654. maximum binary tree

You are given an integer array nums with no duplicates. A maximum binary tree can be built recursively from nums using the following algorithm:

1. Create a root node whose value is the maximum value in nums.
2. Recursively build the left subtree on the subarray prefix to the left of the maximum value.
3. Recursively build the right subtree on the subarray suffix to the right of the maximum value.

Return the maximum binary tree built from nums.

solution

# O(nlogn), worst case O(n^2) in linked list case
def constructMaximumBinaryTree(self, nums: List[int]) -> Optional[TreeNode]:
	n = len(nums)
	def construct(l, r):
		if l > r:
			return None
	  
		max_seen = -inf
		idx = -1
		for i in range(l, r+1):
			if nums[i] > max_seen:
				max_seen = nums[i]
				idx = i
		root = TreeNode(max_seen)
		root.left = construct(l, idx-1)
		root.right = construct(idx+1, r)
		return root
	  
	return construct(0, n-1)