In a binary search tree augmented with subtree sizes, if `X.left.weight + 1` equals 5, what information does this provide about dynamic order statistics?
Understand the Problem
The question pertains to a binary search tree (BST) augmented with subtree sizes. It asks us to interpret the meaning of X.left.weight + 1 = 5 in the context of dynamic order statistics. Specifically, we need to determine what this numerical value tells us about the rank or position of node X within its subtree. X.left.weight represents the number of nodes in the left subtree of X.
Answer
The left subtree of node X has 4 nodes, aiding in finding order statistics like the i-th smallest element.
In a binary search tree augmented with subtree sizes, X.left.weight + 1 = 5 implies that the left subtree of node X has a size (number of nodes) of 4. This is useful for dynamic order statistics because it allows you to efficiently find the i-th smallest element in the subtree rooted at X or determine the rank of X within that subtree.
Answer for screen readers
In a binary search tree augmented with subtree sizes, X.left.weight + 1 = 5 implies that the left subtree of node X has a size (number of nodes) of 4. This is useful for dynamic order statistics because it allows you to efficiently find the i-th smallest element in the subtree rooted at X or determine the rank of X within that subtree.
More Information
Dynamic order statistics involves maintaining and querying order information (like rank or the i-th smallest element) in a data structure that can be efficiently updated (insertions and deletions).
Tips
It is easy to confuse weight and size. Ensure you are using the correct definitions when calculating order statistics.
Sources
- 14.1 Dynamic order statistics - CLRS Solutions - walkccc.me - walkccc.me
- [PDF] Dynamic Order Statistics More Data structure ???? Isn't it an ... - .cs.arizona.edu
- Order Statistics In Binary Search Trees - blog.heycoach.in
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