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450. Delete Node in a BST

Description

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.

 

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

 

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

Solutions

Solution 1

Thinking

Deletion must keep the BST ordered. A node with one child is replaced by that child; a node with two children needs a successor or predecessor.

Recurse left or right by comparison. On a hit: return the right child if there is no left, the left child if there is no right; otherwise hang the whole left subtree off the leftmost node of the right subtree and return the right subtree.

That leftmost node is the in-order successor and has no left child, so the in-order sequence stays sorted after one descent.

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# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def deleteNode(self, root: Optional[TreeNode], key: int) -> Optional[TreeNode]:
        if root is None:
            return None
        if root.val > key:
            root.left = self.deleteNode(root.left, key)
            return root
        if root.val < key:
            root.right = self.deleteNode(root.right, key)
            return root
        if root.left is None:
            return root.right
        if root.right is None:
            return root.left
        node = root.right
        while node.left:
            node = node.left
        node.left = root.left
        root = root.right
        return root

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/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public TreeNode deleteNode(TreeNode root, int key) {
        if (root == null) {
            return null;
        }
        if (root.val > key) {
            root.left = deleteNode(root.left, key);
            return root;
        }
        if (root.val < key) {
            root.right = deleteNode(root.right, key);
            return root;
        }
        if (root.left == null) {
            return root.right;
        }
        if (root.right == null) {
            return root.left;
        }
        TreeNode node = root.right;
        while (node.left != null) {
            node = node.left;
        }
        node.left = root.left;
        root = root.right;
        return root;
    }
}

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/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    TreeNode* deleteNode(TreeNode* root, int key) {
        if (!root) return root;
        if (root->val > key) {
            root->left = deleteNode(root->left, key);
            return root;
        }
        if (root->val < key) {
            root->right = deleteNode(root->right, key);
            return root;
        }
        if (!root->left) return root->right;
        if (!root->right) return root->left;
        TreeNode* node = root->right;
        while (node->left) node = node->left;
        node->left = root->left;
        root = root->right;
        return root;
    }
};

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/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func deleteNode(root *TreeNode, key int) *TreeNode {
    if root == nil {
        return nil
    }
    if root.Val > key {
        root.Left = deleteNode(root.Left, key)
        return root
    }
    if root.Val < key {
        root.Right = deleteNode(root.Right, key)
        return root
    }
    if root.Left == nil {
        return root.Right
    }
    if root.Right == nil {
        return root.Left
    }
    node := root.Right
    for node.Left != nil {
        node = node.Left
    }
    node.Left = root.Left
    root = root.Right
    return root
}

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/**
 * Definition for a binary tree node.
 * class TreeNode {
 *     val: number
 *     left: TreeNode | null
 *     right: TreeNode | null
 *     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
 *         this.val = (val===undefined ? 0 : val)
 *         this.left = (left===undefined ? null : left)
 *         this.right = (right===undefined ? null : right)
 *     }
 * }
 */

function deleteNode(root: TreeNode | null, key: number): TreeNode | null {
    if (root == null) {
        return root;
    }
    const { val, left, right } = root;
    if (val > key) {
        root.left = deleteNode(left, key);
    } else if (val < key) {
        root.right = deleteNode(right, key);
    } else {
        if (left == null && right == null) {
            root = null;
        } else if (left == null || right == null) {
            root = left || right;
        } else {
            if (right.left == null) {
                right.left = left;
                root = right;
            } else {
                let minPreNode = right;
                while (minPreNode.left.left != null) {
                    minPreNode = minPreNode.left;
                }
                const minVal = minPreNode.left.val;
                root.val = minVal;
                minPreNode.left = deleteNode(minPreNode.left, minVal);
            }
        }
    }
    return root;
}

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// Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//     TreeNode {
//       val,
//       left: None,
//       right: None
//     }
//   }
// }
use std::cell::RefCell;
use std::rc::Rc;
impl Solution {
    fn dfs(root: &Option<Rc<RefCell<TreeNode>>>) -> i32 {
        let node = root.as_ref().unwrap().borrow();
        if node.left.is_none() {
            return node.val;
        }
        Self::dfs(&node.left)
    }

    pub fn delete_node(
        mut root: Option<Rc<RefCell<TreeNode>>>,
        key: i32,
    ) -> Option<Rc<RefCell<TreeNode>>> {
        if root.is_some() {
            let mut node = root.as_mut().unwrap().borrow_mut();
            match node.val.cmp(&key) {
                std::cmp::Ordering::Less => {
                    node.right = Self::delete_node(node.right.take(), key);
                }
                std::cmp::Ordering::Greater => {
                    node.left = Self::delete_node(node.left.take(), key);
                }
                std::cmp::Ordering::Equal => {
                    match (node.left.is_some(), node.right.is_some()) {
                        (false, false) => {
                            return None;
                        }
                        (true, false) => {
                            return node.left.take();
                        }
                        (false, true) => {
                            return node.right.take();
                        }
                        (true, true) => {
                            if node.right.as_ref().unwrap().borrow().left.is_none() {
                                let mut r = node.right.take();
                                r.as_mut().unwrap().borrow_mut().left = node.left.take();
                                return r;
                            } else {
                                let val = Self::dfs(&node.right);
                                node.val = val;
                                node.right = Self::delete_node(node.right.take(), val);
                            }
                        }
                    };
                }
            }
        }
        root
    }
}

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