<p>On a social network consisting of <code>m</code> users and some friendships between users, two users can communicate with each other if they know a common language.</p>

<p>You are given an integer <code>n</code>, an array <code>languages</code>, and an array <code>friendships</code> where:</p>

<ul>
	<li>There are <code>n</code> languages numbered <code>1</code> through <code>n</code>,</li>
	<li><code>languages[i]</code> is the set of languages the <code>i<sup>​​​​​​th</sup></code>​​​​ user knows, and</li>
	<li><code>friendships[i] = [u<sub>​​​​​​i</sub>​​​, v<sub>​​​​​​i</sub>]</code> denotes a friendship between the users <code>u<sup>​​​​​</sup><sub>​​​​​​i</sub></code>​​​​​ and <code>v<sub>i</sub></code>.</li>
</ul>

<p>You can choose <strong>one</strong> language and teach it to some users so that all friends can communicate with each other. Return <i data-stringify-type="italic">the</i> <i><strong>minimum</strong> </i><i data-stringify-type="italic">number of users you need to teach.</i></p>
Note that friendships are not transitive, meaning if <code>x</code> is a friend of <code>y</code> and <code>y</code> is a friend of <code>z</code>, this doesn&#39;t guarantee that <code>x</code> is a friend of <code>z</code>.
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 2, languages = [[1],[2],[1,2]], friendships = [[1,2],[1,3],[2,3]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> You can either teach user 1 the second language or user 2 the first language.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 3, languages = [[2],[1,3],[1,2],[3]], friendships = [[1,4],[1,2],[3,4],[2,3]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Teach the third language to users 1 and 3, yielding two users to teach.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 500</code></li>
	<li><code>languages.length == m</code></li>
	<li><code>1 &lt;= m &lt;= 500</code></li>
	<li><code>1 &lt;= languages[i].length &lt;= n</code></li>
	<li><code>1 &lt;= languages[i][j] &lt;= n</code></li>
	<li><code>1 &lt;= u<sub>​​​​​​i</sub> &lt; v<sub>​​​​​​i</sub> &lt;= languages.length</code></li>
	<li><code>1 &lt;= friendships.length &lt;= 500</code></li>
	<li>All tuples <code>(u<sub>​​​​​i, </sub>v<sub>​​​​​​i</sub>)</code> are unique</li>
	<li><code>languages[i]</code> contains only unique values</li>
</ul>

class Solution {
public:
    bool check(vector<int>& a, vector<int>& b)
{
    
    int M = a.size();
 
    
    int N = b.size();
 
  
    int p1 = 0, p2 = 0;
 
  
    while (p1 < M && p2 < N) {
 
        if (a[p1] < b[p2])
            p1++;
        else if (a[p1] > b[p2])
            p2++;
        else
            return true;
    }
    return false;
}

int minimumTeachings(
    int N, vector<vector<int> >& languages,
    vector<vector<int> > friendships)
{
    
    int m = languages.size();
 
    
    int t = friendships.size();
 
  
    unordered_set<int> total;
 
 
    unordered_map<int, int> overall;
 
  
    for (int i = 0; i < m; i++)
        sort(languages[i].begin(),
             languages[i].end());
 
    
    for (int i = 0; i < t; i++) {
        
        if (!check(languages[friendships[i][0] - 1],
                   languages[friendships[i][1] - 1])) {
 
           
            total.insert(friendships[i][0]);
            total.insert(friendships[i][1]);
        }
    }
 
    
    int s = total.size();
 
   
    int result = s;
 
   
    for (auto p : total) {
 
        for (int i = 0;
             i < languages[p - 1].size(); i++)
 
           
            overall[languages[p - 1][i]]++;
    }
 
   
    for (auto c : overall)
 
        
        result = min(result, s - c.second);
 
   
    return result;
    }
};
65300