<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 disjoint{
    public:
    vector<int> parent;
    vector<int> size;
    disjoint(int n){
        parent.resize(n+1);
        size.resize(n+1,1);
        for(int i=0;i<=n;i++){
            parent[i]=i;
        }
    }
    int par(int u){
        if(parent[u]==u) return u;
        return parent[u]=par(parent[u]);
    }
    void merge(int u,int v){
        int ult_u=par(u);
        int ult_v=par(v);
        if(ult_u==ult_v){
            return;
        }
        parent[ult_v]=ult_u;
    }
};
class Solution {
public:
    bool validateBinaryTreeNodes(int n, vector<int>& leftChild, vector<int>& rightChild) {
        disjoint ds(n);
        for(int i=0;i<n;i++){
            if(leftChild[i]!=-1){
                if( ds.par(leftChild[i])==leftChild[i]  && ds.par(i)!=ds.par(leftChild[i])){
                    ds.merge(i,leftChild[i]);
                }else{
                    cout<<i<<" ";
                    return false;
                } 
            }
        }
        for(int i=0;i<n;i++){
            if(rightChild[i]!=-1){
                if( ds.par(rightChild[i])==rightChild[i] && ds.par(i)!=ds.par(rightChild[i]) ){
                    ds.merge(i,rightChild[i] );
                }else{
                    cout<<i<<" ";
                    return false;
                }
            } 
        }
        unordered_map<int,int> mp;
        for(int i=0;i<n;i++){
            mp[ds.par(i)]=1;
        }
        if(mp.size()==1) return true;
        return false;
    }
};
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