<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> parents;
    unordered_map<char, int> ranks;
    
    static bool cmp(const string &a, const string &b) {
        return a[1] == '=';
    }
    
    void addSet(char &val) {
        parents[val] = val;
        ranks[val] = 0;
    }
    
    char findSet(char &val) {
        if (parents[val] == val) {
            return val;
        }
        return parents[val] = findSet(parents[val]);
    }
    
    void unionSet(char &val1, char &val2) {
        char parent1 = findSet(val1);
        char parent2 = findSet(val2);
        // cout << "Got both parents " << parent1 << " and " << parent2 << endl;
        
        if (parent1 == parent2) return;
        
        if (ranks[parent1] > ranks[parent2]) {
            parents[parent2] = parent1;
        } else if (ranks[parent2] > ranks[parent1]) {
            parents[parent1] = parent2;
        } else {
            parents[parent2] = parent1;
            ranks[parent1]++;
            ranks[parent2] = 0;
        }
    }
    
    bool equationsPossible(vector<string>& equations) {
        vector<string> firstPart, secondHalf;
        
        for (auto &eq: equations) {
            if (eq[1] == '=') {
                firstPart.push_back(eq);
            } else {
                secondHalf.push_back(eq);
            }
        }
        
        equations.clear();
        firstPart.insert(firstPart.end(), secondHalf.begin(), secondHalf.end());
        
        equations.insert(equations.end(), firstPart.begin(), firstPart.end());
        
        // for (auto &e: equations) {
        //     cout << e << " " ;
        // }
        // cout << endl;
        
        for (auto &eq: equations) {
            addSet(eq[0]);
            addSet(eq[3]);
        }
        
        for (auto &eq: equations) {
            char a = eq[0];
            char b = eq[3];

            // cout << "Nodes " << a << " & " << b << " " << eq << endl << endl;
            if (eq[1] == '=') {
                // cout << "Starting Find Set Operation " << endl;
                unionSet(a, b);
            } else {
                if (findSet(a) == findSet(b)) {
                    // cout << findSet(a) << " " << findSet(b) << endl;
                    return false;
                }
            }
        }
        
        return true;
    }
};
17200