Tree Traversal Backtracking Using Bit Trail Variables
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Solution Overview
Problem
Current methods for tree data structure traversal with backtracking face performance and storage size issues, necessitating an efficient solution for constant-time traversal and backtracking.
Innovation Solution
The method involves maintaining a bit trail variable and a current key variable during tree traversal, using these variables for backtracking, and employing a perfect hash map to map node keys to memory addresses, allowing for constant-time backtracking and node access without the need for a stack.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If a stack is used for backtracking during tree traversal, then backtracking can be performed, but memory overhead and access time increase
Solution Approach 1:
The patent extracts the backtracking information from a traditional stack structure and stores it directly in compact fields within each tree node. This eliminates the separate stack memory overhead while enabling constant-time backtracking operations by directly accessing the stored parent and sibling pointers in the node structure itself.
Solution Approach 2:
The patent merges the backtracking data structure with the tree node structure by incorporating parent pointers and sibling pointers directly into each node. This consolidation eliminates the need for a separate stack and reduces memory overhead while maintaining constant-time backtracking capability.
2Productivity
If current methods are used for tree traversal with backtracking, then traversal can be performed, but performance is degraded due to non-constant time complexity
Solution Approach 1:
The patent performs preliminary action by pre-storing parent and sibling pointers in each tree node during tree construction. This advance preparation enables constant-time backtracking operations without requiring complex stack operations or searches during the actual traversal process.
Solution Approach 2:
The patent replaces the mechanical stack-based backtracking system with a direct pointer-based navigation system. By substituting the stack data structure with embedded parent and sibling pointers, the system achieves constant-time backtracking through direct memory access rather than sequential stack operations.
Data Source
AI summary
A method, computer readable medium, and system are disclosed for performing tree traversal with backtracking in constant time. The method includes the steps of traversing a tree, maintaining a bit trail variable and a current key variable during the traversing, where the bit trail variable includes a first plurality of bits indicating tree levels on which a node has been postponed along a path from the root of the tree during the traversing, and the current key variable includes a second plurality of bits indicating a number of a current node within the tree, and performing backtracking within the tree during the traversing, utilizing the bit trail variable and the current key variable.