<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 {
public:
    void helper(TreeNode* root, int start, unordered_map<TreeNode*, TreeNode*>& parentChildMap, TreeNode*& target){
        if(root == NULL) return;

        if(root -> val == start){
            target = root;
            return;
        }

        if(root -> left){
            parentChildMap[root -> left] = root;
            helper(root -> left, start, parentChildMap, target);
        }
        if(root -> right){
            parentChildMap[root -> right] = root;
            helper(root -> right, start, parentChildMap, target);
        }
    }

    int heightCalc(TreeNode* node){
        if(node == NULL) return 0;

        int left = 1 + heightCalc(node -> left);
        int right = 1 + heightCalc(node -> right);
        return max(left, right);
    }

    int parentTreeTime(TreeNode* node, unordered_map<TreeNode*, TreeNode*>& parentChildMap){
        if(parentChildMap[node] == NULL) return 0;

        int time = 0;
        unordered_map<int, bool> visited;
        visited[node -> val] = true;

        queue<pair<TreeNode*, int>> q;
        q.push({parentChildMap[node], 1});

        while(!q.empty()){
            auto frontPair = q.front();
            q.pop();
            auto frontNode = frontPair.first;
            auto timeTillNode = frontPair.second;
            time = max(time, timeTillNode);

            visited[frontNode -> val] = true;

            if(parentChildMap[frontNode] != NULL && !visited[parentChildMap[frontNode] -> val]){
                q.push({parentChildMap[frontNode], timeTillNode + 1});
            }
            if(frontNode -> left && !visited[frontNode -> left -> val]){
                q.push({frontNode -> left, timeTillNode + 1});
            }
            if(frontNode -> right && !visited[frontNode -> right -> val]){
                q.push({frontNode -> right, timeTillNode + 1});
            }
        }
        return time;
    }

    int amountOfTime(TreeNode* root, int start) {
        TreeNode* target = NULL;
        unordered_map<TreeNode*, TreeNode*> parentChildMap;
        parentChildMap[root] = NULL;

        helper(root, start, parentChildMap, target);
        
        int startLeftTree = heightCalc(target -> left);
        // cout << startLeftTree << endl;
        int startRightTree = heightCalc(target -> right);
        // cout << startRightTree << endl;

        int startParentTree = parentTreeTime(target, parentChildMap);
        // cout << startParentTree << endl;

        return max(startLeftTree, max(startRightTree, startParentTree));
    }
};
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