## 865. 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**.

## Rust Solution

```
struct Solution;
use rustgym_util::*;
trait Postorder {
fn postorder(&self) -> (usize, TreeLink);
}
impl Postorder for TreeLink {
fn postorder(&self) -> (usize, TreeLink) {
use std::cmp::Ordering::*;
if let Some(node) = self {
let node = node.borrow();
let left = &node.left;
let right = &node.right;
let (left_depth, left_tree) = left.postorder();
let (right_depth, rigth_tree) = right.postorder();
match left_depth.cmp(&right_depth) {
Equal => (left_depth + 1, self.clone()),
Less => (right_depth + 1, rigth_tree),
Greater => (left_depth + 1, left_tree),
}
} else {
(0, None)
}
}
}
impl Solution {
fn subtree_with_all_deepest(root: TreeLink) -> TreeLink {
root.postorder().1
}
}
#[test]
fn test() {
let root = tree!(
3,
tree!(5, tree!(6), tree!(2, tree!(7), tree!(4))),
tree!(1, tree!(0), tree!(8))
);
let res = tree!(2, tree!(7), tree!(4));
assert_eq!(Solution::subtree_with_all_deepest(root), res);
}
```

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