<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:
    int checkWays(vector<vector<int>>& pairs) {
        unordered_map<int,unordered_set<int>> mp;
        int n=pairs.size();
        for(int i=0;i<n;i++){
            int x=pairs[i][0],y=pairs[i][1];
            mp[x].insert(y);
            mp[y].insert(x);
        }
        int ct=1,x0=1;
        for(auto it:mp){
            if(it.second.size()>ct){
                x0=it.first;
                ct=it.second.size();
            }
        }
        priority_queue<pair<int,int>> pq;
        for(auto it:mp){
            pq.push({it.second.size(),it.first});
        }
        int len=mp.size();
       unordered_set<int> vis;
        int ans=1;
        while(!pq.empty()){
            auto it=pq.top();
            pq.pop();
            int node=it.second,deg=it.first;
            int par=-1,maxDeg=INT_MAX;
            for(auto it2:mp[node]){
                if(vis.count(it2)&&mp[it2].size()<maxDeg){
                    par=it2;
                    maxDeg=mp[it2].size();
                }
            }
            vis.insert(node);
            if(par==-1){
                if(deg!=len-1){
                    return 0;
                }
                continue;
            }
            for(auto it2:mp[node]){
                if(it2==par)continue;
                if(!mp[par].count(it2))return 0;
            }
            if(maxDeg==deg){
                ans=2;
            }

        }
        
        return ans;
    }
};
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