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Problem · Tree

Closest Binary Search Tree Value Variant

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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 multiple values are equally close, return the smallest such value.

A binary search tree satisfies: the left subtree of every node contains only keys less than the node's key, the right subtree contains only keys greater than the node's key, and both subtrees are themselves BSTs.

The tree is provided as a level-order (breadth-first) array root, where index 0 is the root and the children of the node at index i are at indices 2*i + 1 and 2*i + 2. Because it is a BST, you can walk down from the root toward target in O(height) time, tracking the closest value seen and preferring the smaller value on ties.

Examples

01 · Example 1

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

|4 - 3.714286| = 0.286 is smaller than |3 - 3.714286| = 0.714, so 4 is closest.

02 · Example 2

root = [1]
target = 4.428571
return = 1

The tree has a single node, so 1 is the only and therefore closest value.

03 · Example 3

root = [2, 1, 3]
target = 2.5
return = 2

Both 2 and 3 are 0.5 away from 2.5. Return the smaller value, 2.

Constraints

1 <= number of nodes <= 10^4
0 <= Node.val <= 10^9
-10^9 <= target <= 10^9
The input array is a level-order serialization of a valid binary search tree.