<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<bool> visited;
    bool result = true;
    void searchPath(int source, int dest, vector<vector<int>>& adj) {
        if (source == dest){
            result = false;
            
        }   
        if (!visited[source]) {
            visited[source]=true;
            for (auto it : adj[source]) {
                if(!visited[it])
                    searchPath(it, dest, adj);
            }

        }
    }
    bool equationsPossible(vector<string>& equations) {
        visited.resize(27, false);
        vector<vector<int>> adj(501);
        for (int i = 0; i < equations.size(); i++) {
            if (equations[i][1] == '=') {
                int a = equations[i][0] - 'a';
                int b = equations[i][3] - 'a';
                adj[a].push_back(b);
                adj[b].push_back(a);
            }
        }
        
        for (int i = 0; i < equations.size(); i++) {
            if (equations[i][1] == '!') {
                int a = equations[i][0] - 'a';
                int b = equations[i][3] - 'a';
                if(a==b) return false;
                for(int j=0;j<27;j++){
                    visited[j]=false;
                }
                searchPath(a, b, adj);
                
            }

        }
        return result;
    }
};
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