<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) {

        vector<int> dx = {1, 0, -1, 0};
        vector<int> dy = {0, 1,  0, -1};

        int n = routes.size();
        unordered_map<int, vector<int>> graph;
        unordered_set<int> seen;
        unordered_set<int> t;
        int s = -1;
        int d = -1;

        if (source == target) {
            return 0;
        }

        // If in same route then return 1
        for (int i = 0; i < routes.size(); i++) {
            if (containsBoth(routes[i], source, target)) {
                return 1;
            }
        }

        // Sort each routes.
        for (int i = 0; i < routes.size(); i++) {
            sort(routes[i].begin(), routes[i].end());
        }


        //check if routes intersects
        for (int i = 0; i < n; i++) {
            for(int j = i + 1; j < n; j++) {
                if (isIntersecting(routes[i], routes[j])) {
                    graph[i].push_back(j);
                    graph[j].push_back(i);
                }
            }
        }

        queue<int> q;
       
       
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < routes[i].size(); j++)
            {
                if (routes[i][j] == source) {
                    q.push(i);
                    seen.insert(i);
                    break;
                }
            }
        }


        int path = 1;


        while(!q.empty()) {
            int sz = q.size();
            
            for (int i = 0 ; i < sz; i++) {
                int current = q.front();
                q.pop();

                if (containsTarget(routes[current], target)) {
                    return path;
                }

                for (int adj: graph[current]) {
                    if (seen.find(adj) == seen.end()) {
                        seen.insert(adj);
                        q.push(adj);
                    }
                    
                }
            }
            path++;
            
        }

        return -1;
    }

    bool containsTarget(vector<int> &routes, int target) {
        for (int route: routes) {
            if (route == target) {
                return true;
            }
        }
        return false;
    }

    bool isIntersecting(vector<int> &a, vector<int> &b) {

        int i = 0, j = 0;

        while(i < a.size() && j < b.size()) {
            if (a[i] == b[j])
                return true;
            if(a[i] < b[j])
                i++;
            else
                j++;
        }
        return false;
    }

    bool containsBoth(vector<int> &a, int s, int d) {
        bool s1 = false, d1 = false;
        for (int i = 0 ; i < a.size(); i++) {
            if (a[i] == s) {
                s1 = true;
            }
            if (a[i] == d) {
                d1 = true;
            }
        }

        return s1 && d1;
    }
};
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