<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:
    bool validateBinaryTreeNodes(int n, vector<int>& leftChild, vector<int>& rightChild) {
        vector<int> par(n,-1);
        vector<vector<int>> g(n);

        for(int i = 0 ; i < n ; i++){
            if(leftChild[i]!=-1 && par[leftChild[i]] != -1) return false;
            if(rightChild[i]!=-1 && par[rightChild[i]] != -1  ) return false;
            if(leftChild[i]!=-1) {par[leftChild[i]] = i; g[i].push_back(leftChild[i]) ; }
            if(rightChild[i]!=-1) {par[rightChild[i]] = i ; g[i].push_back(rightChild[i]) ;}


        }

        for(auto i : g){
            for(auto j : i){
                cout << j << " ";
            }
            cout << endl;
        }

        for(auto i : par){
            cout << i << " ";
        }
        cout << endl;

        int root = 0;
        int node = -1;
        for(int i = 0 ; i < n ; i++){
            if(par[i] == -1){
                root++;
                node = i;
            }
        }

        if(root != 1){
            return false;
        }

        vector<int> vis(n,-1);

        if(root == 1){
            deque<int> q;
            q.push_back(node);
            vis[node] = 0;

            while(!q.empty()){

                int z = q.front();
                q.pop_front();

                for(auto i : g[z]){
                    if(vis[i] !=  -1) return false;
                    q.push_back(i);
                    vis[i] = 0;
                }

            }
            cout << endl;

            for(auto i : vis){
                cout << i << " ";
                if(i == -1){
                    
                    return false;
                }
            }
        }

        return true;
    }
};
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