<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:
    void DFS(vector<vector<char>>& ed, vector<int>& visit, unordered_set<char>& st, int i){
        visit[i] = 1;
        st.insert(i + 'a');
        for (char c : ed[i]){
            if (!visit[c - 'a']){
                DFS(ed, visit, st, c - 'a');
            }
        }
    }

    bool equationsPossible(vector<string>& equations) {
        vector<vector<char>> edgesEqual(26), edgesNoEqual(26);
        for (auto& q : equations){
            char v1 = q[0];
            char v2 = q[3];
            if (q[1] == '='){
                edgesEqual[v1 - 'a'].push_back(v2);
                edgesEqual[v2 - 'a'].push_back(v1);
            }
            else{
                edgesNoEqual[v1 - 'a'].push_back(v2);
                edgesNoEqual[v2 - 'a'].push_back(v1);
            }
        }
        vector<int> visit(26);
        for (int i = 0; i < 26; i++){
            if (!visit[i]){
                unordered_set<char> st;
                DFS(edgesEqual, visit, st, i);
                for (char c : st){
                    for (char w : edgesNoEqual[c - 'a']){
                        if (st.contains(w)){
                            return false;
                        }
                    }
                }
            }
        }
        return true;
    }
};
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