Question

450. Delete Node in a BST

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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

# 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

/**
 * 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;
  }
}

/**
 * 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;
  }
};

/**
 * 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
}

/**
 * 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;
}

// 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::rc::Rc;
use std::cell::RefCell;
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
  }
}