How do you solve Binary Search Tree to Greater Sum Tree on LeetCode?

Binary Search Tree to Greater Sum Tree (LeetCode #1038) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(h) space complexity. Key insight: Using reverse in-order traversal allows us to efficiently calculate the cumulative sum in a single pass.

What is the brute force solution for Binary Search Tree to Greater Sum Tree?

The brute force approach for Binary Search Tree to Greater Sum Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. In this approach, we traverse the entire tree for each node to calculate the sum of all greater nodes. This is straightforward but inefficient as it requires multiple passes through the tree. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Binary Search Tree to Greater Sum Tree?

Always clarify the properties of the data structure you're working with before diving into the solution. Think about the traversal methods that suit the problem; for BSTs, in-order and reverse in-order are key. Practice explaining your thought process as you code; it helps solidify your understanding.

What are common mistakes when solving Binary Search Tree to Greater Sum Tree?

Students often forget to handle the right subtree first in reverse in-order traversal. Confusing the in-order and reverse in-order traversal can lead to incorrect results.

#1038

Binary Search Tree to Greater Sum Tree

Medium

TreeDepth-First SearchBinary Search TreeBinary TreeDepth-First SearchTree Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(h)

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Intuition

Time O(n)Space O(h)

By using a reverse in-order traversal, we can efficiently calculate the cumulative sum of values as we traverse the tree. This allows us to update each node in a single pass.

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Algorithm

3 steps

1Step 1: Initialize a variable to keep track of the cumulative sum.
2Step 2: Perform a reverse in-order traversal (right -> node -> left).
3Step 3: For each node, add its value to the cumulative sum and update the node's value.

solution.py18 lines

1# Full working Python code
2class TreeNode:
3    def __init__(self, val=0, left=None, right=None):
4        self.val = val
5        self.left = left
6        self.right = right
7
8class Solution:
9    def convertBST(self, root: TreeNode) -> TreeNode:
10        self.cumulative_sum = 0
11        def reverse_in_order(node):
12            if node:
13                reverse_in_order(node.right)
14                self.cumulative_sum += node.val
15                node.val = self.cumulative_sum
16                reverse_in_order(node.left)
17        reverse_in_order(root)
18        return root

ℹ

Complexity note: The time complexity is O(n) since we visit each node exactly once. The space complexity is O(h) due to the recursion stack, where h is the height of the tree.

1Using reverse in-order traversal allows us to efficiently calculate the cumulative sum in a single pass.
2Understanding the properties of a BST is crucial for optimizing the traversal.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.