<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:
    int equals[26][26] = {0};
    
    vector<int> graph[26];
    
    
    void dfs(int cur, int root,  bool vis[]) {
        if(vis[cur]) return;
        vis[cur] = true;
        
        equals[root][cur] = 1;
        
        for(int child : graph[cur]) {
            dfs(child, root, vis);
        }
    }
     
    bool equationsPossible(vector<string>& equations) {
        
        for(const auto &equation : equations) {
            if(equation[1] == '!') continue;
            
            int u = equation[0] - 'a';
            int v = equation[3] - 'a';
            
            graph[u].push_back(v);
            graph[v].push_back(u);
        }   
        
        for(int i = 0; i < 26; i ++) {
            bool vis[26] = {0};
            dfs(i, i, vis);
        }
        
        for(auto &equation : equations) {
            if(equation[1] == '=') continue;
            if(equals[equation[0]-'a'][equation[3]-'a']) return false;
        }
        
        return true;
    }
    
    
};
15100