538 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:

            4 (30)
          /        \
         /          \
    1 (36)           6 (21)
  /   \             /   \
 /     \           /     \
0 (36)  2 (35)   5 (26)  7 (15)
          \                \
           3 (33)           8 (8)


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.

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# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def __init__(self):
        self.total = 0

    def convertBST(self, root: Optional[TreeNode]) -> Optional[TreeNode]:
        def dfs(node):
            if not node:
                return
            dfs(node.right)
            self.total += node.val
            node.val = self.total
            dfs(node.left)
        dfs(root)
        return root