12. Smallest Subtree with all the Deepest Nodes.cpp

/*
Smallest Subtree with all the Deepest Nodes
===========================================

Given the root of a binary tree, the depth of each node is the shortest distance to the root.

Return the smallest subtree such that it contains all the deepest nodes in the original tree.

A node is called the deepest if it has the largest depth possible among any node in the entire tree.

The subtree of a node is tree consisting of that node, plus the set of all descendants of that node.

Note: This question is the same as 1123: https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/

Example 1:
Input: root = [3,5,1,6,2,0,8,null,null,7,4]
Output: [2,7,4]
Explanation: We return the node with value 2, colored in yellow in the diagram.
The nodes coloured in blue are the deepest nodes of the tree.
Notice that nodes 5, 3 and 2 contain the deepest nodes in the tree but node 2 is the smallest subtree among them, so we return it.

Example 2:
Input: root = [1]
Output: [1]
Explanation: The root is the deepest node in the tree.

Example 3:
Input: root = [0,1,3,null,2]
Output: [2]
Explanation: The deepest node in the tree is 2, the valid subtrees are the subtrees of nodes 2, 1 and 0 but the subtree of node 2 is the smallest.

Constraints:
The number of nodes in the tree will be in the range [1, 500].
0 <= Node.val <= 500
The values of the nodes in the tree are unique.
*/

/**
 * 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
{
  int maxDepth = -1;
  TreeNode *ans = nullptr;

  int post(TreeNode *node, int depth)
  {
    if (!node)
      return depth;
    int left = post(node->left, depth + 1);
    int right = post(node->right, depth + 1);

    if (left == right)
    {
      maxDepth = max(maxDepth, left);
      if (left == maxDepth)
      {
        ans = node;
      }
    }
    return max(left, right);
  }

public:
  TreeNode *subtreeWithAllDeepest(TreeNode *root)
  {
    post(root, 0);
    return ans;
  }
};