# https://leetcode.com/problems/convert-bst-to-greater-tree/
"""
Given the root of a Binary Search Tree (BST), convert it to a Greater Tree such that every key of the original BST is changed to the original key plus the sum of all keys greater than the original key in BST.

As a reminder, a binary search tree is a tree that satisfies these constraints:

The left subtree of a node contains only nodes with keys less than the node's key.
The right subtree of a node contains only nodes with keys greater than the node's key.
Both the left and right subtrees must also be binary search trees.

Example 1:
Input: root = [4,1,6,0,2,5,7,null,null,null,3,null,null,null,8]
Output: [30,36,21,36,35,26,15,null,null,null,33,null,null,null,8]

Example 2:
Input: root = [0,null,1]
Output: [1,null,1]

Constraints:
The number of nodes in the tree is in the range [0, 104].
-104 <= Node.val <= 104
All the values in the tree are unique.
root is guaranteed to be a valid binary search tree.
"""
from typing import Optional

from puzzles.utils import TreeNode


def convert_BST(root: Optional[TreeNode]) -> Optional[TreeNode]:
    def add(node):
        nonlocal total
        if not node:
            return
        add(node.right)
        total += node.val
        node.val = total
        add(node.left)

    total = 0
    add(root)
    return root
