<p>You are given an array <code>pairs</code>, where <code>pairs[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>, and:</p>

<ul>
	<li>There are no duplicates.</li>
	<li><code>x<sub>i</sub> &lt; y<sub>i</sub></code></li>
</ul>

<p>Let <code>ways</code> be the number of rooted trees that satisfy the following conditions:</p>

<ul>
	<li>The tree consists of nodes whose values appeared in <code>pairs</code>.</li>
	<li>A pair <code>[x<sub>i</sub>, y<sub>i</sub>]</code> exists in <code>pairs</code> <strong>if and only if</strong> <code>x<sub>i</sub></code> is an ancestor of <code>y<sub>i</sub></code> or <code>y<sub>i</sub></code> is an ancestor of <code>x<sub>i</sub></code>.</li>
	<li><strong>Note:</strong> the tree does not have to be a binary tree.</li>
</ul>

<p>Two ways are considered to be different if there is at least one node that has different parents in both ways.</p>

<p>Return:</p>

<ul>
	<li><code>0</code> if <code>ways == 0</code></li>
	<li><code>1</code> if <code>ways == 1</code></li>
	<li><code>2</code> if <code>ways &gt; 1</code></li>
</ul>

<p>A <strong>rooted tree</strong> is a tree that has a single root node, and all edges are oriented to be outgoing from the root.</p>

<p>An <strong>ancestor</strong> of a node is any node on the path from the root to that node (excluding the node itself). The root has no ancestors.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img src="https://assets.leetcode.com/uploads/2020/12/03/trees2.png" style="width: 208px; height: 221px;" />
<pre>
<strong>Input:</strong> pairs = [[1,2],[2,3]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> There is exactly one valid rooted tree, which is shown in the above figure.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/03/tree.png" style="width: 234px; height: 241px;" />
<pre>
<strong>Input:</strong> pairs = [[1,2],[2,3],[1,3]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are multiple valid rooted trees. Three of them are shown in the above figures.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> pairs = [[1,2],[2,3],[2,4],[1,5]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no valid rooted trees.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= pairs.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= x<sub>i </sub>&lt; y<sub>i</sub> &lt;= 500</code></li>
	<li>The elements in <code>pairs</code> are unique.</li>
</ul>

class Solution {
public:
    unordered_map<int, unordered_set<int>> graph;
    void dfs(int node, vector < unordered_set <int> >& comp, unordered_set <int>& visited){
        if(visited.count(node)) return;
        visited.insert(node);
        comp.back().insert(node);
        for(auto& it : graph[node]){
            dfs(it, comp, visited);
        }
    }
    int helper(unordered_set <int>& nodes){
        int n = nodes.size();
        int req = n - 1;
        int cnt = 0;
        int root = -1;
        for(auto& it: nodes){
            if(graph[it].size() == req){
                cnt++;
                root = it;
                if(cnt == 2) break;
            }
        }
        if(cnt == 0) return 0;
        
        for(auto& it : nodes){
            graph[it].erase(root);
        }
        vector < unordered_set <int> > temp;
        unordered_set <int> visited;
        for(auto& it : nodes){
            if(!visited.count(it) && it != root){
                unordered_set <int> tempunordered_set;
                temp.push_back(tempunordered_set);
                dfs(it, temp, visited);
            }
        }
        
        bool two = false;
        bool zero=  false;
        for(int i = 0; i < temp.size(); i++){
            int x = helper(temp[i]);
            if(x == 2)two = true;
            if(x == 0) zero = true;
            if(zero) return 0;
        }
        if(zero) return 0;
        if(two) return 2;
        if(cnt >= 2) return 2;
        return 1;
    }
    int checkWays(vector<vector<int>>& pairs) {
        unordered_set <int> nodes;
        for(auto& it: pairs){
            graph[it[0]].insert(it[1]);
            graph[it[1]].insert(it[0]);
            nodes.insert(it[0]);
            nodes.insert(it[1]);
        }
        return helper(nodes);
    }
};
224500