Transform a BST to greater sum tree
Given a BST, transform it into a greater sum tree where each node contains sum of all nodes greater than that node.
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Method 1 (Naïve):
This method doesn’t require the tree to be a BST. Following are the steps.
1. Traverse node by node(Inorder, preorder, etc.)
2. For each node find all the nodes greater than that of the current node, sum the values. Store all these sums.
3. Replace each node value with their corresponding sum by traversing in the same order as in Step 1.
This takes O(n^2) Time Complexity.
Method 2 (Using only one traversal)
By leveraging the fact that the tree is a BST, we can find an O(n) solution. The idea is to traverse BST in reverse inorder. Reverse inorder traversal of a BST gives us keys in decreasing order. Before visiting a node, we visit all greater nodes of that node. While traversing we keep track of the sum of keys which is the sum of all the keys greater than the key of the current node.
Inorder Traversal of given tree 1 2 7 11 15 29 35 40 Inorder Traversal of transformed tree 139 137 130 119 104 75 40 0
The time complexity of this method is O(n) as it does a simple traversal of the tree.
This article is contributed by Bhavana. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above