<p>You are given the <code>root</code> of a binary tree with <strong>unique</strong> values, and an integer <code>start</code>. At minute <code>0</code>, an <strong>infection</strong> starts from the node with value <code>start</code>.</p>

<p>Each minute, a node becomes infected if:</p>

<ul>
	<li>The node is currently uninfected.</li>
	<li>The node is adjacent to an infected node.</li>
</ul>

<p>Return <em>the number of minutes needed for the entire tree to be infected.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/06/25/image-20220625231744-1.png" style="width: 400px; height: 306px;" />
<pre>
<strong>Input:</strong> root = [1,5,3,null,4,10,6,9,2], start = 3
<strong>Output:</strong> 4
<strong>Explanation:</strong> The following nodes are infected during:
- Minute 0: Node 3
- Minute 1: Nodes 1, 10 and 6
- Minute 2: Node 5
- Minute 3: Node 4
- Minute 4: Nodes 9 and 2
It takes 4 minutes for the whole tree to be infected so we return 4.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/06/25/image-20220625231812-2.png" style="width: 75px; height: 66px;" />
<pre>
<strong>Input:</strong> root = [1], start = 1
<strong>Output:</strong> 0
<strong>Explanation:</strong> At minute 0, the only node in the tree is infected so we return 0.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>5</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
	<li>Each node has a <strong>unique</strong> value.</li>
	<li>A node with a value of <code>start</code> exists in the tree.</li>
</ul>

class Solution {
public:
   
   TreeNode* first = NULL;
   
   void find(TreeNode* root, int start){
    if(root==NULL) return;
    if(root->val==start){
        first=root;
        return;
    }
    find(root->left,start);
    find(root->right,start);
   }

   void mapParent(TreeNode* root, unordered_map<TreeNode*,TreeNode*> &mp){
      if(root==NULL) return;
      if(root->left) mp.insert({root->left,root});
      if(root->right) mp.insert({root->right,root});
      mapParent(root->left,mp);
      mapParent(root->right,mp);
   }
    

    int amountOfTime(TreeNode* root, int start) {
       find(root,start);
       set<TreeNode*> s;
       s.insert(first);

       unordered_map<TreeNode*,TreeNode*> mp;
       mapParent(root,mp);

       queue<pair<TreeNode*,int>> q;
       q.push({first,0});
       
    int maxLevel = 0;

       while(!q.empty()){
        auto it = q.front();
        q.pop();

        TreeNode* temp = it.first;
        int level = it.second;
        
        if(temp->left and s.find(temp->left)==s.end()){
            q.push({temp->left,level+1});
            s.insert(temp->left);
        }
        if(temp->right and s.find(temp->right)==s.end()){
            q.push({temp->right,level+1});
            s.insert(temp->right);
        }

        if(mp.find(temp)!=mp.end() and s.find(mp[temp])==s.end()){
            q.push({mp[temp],level+1});
            s.insert(mp[temp]);
        }

         maxLevel = max(maxLevel,level);
       }          
    return maxLevel;
    }
};
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