<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:
    
    bool multiple=false; 
    int checkWays(vector<vector<int>>& pairs) {
        map<int,vector<int>>m;
        vector<int>degrees(501,0);
        vector<vector<bool>>connected(501,vector<bool>(501,false));
        
        for(int i=0;i<pairs.size();++i){
            int x_i=pairs[i][0];
            int y_i=pairs[i][1];
            if(m.find(x_i)==m.end()){
                m[x_i]={y_i};
            }
            else{
                m[x_i].push_back(y_i);
            }
            if(m.find(y_i)==m.end()){
                m[y_i]={x_i};
            }
            else{
                m[y_i].push_back(x_i);
            }
            degrees[x_i]++;
            degrees[y_i]++;
            connected[x_i][y_i]=true;
            connected[y_i][x_i]=true;
        }
        vector<int>keys;
        for(auto i: m){
            keys.push_back(i.first);
        }
        int size = keys.size();
        int root=-1;
        for(int i=0;i<size;++i){
            sort(m[keys[i]].begin(),m[keys[i]].end(),[&degrees](int a, int b){
                return degrees[a]>degrees[b];
            });
            if(degrees[keys[i]]==size-1){
                root=keys[i];
            }
        }
        if(root<0){
            return 0;
        }
        vector<bool>visited(501,false);
        vector<int>ancestors={};
        if(!dfs(root,ancestors,visited,m,degrees,connected)){
            return 0;
        }

        if(multiple){
            return 2;
        }
        else{
            return 1;
        }  
    }

    bool dfs(int x,vector<int>& ancestors,vector<bool>& visited,map<int,vector<int>>& m,vector<int>& degrees,vector<vector<bool>>& connected){
        if(visited[x]){
            return true;
        }
        for(int i=0;i<ancestors.size();++i){
            if(!connected[ancestors[i]][x]){
                cout<<x<<" "<<ancestors[i]<<endl;
                return false;
            }
        }
        visited[x]=true;
        ancestors.push_back(x);
        for(int i=0;i<m[x].size();++i){
            if(degrees[x]==degrees[m[x][i]]){
                multiple=true;
            }
            if(!dfs(m[x][i],ancestors,visited,m,degrees,connected)){
                return false;
            }
        }
        ancestors.pop_back();
        return true;
    }
};
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