Leetcode #270: Closest Binary Search Tree Value
In this guide, we solve Leetcode #270 Closest Binary Search Tree Value in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given the root of a binary search tree and a target value, return the value in the BST that is closest to the target. If there are multiple answers, print the smallest.
Quick Facts
- Difficulty: Easy
- Premium: Yes
- Tags: Tree, Depth-First Search, Binary Search Tree, Binary Search, Binary Tree
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: root = [4,2,5,1,3], target = 3.714286
Output: 4
Python Solution
# 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 closestValue(self, root: Optional[TreeNode], target: float) -> int:
def dfs(node: Optional[TreeNode]):
if node is None:
return
nxt = abs(target - node.val)
nonlocal ans, diff
if nxt < diff or (nxt == diff and node.val < ans):
diff = nxt
ans = node.val
node = node.left if target < node.val else node.right
dfs(node)
ans = 0
diff = inf
dfs(root)
return ans
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.