Unbalanced Binary Tree Construction via Boundary Value Calculation
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Solution Overview
Problem
Existing binary tree data structures like AVLTree and RBTree require frequent rebalancing, leading to performance degradation and high memory usage, especially in applications with frequent node additions and deletions, while RadixTree avoids rebalancing but consumes excessive memory for search routes.
Innovation Solution
A method for constructing an unbalanced binary tree by calculating the binary boundary value to determine the relationship between new and existing nodes, using dichotomy to divide the value space and employing binary operations to efficiently insert nodes, reducing the need for rebalancing and memory usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If AVLTree or RBTree is used to maintain balance, then search speed is improved, but memory overhead and performance degradation occur due to frequent rotation operations
Solution Approach 1:
The patent extracts the rebalancing operation from the node insertion/deletion process. Instead of performing rotations during each modification operation, the invention separates the insertion/deletion from balance maintenance, allowing nodes to be added or removed without triggering complex rotation sequences, thus reducing operation complexity while preserving search efficiency through periodic or lazy rebalancing strategies
2Productivity
If RadixTree is used to avoid rebalancing, then operation overhead is reduced, but memory consumption increases due to extra search route construction
Solution Approach 1:
The patent applies asymmetry by using an unbalanced binary tree structure instead of forcing balance. The tree allows uneven distribution of nodes across left and right subtrees, eliminating the need for complex search routes and additional memory structures. This asymmetric approach reduces memory consumption while maintaining acceptable operation efficiency through the calculated binary boundary value insertion method
3Quantity of substance
If unbalanced binary tree is used to reduce memory usage, then memory efficiency is improved, but search performance degrades due to increased tree depth
Solution Approach 1:
The patent changes the parameter of tree structure from balanced to unbalanced, accepting increased depth in exchange for memory efficiency. The calculated binary boundary value insertion method optimizes the unbalanced structure by strategically placing nodes based on key value comparisons, which mitigates the negative impact of increased depth on search performance while maintaining memory efficiency
4Adaptability or versatility
If frequent node additions and deletions are performed, then data dynamism is improved, but performance degradation occurs due to repeated rebalancing operations
Solution Approach 1:
The patent applies preliminary action by pre-calculating the binary boundary value during the insertion process. This calculation determines the optimal insertion position before actual node placement, allowing the tree to accommodate frequent additions and deletions without requiring immediate rebalancing. The preliminary boundary calculation enables efficient dynamic updates while maintaining performance
Data Source
AI summary
Each node of the binary tree contains an integer key value. When a new node is inserted into the binary tree, if the new node has a key value not equal to the key value of a node in the binary tree, there are necessarily a smaller key value A and a greater key value B, a binary boundary value C is calculated using the key values A and B; the relation between the new node and the node in the binary tree and the route for the new node to be inserted are determined based on the binary boundary value C. If A≠0, there must be an odd integer N and an integer power F of 2 for the key values A and B to satisfy (N−1)×F<A≤N×F and N×F≤B<(N+1)×F, then the binary boundary value C=N×F; and if A=0, then the binary boundary value C is equal to 0.