<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:
    bool equationsPossible(vector<string>& equations) {
        vector<unordered_set<char>> v(128);
        
        for(string &e: equations)
        {
            if(e[1] == '=')
            {
                v[e[0]].insert(e[3]);
                v[e[3]].insert(e[0]);
            }
        }
        for(int i = 'a'; i <= 'z'; i++)
        {
            auto t_set = v[i];
            for(auto j: t_set)
            {
                v[i].insert(v[j].begin(), v[j].end());
            }
        }

        for(string &e: equations)
        {
            if(e[1] == '!')
            {
                if(e[0] == e[3])
                {
                    return false;
                }
                if(!v[e[0]].empty() && v[e[0]].find(e[3]) != v[e[0]].end())
                {
                    return false;
                }
                if(!v[e[3]].empty() && v[e[3]].find(e[0]) != v[e[3]].end())
                {
                    return false;
                }
            }
        }
        return true;
    }
};
18100