<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:
    void makeParents(TreeNode* root , unordered_map<TreeNode* , TreeNode*> &parent){
        queue<TreeNode*> q;
        q.push(root);
        while(!q.empty()){
            auto node = q.front();
            q.pop();
            if(node->left) {
                parent[node->left] = node;
                q.push(node->left);
            }
            if(node->right) {
                parent[node->right] = node;
                q.push(node->right);
            }      
        }
    }

    TreeNode* findNode(TreeNode* root , int target){
        queue<TreeNode*> q;
        unordered_map<TreeNode*,bool> visited;
        q.push(root);
        while(!q.empty()){
            auto node = q.front();
            q.pop();
            if(node->val == target){
                return node;
            }
            if(node->left && !visited[node->left]){
                q.push(node->left);
                visited[node->left] = true;
            }
            if(node->right && !visited[node->right]){
                q.push(node->right);
                visited[node->right] = true;
            }
        }
        return nullptr;
    }

    int amountOfTime(TreeNode* root, int start) {
        int ans = 0;
        if(!root) return ans;
        queue<TreeNode*> q;
        unordered_map<TreeNode* , TreeNode*> mp;
        unordered_map<TreeNode* , bool> visited;
        makeParents(root,mp);
        auto temp = findNode(root,start);
        if(!temp) return ans;
        auto target = temp;

        q.push(target);
        visited[target] = true;
        while(!q.empty()){
            int size = q.size();
            bool hasNewNodes = false;
            for(int i = 0 ; i < size ; i++){
                auto node = q.front();
                q.pop();
                int c = 0;
                if(node->left && !visited[node->left]){
                    q.push(node->left);
                    visited[node->left] = true;
                    c++;
                }
                if(node->right && !visited[node->right]){
                    q.push(node->right);
                    visited[node->right] = true;
                    c++;
                }
                if(mp[node] && !visited[mp[node]]){
                    q.push(mp[node]);
                    visited[mp[node]] = true;
                    c++;
                }
                if(c > 0)  hasNewNodes = true;;
            }
            if( hasNewNodes) ++ans;
        }
    return ans;
    }
};
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