<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 {

private:
    vector<int> parent, size;
    
    int Find(int node){
        if (parent[node] == node) return node;
        return parent[node] = Find(parent[node]);
    }

    void Union(int node1, int node2){
        int root1 = Find(node1);
        int root2 = Find(node2);
        if (root1 == root2) return;
        if (size[root1] < size[root2]){
            size[root2] += size[root1];
            parent[root1] = root2;
        }
        else{
            size[root1] += size[root2];
            parent[root2] = root1;
        }
    }

public:
    bool validateBinaryTreeNodes(int n, vector<int>& leftChild, vector<int>& rightChild) {
        parent.resize(n);
        size.resize(n, 1);
        for(int i = 0; i < n; i++){
            parent[i] = i;
        }

        for(int node = 0; node < n; node++){
            if (leftChild[node] != -1){
                if (size[leftChild[node]] > 1 || Find(leftChild[node]) == Find(node)) return false;
                Union(leftChild[node], node);
            }
            if (rightChild[node] != -1){
                if (size[rightChild[node]] > 1 || Find(rightChild[node]) == Find(node)) return false;
                Union(rightChild[node], node);
            }
        }

        int maxSize = 0;
        for(int node = 0; node < n; node++){
            maxSize = max(maxSize, size[node]);
        }
        cout << maxSize << endl;
        return maxSize == n;
    }
};
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