<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:
    vector<int> parent,size;
    int findParent(int num)
    {
        if(num == parent[num])
            return num;
        return parent[num] = findParent(parent[num]);
    }

    void preformUnion(int first,int last)
    {
        int upf  = findParent(first);
        int upl = findParent(last);

        if(upf == upl)
            return;
        if(size[upf] < size[upl])
        {
            parent[upf] = upl;
            size[upl] += size[upf];
        }
        else
        {
            parent[upl] = upf;
            size[upf] += size[upl];
        }
    }

    bool equationsPossible(vector<string>& equations) {
        int n = equations.size();
        if(!n)
            return false;
        parent.resize(26);
        size.resize(26,1);
        for(int i = 0;i<26;i++)
        {
            parent[i] = i;
        }
        unordered_map<int,vector<int>> mp;

        for(int i = 0;i<n;i++)
        {
            char first = equations[i][0];
            char last = equations[i][3];
            string operators = equations[i].substr(1,2);
            // cout<<operators<<endl;
            if(operators == "==")
            {
                preformUnion(first - 'a',last -'a');
            }
            else if(operators == "!=")
            {
                // cout<<first<<" "<<last<<endl;
                int parentFirst = findParent(first-'a');
                int parentLast = findParent(last-'a');
                mp[first-'a'].push_back(last-'a');
                if(parentFirst == parentLast)
                    return false;
            }
        }
        // cout<<mp.size()<<endl;

        for(auto it = mp.begin();it!=mp.end();it++)
        {
            int parent1 = findParent(it->first);
            for(auto x: it->second)
            {
                int parent2 = findParent(x);
                if(parent1 == parent2)
                    return false;
            }
        }
        
        return true;
        
    }
};


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