<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:
        if source == target:
            return 0

        max_stop = max(max(route) for route in routes)
        if target > max_stop or source > max_stop:
            return -1

        n = len(routes)
        min_buses_to_reach = [float("inf")] * (max_stop + 1)
        min_buses_to_reach[source] = 0

        flag = True
        while flag:
            flag = False
            for route in routes:
                mini = float("inf")
                for stop in route:
                    mini = min(mini, min_buses_to_reach[stop])
                mini += 1
                for stop in route:
                    if min_buses_to_reach[stop] > mini:
                        min_buses_to_reach[stop] = mini
                        flag = True

        return (
            min_buses_to_reach[target]
            if min_buses_to_reach[target] < float("inf")
            else -1
        )

        # almost works:
        # if source == target:
        #     return 0

        # stops_per_route = defaultdict(set)
        # routes_per_stop = defaultdict(set)
        # visited = set()

        # q = deque([])

        # for r_i, route in enumerate(routes):
        #     for stop in route:
        #         stops_per_route[r_i].add(stop)
        #         routes_per_stop[stop].add(r_i)
        #         if stop == source:
        #             q.append((0,r_i,stop))

        # while q:
        #     changes, route_i, stop = q.popleft()
        #     if stop == target:
        #         return changes

        #     visited.add(stop)

        #     for r in routes_per_stop[stop]:
        #         for s in stops_per_route[r]:
        #             if s not in visited:
        #                 if route_i != r:
        #                     changes += 1
        #                 q.append((changes, r, s))

        # return -1
        
29983