<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> ind(n, 0);

        vector<vector<int>> adj(n);
       
        for (int i = 0; i < n; i++) {
            if (leftChild[i] != -1) {
                ind[leftChild[i]]++;
                if (ind[leftChild[i]] > 1) return false; 
                adj[i].push_back(leftChild[i]);
            }
            if (rightChild[i] != -1) {

                ind[rightChild[i]]++;
                if (ind[rightChild[i]] > 1) return false;
                adj[i].push_back(rightChild[i]);
            }
        }

        // Step 2: Find root
        int root = -1;
        for (int i = 0; i < n; i++) {
            if (ind[i] == 0) {
                if (root == -1) {
                    root = i;
                } else {
                    return false; 
                }
            }
        }

        
        if (root == -1) return false;

        
       

       
        vector<bool> vis(n, false);
        queue<int> q;
        q.push(root);
        vis[root] = true;
        int cnt = 0;

        while (!q.empty()) {
            int node = q.front();
            q.pop();
            cnt++;
            for (auto it : adj[node]) {
                if (!vis[it]) {
                    vis[it] = true;
                    q.push(it);
                }
            }
        }

        // All nodes must be visited in a valid tree
        return cnt == n;
    }
};





// class Solution {
// public:
//     bool validateBinaryTreeNodes(int n, vector<int>& leftChild, vector<int>& rightChild) {
//         vector<int>ind(n,0);
//         vector<vector<int>>adj(n);

//         for(int i=0; i<n; i++){
//             if(leftChild[i]!=-1){
//                 adj[i].push_back(leftChild[i]);
//                 ind[leftChild[i]]++;
//             //   if (ind[leftChild[i]] > 1) return false; 
//             }
//             if(rightChild[i]!=-1){
//                 adj[i].push_back(rightChild[i]);
//                 ind[rightChild[i]]++;
//                 //  if (ind[rightChild[i]] > 1) return false;
//             }
//         }
//         int root=-1;
//         for(int i=0; i<n; i++){
//             if(ind[i]==0){
//                 if(root==-1){
//                     root=i;
//                 }
//                 else{
//                     return false;
//                 }

//             }
//         }
       
//         if(root==-1){
//             return false;
//         }
//         vector<bool>vis(n, false);
//         int cnt=0;
//         queue<int>q;
//         q.push(root);
//         cnt=1;
//         vis[root]=true;

//         while(!q.empty()){
//             int node=q.front();
//             q.pop();

//               cnt++;
//             for(auto it: adj[node]){
//                 if(!vis[it]){
//                    vis[it]=true;
                  
//                    q.push(it);
//                 }
//             }
//         }
//         if(cnt!=n){
//             return false;
//         }
//         return true;
//     }
// };
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