<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:
    unordered_map<char, char>parent;
    unordered_map<char, int> sz;

    char findParent(char a){
        while(a != parent[a]){
            a = parent[a];
        }
        return a;
    }

    bool same(char a, char b){
        return findParent(a) == findParent(b);
    }

    void unite(char a, char b){
        a = findParent(a);
        b = findParent(b);

        if(sz[a] < sz[b]) swap(a, b);
        sz[a] += sz[b];
        parent[b] = a;
    }

    bool equationsPossible(vector<string>& equations) {
        int n = equations.size();

        vector<string> equals, negat;

        for(string equation: equations){
            char a = equation[0];
            char b = equation[3];

            parent[a] = a;
            parent[b] = b;
            sz[a] = 1;
            sz[b] = 1;

            if(equation[1] == '='){
                equals.push_back(equation);
            } else {
                negat.push_back(equation);
            }
        }

        for(string elem: equals){
            char a = elem[0];
            char b = elem[3];
                if(!same(a, b)){
                    unite(a, b);
                }
        }

        for(string elem: negat){
            char a = elem[0];
            char b = elem[3];
            if(same(a,b)){
                return false;
            }
        }

        return true;
    }
};
16500