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);
}