<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,set<int>>graph;

    void dfs(int node,int &mark, unordered_set<int>&visited, unordered_map<int,unordered_set<int>>&comp){
         visited.insert(node);
         comp[mark].insert(node);
         for(auto ch : graph[node]){
            if(visited.find(ch) == visited.end()){
                dfs(ch,mark,visited,comp);
            }
         }
    }
    int solve(unordered_set<int>nodes){
        
        if(nodes.size() == 0){
            return 1;
        }

        vector<int>possibleroots;
        int n= nodes.size();
        for(auto node :nodes ){
            if(graph[node].size() == (n-1))possibleroots.push_back(node);
        }

        if(possibleroots.size() == 0)return 0 ;
        
        int newroot = possibleroots[0];

        for(int node : graph[newroot]){
            graph[node].erase(newroot);
        }

        unordered_set<int>visited;
         
        int mark = 0 ;
        unordered_map<int,unordered_set<int>>comp;
        for(int node : nodes){
            if(visited.find(node) == visited.end() && node != newroot){
                dfs(node,mark,visited,comp);
                mark++;
            }
        }
        
        //leaf node
        if(comp.size() == 0)return 1;
        
        // recursively calc answer for each comp
        vector<int>numways(comp.size());
        for(int i =0 ; i<comp.size(); i++){
              numways[i] = solve(comp[i]);
        }
        
        int ans =  1;
        for(int i =0 ; i<comp.size(); i++){
            if(numways[i] == 0)return 0 ;
            if(numways[i] == 2)ans = 2;
        }
                                                    
        if(possibleroots.size()  >= 2)ans = 2;
        return ans ;
    }
    int checkWays(vector<vector<int>>& pairs) {
        unordered_set<int>nodes;
        for(auto c : pairs){
            nodes.insert(c[0]);
            nodes.insert(c[1]);
            graph[c[0]].insert(c[1]);
            graph[c[1]].insert(c[0]);
        }
        return solve(nodes);
    }
};
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