<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 isValidTree(int root, vector<int> &leftChild, vector<int> &rightChild) {
        queue<int> q {};
        set<int> st {};
        q.push(root);
        st.insert(root);
        
        while(q.size()) {
            int top = q.front();
            q.pop();
            
            int left = leftChild[top];
            int right = rightChild[top];
            
            cout << top << " -> " << left << ", " << right << endl; 
            
            if(left != -1) {
                if(st.find(left) != st.end())
                    return false;
                st.insert(left);
                q.push(left);
            }
            if(right != -1) {
                if(st.find(right) != st.end())
                    return false;
                st.insert(right);
                q.push(right);
            }
        }
        
        return st.size() == leftChild.size();
    }
    
    bool validateBinaryTreeNodes(int n, vector<int>& leftChild, vector<int>& rightChild) {
        vector<bool> hasParent(n, false);
        for(int x: leftChild) {
            if(x != -1) {
                hasParent[x] = true;
            }
        }
        for(int x: rightChild) {
            if(x != -1) {
                if(hasParent[x])
                    return false;
                hasParent[x] = true;
                
            }
        }
        
        int root = -1;
        for(int i=0; i<n; i++) {
            if(hasParent[i] == false) {
                if(root != -1)
                    return false;
                root = i;
            }
        }
        if(root == -1)
            return false;
        return isValidTree(root, leftChild, rightChild);
    }
};
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