<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 dsu{
public:
    vector<int> par;
    vector<int> size;

    dsu(int n)
    {
        par.resize(n+1,0);
        size.resize(n+1,1);
        for(int i=0;i<=n;i++) par[i] = i;
    }

    int fup(int p)
    {
        if(par[p] == p) return p;
        return par[p] = fup(par[p]);
    }

    void ubs(int u,int v)
    {
        int up = fup(u);
        int vp = fup(v);
        if(up == vp) return;
        if(size[up] > size[vp])
        {
            par[vp] = up;
            size[up] += size[vp];
        }
        else
        {
            par[up] = vp;
            size[vp] += size[up];
        }
    }

};
class Solution {
public:
    bool equationsPossible(vector<string>& e) {
        vector<char> ps(26,' ');
        dsu ds(26);
        for(auto x:e)
        {
            int u = x[0] - 'a';
            int v = x[3] - 'a';
            char sy = x[1];

            int up = ds.fup(u);
            int vp = ds.fup(v);

            if(sy == '=')
            {
                if(up != vp)
                {
                    ds.ubs(u,v);
                }
            }
        }

        for(auto x:e)
        {
            int u = x[0] - 'a';
            int v = x[3] - 'a';
            char sy = x[1];

            int up = ds.fup(u);
            int vp = ds.fup(v);

            if(sy == '!')
            {
                if(up == vp)
                {
                    return 0;
                }
            }
        }

        return 1;
    }
};
15100