<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) {
        
        // parent[i] -> parent, i -> child
        vector<int> parent(n, -1);

        for(int i = 0; i < n; i++){

            int node = i;
            int left = leftChild[node];
            int right = rightChild[node];

            if(left != -1){
                if(parent[left] == -1) parent[left] = node;
                else if(parent[left] != node) return false;
            }

            if(right != -1){
                if(parent[right] == -1) parent[right] = node;
                else if(parent[right] != node) return false;
            }
        }

        // for(auto it: parent) cout << it <<" ";

        int count = 0;
        int root = -1;

        for(int i = 0; i < n; i++){
            if(parent[i] == -1) {
                count++;
                root = i;
            }
        }
        if(count != 1) return false;

        
        // check cycle
        vector<int> visited(n, 0);
        queue<int> q;
        q.push(root);
        visited[root] = 1;

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

            vector<int> childs = {leftChild[node], rightChild[node]};

            for(auto nbr : childs){
                if(nbr == -1) continue;
                if(visited[nbr] == 1) return false;

                q.push(nbr);
                visited[nbr] = 1;
            }
        }

        for(auto it: visited){
            if(it == 0) return false;
        }
        // cout <<"hi" << endl;
        return true;

    }
};
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