<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>


# from collections import deque


class Solution:
    def numBusesToDestination(self, routes, source: int, target: int) -> int:
        if source == target: return 0

        n = len(routes)
        r_map = {}
        for i in range(n):
            for it in routes[i]:
                r_map[it] = r_map.get(it, []) + [i]

        ans = -1
        for bus_idx in r_map.get(source, []):
            dq = deque([[bus_idx, 1]])
            is_bus_vis = {bus_idx: True}
            is_site_vis = {source: True}
            while dq:
                cur, dep = dq.popleft()
                # print('bus id', cur, 'change', dep)
                for nxt in routes[cur]:
                    if nxt == target:
                        dq = None
                        ans = min(ans, dep) if ans != -1 else dep
                        break
                    elif nxt not in is_site_vis:
                        # print('    add site', nxt, 'with buses of', r_map[nxt])
                        for bus_nxt in r_map[nxt]:
                            if bus_nxt not in is_bus_vis:
                                dq.append([bus_nxt, dep+1])
                                is_bus_vis[bus_nxt] = True
                        is_site_vis[nxt] = True
                # print('bus end,', dq)
        return ans


# s = Solution()
# res = s.numBusesToDestination([[1,2,7],[3,6,7]], source = 1, target = 6)
# # res = s.numBusesToDestination([[7,12],[4,5,15],[6],[15,19],[9,12,13]], source = 15, target = 12)
# print(res)

42703