<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


        s2b={}
        b2s={}
        for i in range(len(routes)):
            for s in routes[i]:
                s2b[s]=s2b.get(s,set())
                s2b[s].add(i)
                b2s[i]=b2s.get(i,set())
                b2s[i].add(s)

        to_visit = set([source])
        visited_b = set()
        visited = set()
        if source not in s2b :
            return -1
        # res={source:0}
        for iteration in range(500):
            # print(iteration)
            if len(to_visit) < 0:
                break
            new_to_visit = set()
            while len(to_visit) > 0:
                node = to_visit.pop()
                visited.add(node)
                for b in s2b[node]:
                    if b in visited_b:
                        continue
                    visited_b.add(b)
                    for s in b2s[b]:
                        if s == target:
                            return iteration+1
                        if s not in visited:
                            new_to_visit.add(s)
            to_visit = new_to_visit
                
                
            #     if node in res:
            #         for b in s2b[node]:
            #             visited_b.add(b)
            #             if b in visited_b:
            #                 continue
            #             for s in b2s[b]:
            #                 ori=res.get(s,float(inf))
            #                 res[s] =  min(ori,res[node]+1)
            #                 if s not in visited and res[s] < res.get(target,float(inf)) and res[s] <ori:
            #                     new_to_visit.add(s)
            # print(len(visited),len(new_to_visit))
            # to_visit = new_to_visit
        return -1
              
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