<p>You have <code>n</code> binary tree nodes numbered from <code>0</code> to <code>n - 1</code> where node <code>i</code> has two children <code>leftChild[i]</code> and <code>rightChild[i]</code>, return <code>true</code> if and only if <strong>all</strong> the given nodes form <strong>exactly one</strong> valid binary tree.</p>

<p>If node <code>i</code> has no left child then <code>leftChild[i]</code> will equal <code>-1</code>, similarly for the right child.</p>

<p>Note that the nodes have no values and that we only use the node numbers in this problem.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/08/23/1503_ex1.png" style="width: 195px; height: 287px;" />
<pre>
<strong>Input:</strong> n = 4, leftChild = [1,-1,3,-1], rightChild = [2,-1,-1,-1]
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/08/23/1503_ex2.png" style="width: 183px; height: 272px;" />
<pre>
<strong>Input:</strong> n = 4, leftChild = [1,-1,3,-1], rightChild = [2,3,-1,-1]
<strong>Output:</strong> false
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/08/23/1503_ex3.png" style="width: 82px; height: 174px;" />
<pre>
<strong>Input:</strong> n = 2, leftChild = [1,0], rightChild = [-1,-1]
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>n == leftChild.length == rightChild.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>-1 &lt;= leftChild[i], rightChild[i] &lt;= n - 1</code></li>
</ul>

class Solution {
public:
    void helper(auto&adj,auto&vis,int par){
        vis[par] = true;
        for(auto x:adj[par]){
            if(!vis[x]){
                helper(adj,vis,x);
            }
        }
    }
    bool validateBinaryTreeNodes(int n, vector<int>& leftChild, vector<int>& rightChild) {
        map<int,int>mp;
        for(int i = 0 ; i < rightChild.size();i++){
            if(rightChild[i] != -1 ){
                if(mp.find(rightChild[i])!= mp.end())
                    return false;
                mp[rightChild[i]] = i;
            }
            if(leftChild[i] != -1 ){
                if(mp.find(leftChild[i])!= mp.end())
                    return false;
                mp[leftChild[i]] = i;
            }
        }
        int root = -1;
        for(int i = 0 ; i < rightChild.size();i++){
            if(mp.find(i) == mp.end()) {
                if(root != -1)
                    return false;
                root = i;
            }
        }
        if(root == -1)
            return false;
        unordered_map<int,list<int>>adj;
        for(int i = 0 ; i < rightChild.size() ;i++){
            if(rightChild[i] != -1)
                adj[i].push_back(rightChild[i]);
            if(leftChild[i] != -1)
                adj[i].push_back(leftChild[i]);
        }
        unordered_map<int,bool>vis;
        helper(adj,vis,root);
        if(vis.size() != n)
            return false;
        return true;

        
    }
};
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