<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 isBinaryTreeValid(int current, vector<int>& leftChild,
                           vector<int>& rightChild, vector<bool>& visited) {

        if (leftChild[current] != -1) {
            if (visited[leftChild[current]]){ 
                return false;
            }
            visited[leftChild[current]] = true; 
            if (!isBinaryTreeValid(leftChild[current], leftChild, rightChild, visited)){
                return false;
            }
        }

        if (rightChild[current] != -1) {
            if (visited[rightChild[current]]){
                return false;
            }
            visited[rightChild[current]] = true; 
            if (!isBinaryTreeValid(rightChild[current], leftChild, rightChild, visited)){
                return false;
            }
        }
        return true;
    }

    bool validateBinaryTreeNodes(int n, vector<int>& leftChild,
                                 vector<int>& rightChild) {
        vector<bool> childCount(n, false);

        for (auto child : leftChild) {
            if (child != -1) {
                childCount[child] = true;
            }
        }

        for (auto child : rightChild) {
            if (child != -1) {
                if (childCount[child]) {
                    return false;
                }
                childCount[child] = true;
            }
        }

        int root = -1; 
        for (int i = 0; i < n; ++i) {
            if (!childCount[i]) {
                if (root == -1) {
                    root = i; // Set root node if not assigned
                } 
                else {
                    return false; // Multiple roots found, not a valid binary tree
                }
            }
        }
        if (root == -1) {
            return false; // No root found, not a valid binary tree
        }

        vector<bool> visited(n); 
        visited[root] = true;
        if (!isBinaryTreeValid(root, leftChild, rightChild, visited)) {
            return false;
        }

        // Check if there is multiple components
        for (int i = 0; i < visited.size(); i++) {
            if (!visited[i]) {
                return false;
            }
        }

        return true;
    }
};
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