# 669. Trim a Binary Search Tree

## Description

Given the root of a binary search tree and the lowest and highest boundaries as low and high, trim the tree so that all its elements lies in [low, high]. Trimming the tree should not change the relative structure of the elements that will remain in the tree (i.e., any node's descendant should remain a descendant). It can be proven that there is a unique answer.

Return the root of the trimmed binary search tree. Note that the root may change depending on the given bounds.

Example 1:

Input: root = [1,0,2], low = 1, high = 2
Output: [1,null,2]


Example 2:

Input: root = [3,0,4,null,2,null,null,1], low = 1, high = 3
Output: [3,2,null,1]


Constraints:

• The number of nodes in the tree is in the range [1, 104].
• 0 <= Node.val <= 104
• The value of each node in the tree is unique.
• root is guaranteed to be a valid binary search tree.
• 0 <= low <= high <= 104

## Solutions

• /**
* 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 trimBST(TreeNode root, int low, int high) {
if (root == null) {
return root;
}
if (root.val > high) {
return trimBST(root.left, low, high);
}
if (root.val < low) {
return trimBST(root.right, low, high);
}
root.left = trimBST(root.left, low, high);
root.right = trimBST(root.right, low, high);
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* trimBST(TreeNode* root, int low, int high) {
if (!root) return root;
if (root->val > high) return trimBST(root->left, low, high);
if (root->val < low) return trimBST(root->right, low, high);
root->left = trimBST(root->left, low, high);
root->right = trimBST(root->right, low, high);
return root;
}
};

• # 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 trimBST(
self, root: Optional[TreeNode], low: int, high: int
) -> Optional[TreeNode]:
def dfs(root):
if root is None:
return root
if root.val > high:
return dfs(root.left)
if root.val < low:
return dfs(root.right)
root.left = dfs(root.left)
root.right = dfs(root.right)
return root

return dfs(root)


• /**
* Definition for a binary tree node.
* type TreeNode struct {
*     Val int
*     Left *TreeNode
*     Right *TreeNode
* }
*/
func trimBST(root *TreeNode, low int, high int) *TreeNode {
if root == nil {
return root
}
if root.Val > high {
return trimBST(root.Left, low, high)
}
if root.Val < low {
return trimBST(root.Right, low, high)
}
root.Left = trimBST(root.Left, low, high)
root.Right = trimBST(root.Right, low, high)
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 trimBST(root: TreeNode | null, low: number, high: number): TreeNode | null {
const dfs = (root: TreeNode | null) => {
if (root == null) {
return root;
}
const { val, left, right } = root;
if (val < low || val > high) {
return dfs(left) || dfs(right);
}
root.left = dfs(left);
root.right = dfs(right);
return root;
};
return dfs(root);
}


• /**
* Definition for a binary tree node.
* function TreeNode(val, left, right) {
*     this.val = (val===undefined ? 0 : val)
*     this.left = (left===undefined ? null : left)
*     this.right = (right===undefined ? null : right)
* }
*/
/**
* @param {TreeNode} root
* @param {number} low
* @param {number} high
* @return {TreeNode}
*/
var trimBST = function (root, low, high) {
function dfs(root) {
if (!root) {
return root;
}
if (root.val < low) {
return dfs(root.right);
}
if (root.val > high) {
return dfs(root.left);
}
root.left = dfs(root.left);
root.right = dfs(root.right);
return root;
}
return dfs(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 {
pub fn trim_bst(
mut root: Option<Rc<RefCell<TreeNode>>>,
low: i32,
high: i32
) -> Option<Rc<RefCell<TreeNode>>> {
if root.is_none() {
return root;
}
{
let mut node = root.as_mut().unwrap().borrow_mut();
if node.val < low {
return Self::trim_bst(node.right.take(), low, high);
}
if node.val > high {
return Self::trim_bst(node.left.take(), low, high);
}
node.left = Self::trim_bst(node.left.take(), low, high);
node.right = Self::trim_bst(node.right.take(), low, high);
}
root
}
}