<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<long long int> parent,size;
        DSU(int n){ 
            parent.resize(n+1);
            size.resize(n+1);
            for(int i=0;i<=n;i++){
                parent[i]=i;
                size[i]=1;
            }
        }
        int find(int v){
            if(v==parent[v]){
                return v;
            }
            return parent[v]=find(parent[v]);
        }
        void Union(int a,int b){
            a=find(a);
            b=find(b);
            if(a!=b){
                if(size[a]<size[b]) swap(a,b);
                parent[b]=a;
                size[a]+=size[b]+0LL;
            }
        }
};

class Solution {
public:
    bool equationsPossible(vector<string>& equations) {
        vector<vector<int>> notequal;
        DSU dsu(26);
        for(auto x:equations){
            int a=x[0]-'a';
            int b=x[3]-'a';
            if(x[1]=='='){
                dsu.Union(a,b);
            }
            else{
                notequal.push_back({a,b});
            }
        }
        for(auto it:notequal){
            if(dsu.find(it[0])==dsu.find(it[1])) return false;
        }
        return true;
    }
};
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