<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>

import collections
class Solution:
    def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
        if source == target:
            return 0
        # is 2 route connected O(r) r = max route len be tween 2
        #
        def is_connected(r1,r2):
            for stop in r1:
                if stop in r2:
                    return True
            return False
        # merge routes that contain src together
        MERGED = -123
        first_node_stops = [] # list of sorted busstop
        for i in range(len(routes)):
            if source in routes[i]:
                first_node_stops += routes[i]
                routes[i] = MERGED
            else:
                routes[i] = set(routes[i])
        routes.append(set(first_node_stops))

        # node i contian target flag
        target_s = set()
        # node i
        # E - map from i -> list of neigbor node
        E = collections.defaultdict(set)
        for i in range(len(routes)):
            if routes[i] != MERGED:
                if target in routes[i]:
                    target_s.add(i)
                for j in range(i+1,len(routes)):
                    if routes[j] != MERGED and is_connected(routes[i],routes[j]):
                        E[j].add(i)
                        E[i].add(j)
        #BFS from src to target
        q = collections.deque()
        visit = set()
        q.append(len(routes)-1)
        d = 0
        while q:
            d+=1
            for _ in range(len(q)):
                node = q.popleft()
                if node in visit:
                    continue
                if node in target_s:
                    return d
                visit.add(node)
                for nei in E[node]:
                    q.append(nei)
        
        return -1



        
        # d = 1
        # [4,5, / 15,19]
        # [1, 2] [2,3] [3,4]

        # src= 1 target = 4

        # routes contain 1 : [1,2] d=1
        # [1x 2]
        # routes contain 2: [2,3] d=2
        # [1x 2x 3]
        # routes contain 3 : [3,4] d=3
        # [1x 2x 3x 4]we found target with d =3

        # map from busstop -> routes that contain that bus stop
        # 1 -> [1,2,7] 
        # 2 -> 127
        # 3 -> 367
        # ..
        # 7 -> [127] [367]  R/#bus_stop

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