333. Largest BST Subtree

Given the root of a binary tree, find the largest subtree, which is also a Binary Search Tree (BST), where the largest means subtree has the largest number of nodes.

A Binary Search Tree (BST) is a tree in which all the nodes follow the below-mentioned properties:

  • The left subtree values are less than the value of their parent (root) node's value.
  • The right subtree values are greater than the value of their parent (root) node's value.

Note: A subtree must include all of its descendants.

Follow up: Can you figure out ways to solve it with O(n) time complexity?

 

Example 1:

Input: root = [10,5,15,1,8,null,7]
Output: 3
Explanation: The Largest BST Subtree in this case is the highlighted one. The return value is the subtree's size, which is 3.

Example 2:

Input: root = [4,2,7,2,3,5,null,2,null,null,null,null,null,1]
Output: 2

 

Constraints:

  • The number of nodes in the tree is in the range [0, 104].
  • -104 <= Node.val <= 104

Rust Solution

struct Solution;
use rustgym_util::*;

trait Postorder {
    fn postorder(&self, max_size: &mut usize) -> Option<(usize, i32, i32)>;
}

impl Postorder for TreeLink {
    fn postorder(&self, max_size: &mut usize) -> Option<(usize, i32, i32)> {
        if let Some(node) = self {
            let node = node.borrow();
            let val = node.val;
            let mut size = 1;
            let mut min = val;
            let mut max = val;
            let left = node.left.postorder(max_size);
            let right = node.right.postorder(max_size);
            if let Some(left) = left {
                if left.2 < val {
                    size += left.0;
                    min = min.min(left.1);
                } else {
                    return None;
                }
            } else {
                return None;
            }
            if let Some(right) = right {
                if val < right.1 {
                    size += right.0;
                    max = max.max(right.2);
                } else {
                    return None;
                }
            } else {
                return None;
            }
            *max_size = (*max_size).max(size);
            Some((size, min, max))
        } else {
            Some((0, std::i32::MAX, std::i32::MIN))
        }
    }
}

impl Solution {
    fn largest_bst_subtree(root: TreeLink) -> i32 {
        let mut res = 0;
        root.postorder(&mut res);
        res as i32
    }
}

#[test]
fn test() {
    let root = tree!(10, tree!(5, tree!(1), tree!(8)), tree!(15, None, tree!(7)));
    let res = 3;
    assert_eq!(Solution::largest_bst_subtree(root), res);
    let root = tree!(1, tree!(3, tree!(4), None), tree!(2, None, tree!(5)));
    let res = 2;
    assert_eq!(Solution::largest_bst_subtree(root), res);
    let root = tree!(
        4,
        tree!(2, tree!(2, tree!(2, tree!(2), None), None), tree!(3)),
        tree!(7, tree!(5), None)
    );
    let res = 2;
    assert_eq!(Solution::largest_bst_subtree(root), res);
}

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