450. Delete Node in a BST

Given a root node reference of a BST and a key, delete the node with the given key in the BST. Return the root node reference (possibly updated) of the BST.

Basically, the deletion can be divided into two stages:

  1. Search for a node to remove.
  2. If the node is found, delete the node.

Follow up: Can you solve it with time complexity O(height of tree)?

 

Example 1:

Input: root = [5,3,6,2,4,null,7], key = 3
Output: [5,4,6,2,null,null,7]
Explanation: Given key to delete is 3. So we find the node with value 3 and delete it.
One valid answer is [5,4,6,2,null,null,7], shown in the above BST.
Please notice that another valid answer is [5,2,6,null,4,null,7] and it's also accepted.

Example 2:

Input: root = [5,3,6,2,4,null,7], key = 0
Output: [5,3,6,2,4,null,7]
Explanation: The tree does not contain a node with value = 0.

Example 3:

Input: root = [], key = 0
Output: []

 

Constraints:

  • The number of nodes in the tree is in the range [0, 104].
  • -105 <= Node.val <= 105
  • Each node has a unique value.
  • root is a valid binary search tree.
  • -105 <= key <= 105

Rust Solution

struct Solution;
use rustgym_util::*;
use std::cmp::Ordering::*;

trait Delete {
    fn delete(self, key: i32) -> TreeLink;
    fn smallest(&self) -> i32;
}

impl Delete for TreeLink {
    fn delete(self, key: i32) -> TreeLink {
        if let Some(link) = self {
            let mut node = link.borrow_mut();
            let left = node.left.take();
            let right = node.right.take();
            let val = node.val;
            match key.cmp(&val) {
                Equal => match (left, right) {
                    (None, None) => None,
                    (Some(left), None) => Some(left),
                    (None, Some(right)) => Some(right),
                    (left, right) => {
                        let smallest = right.smallest();
                        tree!(smallest, left, right.delete(smallest))
                    }
                },
                Less => tree!(val, left.delete(key), right),
                Greater => tree!(val, left, right.delete(key)),
            }
        } else {
            None
        }
    }
    fn smallest(&self) -> i32 {
        if let Some(node) = self {
            let node = node.borrow();
            let val = node.val;
            if node.left.is_some() {
                node.left.smallest()
            } else {
                val
            }
        } else {
            unreachable!()
        }
    }
}

impl Solution {
    fn delete_node(root: TreeLink, key: i32) -> TreeLink {
        root.delete(key)
    }
}

#[test]
fn test() {
    let root = tree!(5, tree!(3, tree!(2), tree!(4)), tree!(6, None, tree!(7)));
    let key = 3;
    let res = tree!(5, tree!(4, tree!(2), None), tree!(6, None, tree!(7)));
    assert_eq!(Solution::delete_node(root, key), res);
}

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