<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:
    
    bool intersect(vector<int> &a, vector<int> &b){
        unordered_set<int> s;
        for(int x : a){
            s.insert(x);
        }
        for(int x : b){
            s.insert(x);
        }
        return s.size() < (a.size() + b.size());
    }
    
    bool intersectV2(vector<int> &a, vector<int> &b){
        if(a.size() > b.size())
            return intersectV2(b,a);
        for(int i : a){
            int l = 0,r = b.size()-1,m;
            while(l <= r){
                m = (l+r)/2;
                //cout<<"m : "<<m<<" | bs : "<<b.size()<<endl;
                if( i == b[m] )
                    return true;
                else if( i > b[m])
                    l = m+1;
                else 
                    r = m-1;
            }    
        }
        return false;
    }
    
    int numBusesToDestination(vector<vector<int>>& routes, int source, int target) {
        for(int i = 0 ; i < routes.size() ; i++){
            sort(routes[i].begin(),routes[i].end());
        }
        if(source == target)
            return 0;
        unordered_map<int,unordered_set<int>> g;
        unordered_set<int> S;
        unordered_set<int> T;
        for(int i = 0 ; i < routes.size() ; i++){
            for( int j = 0 ; j < routes[i].size() ; j++){
                if(routes[i][j] == source){
                    S.insert(i);
                }
                if(routes[i][j] == target){
                    T.insert(i);
                }
            }
            for( int j = i+1 ; j < routes.size() ; j++){
                if(intersectV2(routes[i],routes[j])){
                    g[i].insert(j);
                    g[j].insert(i);
                }
            }
        }
        
        //return 0;
        queue<int> q;
        vector<bool> vis(routes.size(),false);
        for(auto x : S){
            q.push(x);
            vis[x] = true;
        }
        int ans = 1;
        while(!q.empty()){
            int sz = q.size();
            while(sz > 0){
                auto cur = q.front();
                q.pop();
                if(T.find(cur) != T.end())
                    return ans;
                for(auto nxt : g[cur]){
                    if(!vis[nxt]){
                        vis[nxt] = true;
                        q.push(nxt);
                    }
                }
                sz--;
            }
            ans++;
        }
        
        return -1;
    }
};
53448