<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>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
    void assignParents(TreeNode* root,map<TreeNode*,TreeNode*>&mp)
    {
        if(root->left!=NULL)
        {
            mp[root->left]=root;
            assignParents(root->left,mp);
        }
        if(root->right!=NULL)
        {
            mp[root->right]=root;
            assignParents(root->right,mp);
        }
    }
    int maxTime(TreeNode* root,TreeNode* previous,int k,map<TreeNode*,TreeNode*>&mp)
    {
        if(mp[root]==NULL && previous!=NULL )
        {
            if(root->left==NULL || root->right==NULL)
            return k;
        }
        if(root->left==NULL && root->right==NULL && previous!=NULL)
        return k;
        int a=INT_MIN,b=INT_MIN,c=INT_MIN;

        if(root!=NULL)
        {
            
            if(mp[root]!=NULL && mp[root]!=previous)
             a= maxTime(mp[root],root,k+1,mp);

            if(root->left!=NULL && root->left!=previous)
            b= maxTime(root->left,root,k+1,mp);

            if(root->right!=NULL && root->right!=previous)
            c= maxTime(root->right,root,k+1,mp);

        }
        return max(a,max(b,c));

    }
    TreeNode* find(TreeNode* root,int start)
    {
        if(root==NULL)
        return NULL;

        if(root->val==start)
        return root;

        if(root->left!=NULL)
        { 
            TreeNode* leftnode=find(root->left,start);
            if(leftnode!=NULL)
            return leftnode;
        }
         if(root->right!=NULL)
        { 
            TreeNode* rightnode=find(root->right,start);
            if(rightnode!=NULL)
            return rightnode;
        }
        return NULL;
              
           
    }
public:
    int amountOfTime(TreeNode* root, int start) {
        
        if(root==NULL )return 0;
        if(root->left==NULL && root->right==NULL)return 0;

        TreeNode* node=find(root,start);

       
        map<TreeNode*,TreeNode*>mp;
        mp[root]=NULL;
        assignParents(root,mp);

        

        

        return maxTime(node,NULL,0,mp);

    }
};
138700