Peak Tree From a List

Given a list of distinct integers nums, build the tree defined by these rules and return its root:

• the root holds the largest value in the list;
• the left subtree is the tree built from the values before the largest value;
• the right subtree is the tree built from the values after it.

Examples

       6
      / \
     3   5
      \  /
       2 0
        \
         1

Input:  nums = [3, 2, 1, 6, 0, 5]
Output: tree_to_list(...) == [6, 3, 5, None, 2, 0, None, None, 1]

Input:  nums = [1, 3, 2]
Output: [3, 1, 2]

Constraints

• 0 <= len(nums) <= 1000
• All values are distinct

Goals

• Translate a recursive definition on list ranges into tree construction
• Recognise that a monotonic stack builds the same tree in linear time