<p>You are given an array of strings <code>equations</code> that represent relationships between variables where each string <code>equations[i]</code> is of length <code>4</code> and takes one of two different forms: <code>&quot;x<sub>i</sub>==y<sub>i</sub>&quot;</code> or <code>&quot;x<sub>i</sub>!=y<sub>i</sub>&quot;</code>.Here, <code>x<sub>i</sub></code> and <code>y<sub>i</sub></code> are lowercase letters (not necessarily different) that represent one-letter variable names.</p>

<p>Return <code>true</code><em> if it is possible to assign integers to variable names so as to satisfy all the given equations, or </em><code>false</code><em> otherwise</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> equations = [&quot;a==b&quot;,&quot;b!=a&quot;]
<strong>Output:</strong> false
<strong>Explanation:</strong> If we assign say, a = 1 and b = 1, then the first equation is satisfied, but not the second.
There is no way to assign the variables to satisfy both equations.
</pre>

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

<pre>
<strong>Input:</strong> equations = [&quot;b==a&quot;,&quot;a==b&quot;]
<strong>Output:</strong> true
<strong>Explanation:</strong> We could assign a = 1 and b = 1 to satisfy both equations.
</pre>

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

<ul>
	<li><code>1 &lt;= equations.length &lt;= 500</code></li>
	<li><code>equations[i].length == 4</code></li>
	<li><code>equations[i][0]</code> is a lowercase letter.</li>
	<li><code>equations[i][1]</code> is either <code>&#39;=&#39;</code> or <code>&#39;!&#39;</code>.</li>
	<li><code>equations[i][2]</code> is <code>&#39;=&#39;</code>.</li>
	<li><code>equations[i][3]</code> is a lowercase letter.</li>
</ul>

class Solution {
public:
    int findpr(int i,vector<int>pr){
        while(pr[i]!=i){
            i=pr[i];
        }
        return i;
    }
    void uf(int u,int v,vector<int>&pr,vector<int>&rank){
        u=findpr(u,pr);
        v=findpr(v,pr);
        if(rank[u]==rank[v]){
            pr[u]=v;
            rank[v]++;
        }
        else if(rank[v]>rank[u]){
            pr[u]=v;
        }
         else if(rank[v]<rank[u]){
            pr[v]=u;
        }
    } 
    bool equationsPossible(vector<string>& eq) {
        vector<int>pr(27);
        vector<int>rank(27,0);
        for(int i=0;i<27;i++)pr[i]=i;
        vector<pair<int,int>>tocheck;
        for(int i=0;i<eq.size();i++){
            if(eq[i][1]==eq[i][2]){
                uf(eq[i][0]-'a',eq[i][3]-'a',pr,rank);
            }
            else{
                tocheck.push_back({eq[i][0]-'a',eq[i][3]-'a'});
            }
        }
        for(auto it:tocheck){
            if(findpr(it.first,pr)==findpr(it.second,pr))return false;
        }
        return true;
    }
};
18200