<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 {
public:
    int numBusesToDestination(vector<vector<int>>& routes, int source, int target) {
        if(source==target) return 0;
        map<int, vector<int>> parentRelation;
        map<int, vector<int>> parentNodes;
        vector<int> parent(1000000);
        for(int i=0; i<parent.size(); i++) parent[i]=i;

        int uniqueId = 12312;
        for(vector<int> route: routes) {
            int parentStop = uniqueId;
            for(int stop: route) {
                parentRelation[stop].push_back(parentStop);
                parentNodes[parentStop].push_back(stop);
                makeParent(parent, stop, route[0]);
            }
            uniqueId+=1;
        }
        if(getParent(parent, source)!=getParent(parent, target)) return -1;
        
        queue<pair<int, int>> que;
        map<int, bool> visited;
        for(int buses: parentRelation[source]) {
            visited[buses]=true;
            for(int stop: parentNodes[buses]) {
                que.push({stop, 1});
            }
        }
        while(!que.empty()) {
            pair<int, int> pr = que.front();
            if(pr.first==target) return pr.second;
            que.pop();
            for(int tmpParents: parentRelation[pr.first]) {
                if(!visited[tmpParents]) {
                    visited[tmpParents]=true;
                    for(int newStops: parentNodes[tmpParents]) {
                        que.push({newStops, pr.second+1});
                    }
                }
            }
        }
        return -1;
        
    }

    int getParent(vector<int> &parentVec, int child) {
        if(parentVec[child]==child) return child;
        return getParent(parentVec, parentVec[child]);
    }
    void makeParent(vector<int> &parentVec, int child, int parent) {
        parentVec[getParent(parentVec, child)] = getParent(parentVec, parent);
    }
};



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