1038. Binary Search Tree to Greater Sum Tree

Problem

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 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.

Note: This question is the same as 538: https://leetcode.com/problems/convert-bst-to-greater-tree/

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]

Example 3:

Input: root = [1,0,2]
Output: [3,3,2]

Example 4:

Input: root = [3,2,4,1]
Output: [7,9,4,10]

Constraints:

• The number of nodes in the tree is in the range [1, 100].
• 0 <= Node.val <= 100
• All the values in the tree are unique.
• root is guaranteed to be a valid binary search tree.

Problem Summary

Given the root node of a binary search tree whose node values are all distinct, convert it to a Greater Sum Tree such that the new value of each node node is equal to the sum of values greater than or equal to node.val in the original tree.

As a reminder, a binary search tree satisfies the following 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.

Solution Approach

• Based on the ordered property of a binary search tree, to convert it to a Greater Sum Tree, simply traverse in the order of right node - root node - left node, and accumulate the sum.
• This problem is the same as problem 538.

Code

package leetcode

import (
	"github.com/halfrost/leetcode-go/structures"
)

// TreeNode define
type TreeNode = structures.TreeNode

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */

func bstToGst(root *TreeNode) *TreeNode {
	if root == nil {
		return root
	}
	sum := 0
	dfs1038(root, &sum)
	return root
}

func dfs1038(root *TreeNode, sum *int) {
	if root == nil {
		return
	}
	dfs1038(root.Right, sum)
	root.Val += *sum
	*sum = root.Val
	dfs1038(root.Left, sum)
}