# Smallest Subtree with all the Deepest Nodes (M)

## 题目

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 = 
Output: 
Explanation: The root is the deepest node in the tree.
``````

Example 3:

``````Input: root = [0,1,3,null,2]
Output: 
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.

## 代码实现

### Java

``````class Solution {
private Map<TreeNode, Integer> depth = new HashMap<>();
private int maxDepth = -1;

public TreeNode subtreeWithAllDeepest(TreeNode root) {
findDepth(root, 1);
return findAncestor(root);
}

private void findDepth(TreeNode node, int level) {
if (node == null) {
return;
}

maxDepth = Math.max(maxDepth, level);
depth.put(node, level);

findDepth(node.left, level + 1);
findDepth(node.right, level + 1);
}

private TreeNode findAncestor(TreeNode node) {
if (node == null || depth.get(node) == maxDepth) {
return node;
}

TreeNode leftAncestor = findAncestor(node.left);
TreeNode rightAncestor = findAncestor(node.right);

if (leftAncestor != null && rightAncestor != null) {
return node;
} else if (leftAncestor != null) {
return leftAncestor;
} else if (rightAncestor != null) {
return rightAncestor;
} else {
return null;
}
}
}
``````

0865. Smallest Subtree with all the Deepest Nodes (M)