<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 defaultdict as dd
class Solution:
    def __init__(self):
        self.mini=99999999
        self.dp={}
    def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
        if source==target:
            return 0
        n=len(routes)
        di=dd(list)
        for i in range(n):
            for x in routes[i]:
                di[x].append(i)
        print(di)
        res=self.dfs(di,routes,source,target,{},{})
        if res>=99999999:
            return -1
        return res
    
    def dfs(self,di,routes,i,tgt,visited,vis):
        if i==tgt:
            return 0
        if i in self.dp.keys():
            return self.dp[i]
        mini=99999999
        vis[i]=1
        for ind in di[i]:
            if ind not in visited.keys():
                visited[ind]=1
                temp=[]
                for x in routes[ind]:
                    if x not in vis.keys():
                        temp.append(x)
                        self.dp[x]=self.dfs(di,routes,x,tgt,visited,vis)
                        mini=min(mini,self.dp[x])
                for x in temp:
                    if mini+1<self.dp[x]:
                        self.dp[x]=mini+1
                del visited[ind]
        del vis[i]
        return mini+1


                
        

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