Overview
X-Fast Trie is a integer dictionaries method for predecessor queries. It works by hashing binary trie prefixes to search integer keys by level.
SpecializedSource checked
X-Fast Trie
X-Fast Trie addresses predecessor queries by hashing binary trie prefixes to search integer keys by level.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Data Structures
- Difficulty
- Advanced
- Family
- Integer Dictionaries
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 3
- Code example
- Not ready
- Visualization
- Ready
Core Concepts
predecessor queriesinteger dictionarieshash lookupdata structures
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n log n)
Worst
O(n^2)
Space
O(n)
When to Use
- Use X-Fast Trie when solving predecessor queries and you want to benefit from hashing binary trie prefixes to search integer keys by level.
- Choose it when O(n log n) average/worst-case time and O(n) memory match your workload profile.
- Prefer it over Y-Fast Trie or Trie when the problem structure favors predecessor queries.
When Not to Use
- Avoid when the query pattern is too simple to justify the structure's overhead.
- Avoid when memory layout or rebuild cost dominates the expected speedup.
What It Does
- Computes predecessor queries within Integer Dictionaries workloads (O(n log n) time, O(n) space).
- Works by hashing binary trie prefixes to search integer keys by level.
- Maintains key invariants across predecessor queries, integer dictionaries, hash lookup.
Use Cases
- Production and research workloads requiring predecessor queries via hashing binary trie prefixes to search integer keys by level.
- Integer Dictionaries pipelines where O(n log n) time and O(n) space fit system constraints.
- Engineering comparisons against Y-Fast Trie and Trie when tuning predecessor queries.
Inputs
- Keys, values, items, or graph records
- Operations such as insert, delete, or query
Outputs
- Stored structure state
- Query result or updated collection
Pseudocode
- 1.Allocate the node layout, bit-vectors, or hierarchical buckets required by X-Fast Trie.
- 2.Establish structural invariants over predecessor queries and integer dictionaries.
- 3.Execute queries or updates by hashing binary trie prefixes to search integer keys by level.
- 4.Rebalance, split/merge, or refresh auxiliary pointers to preserve logarithmic/sub-logarithmic bounds.
- 5.Return the queried value, membership result, or updated structure handle.
Canonical Example
- Input
- Keys, values, items, or graph records configured for a representative predecessor queries test case
- Output
- Stored structure state satisfying X-Fast Trie invariants
- Explanation
- X-Fast Trie processes the input by hashing binary trie prefixes to search integer keys by level, tracking predecessor queries and integer dictionaries to produce the verified predecessor queries result.
Implementation Notes
- Measure operations separately for insert, delete, query, and rebuild.
- Expose invariants in tests when balancing or compression is involved.
- Account for memory layout when performance matters.
Common Pitfalls
- Choosing the structure without matching it to the query/update pattern.
- Ignoring worst-case behavior behind favorable average-case examples.
- Forgetting memory overhead and rebuild costs.
Interactive Mechanism Walkthrough
Graph Frontier & Edge RelaxationShow hashing binary trie prefixes to search integer keys by level on a small predecessor queries example.
Step 1 of 5: Allocate the node layout, bit-vectors, or hierarchical buckets required by X-Fast Trie.
data-structures-mechanismNotes
X-Fast Trie operates in O(n log n) time and O(n) space within the Integer Dictionaries family. Often compared with Y-Fast Trie and Trie.
Sources (1)
What each reference supports for this entry.
Handbook of Data Structures and Applications
BookData-structures reference for X-fast tries, integer predecessor lookup, and hashed trie levels.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborY-Fast Trie
X-Fast Trie and Y-Fast Trie share a concrete integer dictionaries mechanism for predecessor queries.
Conceptual neighborTrie
X-Fast Trie and Trie share a concrete integer dictionaries mechanism for predecessor queries.
Related Algorithms
Tags
Data StructureHashing