

    def add_starting_nodes(self, q, routes, source):
        for i in range(len(routes)):
            if self.is_stop_exist(routes[i], source):
                q.append(i)

    def is_stop_exist(self, route, stop):
        return stop in route

            
        
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