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Convert Bst To The Greater Sum Tree
MEDIUM
30 mins
11 upvotes
Trees
Binary Search Trees
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Convert Bst To The Greater Sum Tree

Contributed by
Ankush Gupta
Medium
yellow-spark
0/80
Avg time to solve 30 mins
Success Rate 70 %
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11 upvotes

Problem Statement

You have been given a Binary Search Tree of integers. You are supposed to convert it to a greater sum tree such that the value of every node in the given BST is replaced with the sum of the values of all the nodes which are greater than the value of the current node in the tree.

A Binary Search Tree is a tree, whose internal nodes each store a value greater than all the values in the node's left subtree and less than those in its right subtree.

Note :

You need to modify the given tree only. You are not allowed to create a new tree.
For example:
For the given binary search tree

Example

11 will be replaced by {15 + 29 + 35 + 40}, i.e. 119.
2 will be replaced by {7 + 11 + 15 + 29 + 35 + 40}, i.e. 137.
29 will be replaced by {35 + 40}, i.e. 75.
1 will be replaced by {2 + 7 + 11 + 15 + 29 + 35 + 40}, i.e. 139.
7 will be replaced by {11 + 15 + 29 + 35 + 40}, i.e. 130.
15 will be replaced by {15 + 29 + 35 + 40}, i.e. 104.
40 will be replaced by 0 {as there is no node with a value greater than 40}.
35 will be replaced by {40}, i.e. 40.
Detailed explanation ( Input/output format, Notes, Constraints, Images )
Sample Input 1:
2
5 2 7 1 3 6 8 -1 -1 -1 -1 -1 -1 -1 -1
4 2 5 -1 3 -1 6 -1 -1 -1 -1
Sample Output 1:
21 29 8 31 26 15 0
11 18 6 15 0
Explanation of Sample Input 1:
For the first test case, after converting the given binary tree into the greater sum tree, the level order traversal of the tree will be {21, 29, 8, 31, 26, 15, 0}, where 5 will be replaced by {6+7+8} i.e. 21, 3 will be replaced by {5+6+7+8} i.e. 26, 7 will be replaced by {8} i.e. 8, 1 will be replaced by {2+3+5+6+7+8} i.e. 33, 2 will be replaced by {3+5+6+7+8} i.e. 26, 6 will be replaced by {7+8} i.e. 15 and 8 will be replaced by 0 (because no node has a value greater than 8 in the given tree).

For the second test case, after converting the given binary tree into the greater sum tree, the level order traversal of the tree will be {11, 18, 6, 15, 0}, where, 4 will be replaced by {5+6} i.e. 11, 2 will be replaced by {3+4+5+6} i.e. 18, 5 will be replaced by {6} i.e. 6, 3 will be replaced by {4+5+6} i.e. 15 and 6 will be replaced by 0 (because no node has a value greater than 6 in the given tree).
Sample Input 2:
2
11 2 29 1 7 15 40 -1 -1 -1 -1 -1 -1 35 -1 -1 -1
10 5 15 2 7 12 20 -1 -1 -1 -1 -1 -1 -1 -1
Sample Output 2:
119 137 75 139 130 104 0 40
47 64 20 69 57 35 0
Explanation of Sample Input 2:
For the first test case, after converting the given binary tree into the greater sum tree, the level order traversal of the tree will be {119, 137, 75. 130, 104, 0, 40}.

For the second test case, after converting the given binary tree into the greater sum tree, the level order traversal of the tree will be {47, 64, 20, 69, 57, 35, 0}.
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