# Question

Given a non-empty binary search tree and a target value, find the value in the BST that is closest to the target.

Note:

• Given target value is a floating point.
• You are guaranteed to have only one unique value in the BST that is closest to the target.

Example:

Input: root = [4,2,5,1,3], target = 3.714286

4
/ \
2   5
/ \
1   3

Output: 4


# Solution

Walk the BST and find the maximum number smaller than the target and minimum number larger than the target.

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
def closestValue(self, root, target):
"""
:type root: TreeNode
:type target: float
:rtype: int
"""
self.min_val = float('-inf')
self.max_val = float('inf')
self.closest_val = root.val
self.__walk_tree(root, target)
return self.closest_val

def __walk_tree(self, root, target):
if root is None:
if target - self.min_val > self.max_val - target:
self.closest_val = self.max_val
else:
self.closest_val = self.min_val
elif target > root.val:
self.min_val = root.val
self.__walk_tree(root.right, target)
elif target < root.val:
self.max_val = root.val
self.__walk_tree(root.left, target)
else:
self.closest_val = root.val