<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 dfs(int node,vector<int> adj[],vector<bool>& vis,vector<bool>& recStack){
        vis[node]=true;
        recStack[node]=true;
        for(auto it: adj[node]){
            if(!vis[it]){
                if(dfs(it,adj,vis,recStack)){
                    return true;
                }
            }
            else if(recStack[it]==true){
                return true;
            }
        }
        recStack[node]=false;
        return false;
    }
    void find(int node,vector<int> adj[],vector<bool>& vis){
        vis[node]=true;
        for(auto it: adj[node]){
            if(!vis[it]){
                find(it,adj,vis);
            }
        }
    }
    vector<int> findSourceNode(vector<int> adj[],int n,vector<bool>& findSource){
        vector<int> ans;
        for(int i=0;i<n;i++){
            vector<int> v=adj[i];
            for(int j=0;j<v.size();j++){
                findSource[v[j]]=true;
            }
        }
        for(int i=0;i<findSource.size();i++){
            if(findSource[i]==false){
                ans.push_back(findSource[i]);
            }
        }
        return ans;
    }
    bool validateBinaryTreeNodes(int n, vector<int>& leftChild, vector<int>& rightChild) {
        vector<int> adj[n];
        vector<int> revAdj[n];
        for(int i=0;i<n;i++){
            if(leftChild[i]!=-1){
                adj[i].push_back(leftChild[i]);
                revAdj[leftChild[i]].push_back(i);
            }
            if(rightChild[i]!=-1){
                adj[i].push_back(rightChild[i]);
                revAdj[rightChild[i]].push_back(i);
            }
        }
        //find Cycle
        vector<bool> vis(n,false);
        vector<bool> recStack(n,false);
        for(int i=0;i<n;i++){
            vector<int> v=adj[i];
            if(v.size()>2){
                return false;
            }
            if(!vis[i]){
                if(dfs(i,adj,vis,recStack)){
                    return false;
                }
            }
        }
        //a child cannot have more than one parent
        for(int i=0;i<n;i++){
            vector<int> v=revAdj[i];
            if(v.size()>1){
                return false;
            }
        }
        //there cannot be more than on root
        vector<bool> findSource(n,false);
        vector<int>source=findSourceNode(adj,n,findSource);
        if(source.size() > 1){
            return false;
        }
        return true;
    }
};
57237