<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>

"""
8/31/24

patterns

learnings
- set intersection with &
"""
class Solution:
    def numBusesToDestination(self, routes, start, target):
        if start == target: 
            return 0
                
        def build_graph(routes): 
            # convert routes to a list of sets, eg:
            # [ {1,6,7}, {6,1,3}, ...]
            routes = list(map(set, routes))
            
            for i, route in enumerate(routes):
                if start in route:  # possible starting route number
                    seen.add(i)
                    to_visit.append((i, 1))

                if target in route:  # possible ending route number
                    targets.add(i)

                for j in range(i+1, len(routes)):
                    # whoa!
                    # set intersection to check if route_i and route_j are connected
                    if routes[j] & route:  
                        graph[i].add(j)
                        graph[j].add(i)
        
        def bfs():
            while to_visit:
                current, count = to_visit.popleft()
                if current in targets:
                    return count

                # process neighbors
                for neighbor in graph[current]:
                    if neighbor not in seen:
                        to_visit.append((neighbor, count+1))
                        seen.add(neighbor)
            
            return None
        
        to_visit = deque()
        graph = defaultdict(set)  
        seen, targets = set(), set()
        
        build_graph(routes)
        count = bfs()
        return count if count else -1
        
        
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